Chemical Energy & Thermodynamics — Print · Physical Science: Chemistry, Grade 11

Use calorimetry, Hess’s law, entropy, and free energy with explicit systems and signs.

Printable chapter lessons and review.

Energy in Chemical Reactions

Learning goals

Readings for this unit

Before this unit

Energy conservation, bond changes, and system signs.

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Start with something to explain

How can a reaction release energy if breaking its reactant bonds requires energy?

Illustrative evidence case. The selected full account includes both bond breaking and product-bond formation.

Energy signs depend on which system is being describedEnergy signs depend on which system is being describedReaction systemHeat outExothermic system: q < 0 under the stated heat conventionSurroundings receive energy; total energy is accounted for.
Original selected outward heat-transfer diagram. It does not imply a temperature value or that heat is a material fluid stored inside a bond.

Notice and wonder

Record two observations using the stated quantities or relationships. Keep observations separate from possible causes. Write one question that a new measurement could help answer.

How can a reaction release energy if breaking its reactant bonds requires energy?

Your first model

Draw energy inputs and outputs for the same reaction basis instead of labeling one bond as stored releasable heat.

Build the language from the idea

enthalpy change (ΔH)
The heat absorbed or released by a reaction at constant pressure; negative for reactions that release heat, positive for reactions that absorb it.
exothermic reaction
A reaction that releases energy to its surroundings; its ΔH is negative and the surroundings warm up.
endothermic reaction
A reaction that absorbs energy from its surroundings; its ΔH is positive and the surroundings cool down.
bond energy
The energy needed to break one mole of a particular chemical bond; the same amount is released when that bond forms.
activation energy (Ea)
The minimum energy colliding particles must have for a reaction to occur — the 'hump' reactants must climb before they can become products.
specific heat (c)
The energy needed to raise the temperature of 1 gram of a substance by 1°C; for liquid water it is 4.18 J/g°C.

Chemical reactions rearrange electron distributions and chemical bonds. Breaking a specified bond requires energy; forming that bond releases energy. A bond-energy calculation imagines separating reactants and then forming products as an accounting path, not a claim that every real reaction first breaks every bond completely. Net enthalpy depends on initial and final states, including phase and interactions.

An exothermic reaction has negative ΔH: the products have lower enthalpy than the reactants for the stated amounts and conditions. At constant pressure with only pressure-volume work, reaction heat equals ΔH and energy is transferred as heat to surroundings. An average bond-energy account can estimate the net difference, but phases and particle interactions also matter. Fuel combustion and many acid-base reactions are familiar examples; the temperature rise also depends on heat capacity and energy loss.

Energy signs depend on which system is being describedEnergy signs depend on which system is being describedReaction systemHeat outExothermic system: q < 0 under the stated heat conventionSurroundings receive energy; total energy is accounted for.
Original selected outward heat-transfer diagram. It does not imply a temperature value or that heat is a material fluid stored inside a bond.

An endothermic reaction has positive ΔH and, under the appropriate constant-pressure conditions, absorbs heat from surroundings. The observed temperature change depends on the surroundings and experimental arrangement. Some cold packs involve endothermic dissolution, a physical process rather than a new-substance reaction. Photosynthesis stores energy through a light-driven process; light uptake should not be presented as the same mechanism as heat absorption measured by a simple calorimeter. Identify both the process and the energy-transfer pathway.

This is why bond energy lets you predict a reaction's energy before ever running it. If you add up the energy needed to break every reactant bond and subtract the energy released when every product bond forms, the difference is ΔH: ΔH = (energy to break bonds) − (energy to form bonds). Take hydrogen burning in chlorine, H₂ + Cl₂ → 2HCl. Breaking one H–H bond (436 kJ) and one Cl–Cl bond (242 kJ) costs 678 kJ, while forming two H–Cl bonds releases 2 × 431 = 862 kJ. So ΔH = 678 − 862 = −184 kJ per mole — negative, and therefore exothermic.

Breaking bonds requires energy; formation can release more in the full accountBreaking bonds requires energy; formation can release more in the full accountSelected energy magnitude (kJ)Break reactant bonds500Form product bonds650ΔH estimate = energy in − energy out = 500 − 650= −150 kJ for the specified reaction amount
Original invented bond-energy magnitudes for one selected reaction basis, not measured values of particular named bonds.

Activation energy is the energy barrier along a reaction pathway. The transition state can contain partly broken and partly formed bonds; not every bond must be fully broken before reaction occurs. A potential-energy diagram distinguishes the barrier from the overall state difference ΔH. A catalyst changes the pathway and lowers a barrier while leaving the same reactant/product energy difference.

A favorable energy difference can coexist with an activation barrierA favorable energy difference can coexist with an activation barrierEnergy (relative units)010203040506001234Reaction coordinate (schematic)Uncatalyzed pathCatalyzed path
Original qualitative path curves in arbitrary energy units, not a measured potential-energy surface or a rate-versus-time graph.

Calorimetry infers energy transfer from measured temperature changes and an energy account. For a material warming without a phase change, q ≈ mcΔT when its specific heat is approximately constant. Water’s commonly used value is 4.18 J g⁻¹ °C⁻¹ near ordinary conditions. In an insulated reaction setup, include the solution and calorimeter when relating their heat gain to reaction heat loss. Ignoring heat loss or cup heat capacity is an approximation; a temperature reading does not directly guarantee an exact reaction enthalpy.

Model check: Breaking a bond costs energy; the overall reaction can release more when product bonds form. ΔH=500−650=−150kJ for the represented amount; exothermic. Average bond values are approximate.

Build your understanding

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Part 1 · Choose the reaction system and energy sign

A system is the part of the world selected for an energy account; the rest is its surroundings. Exothermic means heat leaves the selected system, giving negative q for that system under the usual chemistry convention. Endothermic means it absorbs heat. At constant pressure with the relevant work assumptions, reaction heat connects with enthalpy change. A warmer thermometer in the surroundings can therefore accompany a negative reaction-system heat. State the boundary before assigning a sign or equating heat with temperature.

Energy signs depend on which system is being describedEnergy signs depend on which system is being describedReaction systemHeat outExothermic system: q < 0 under the stated heat conventionSurroundings receive energy; total energy is accounted for.
Original selected outward heat-transfer diagram. It does not imply a temperature value or that heat is a material fluid stored inside a bond.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

If the surroundings warm because the reaction releases heat, what sign is assigned to the reaction-system heat?

Visual reasoning — after your attempt

Negative under the stated convention. The surroundings receive positive heat from that transfer.

Reaction enthalpy ΔH is the products-minus-reactants enthalpy difference for a specified equation and conditions. At constant pressure under the appropriate work assumptions, qsystem corresponds to ΔH. Exothermic ΔH is negative for the reacting system; surroundings can gain positive heat.

OpenSciEd magnification template linking the observable heater to two particle-scale views before and after adding water; it is a model-building prompt, not a completed reaction diagram.
OpenSciEd 7.2’s flameless-heater template connects an observable device to two empty magnified views. It asks for a model and is not evidence of a particular completed reaction, a calorimeter record or a do-it-yourself construction plan. Pair it with this course’s complete system, bond-energy and heat-transfer accounts. Flameless-heater model at visible and particle scales · OpenSciEd · 7.2 Chemical Reactions & Energy, Lesson 1, source, CC BY 4.0. Figure excerpt rendered from the PDF and resized for the web.

The thermometer’s warming describes the measured surrounding solution, not a positive ΔH for an exothermic reaction. Label both signs.

Pause and explain

Why can warming surroundings accompany negative reaction ΔH?

Check your reasoning after answering

The reaction system loses enthalpy as energy transfers out, while the surroundings gain energy. Signs refer to different chosen systems.

Part 2 · Include bond breaking and bond formation

Bond dissociation requires energy for the specified process, while formation of corresponding bonds releases energy relative to separated fragments. A reaction can release net energy when product formation more than offsets reactant bond-breaking costs. Introductory average bond-energy estimates use gas-phase approximations and are not exact enthalpies for every phase or molecule. Breaking a “high-energy bond” alone is not an energy-release explanation. Compare all reactants and products, their states and the chosen reaction amount.

Breaking bonds requires energy; formation can release more in the full accountBreaking bonds requires energy; formation can release more in the full accountSelected energy magnitude (kJ)Break reactant bonds500Form product bonds650ΔH estimate = energy in − energy out = 500 − 650= −150 kJ for the specified reaction amount
Original invented bond-energy magnitudes for one selected reaction basis, not measured values of particular named bonds.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why is the selected net estimate negative even though breaking reactant bonds needs positive energy?

Visual reasoning — after your attempt

The 650 kJ released in the modeled product formation exceeds the 500 kJ input, giving −150 kJ for the full account.

Breaking bonds requires input, while forming bonds releases energy. A bond-enthalpy estimate uses sums for bonds broken minus sums for bonds formed. Average bond enthalpies give approximate gas-phase estimates and are not interchangeable with exact solution reaction enthalpies.

If breaking costs 500 kJ and formation releases 700 kJ for the equation amount, the estimated ΔH is −200 kJ.

Pause and explain

Why is energy comes from breaking bonds incomplete?

Check your reasoning after answering

Bond breaking takes energy. Net release requires the complete account, including the energy released when new bonds form.

Part 3 · Scale energy with the equation amount

Enthalpy is a state function, and a thermochemical reaction change is associated with a defined transformation and amount basis. Multiplying every coefficient scales the enthalpy change by the same factor; reversing the reaction reverses its sign. A number labeled kJ/mol must specify mol of what—product, reactant or reaction extent. Phase labels also matter because liquid and vapor have different enthalpy states. Keep these details when using a reference value in stoichiometry.

Reaction enthalpy belongs to the equation’s stated amount and directionReaction enthalpy belongs to the equation’s stated amount and directionA → B ΔH = −40 kJ per equation amount2A → 2B ΔH = −80 kJB → A ΔH = +40 kJScale coefficients and energy together; reversal changes the sign.
Original hypothetical transformation values, not real thermochemical data or an assertion about rate.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

What is wrong with reversing A→B while keeping the same negative ΔH sign?

Visual reasoning — after your attempt

It reverses the physical energy change without reversing the account’s sign; the corresponding B→A enthalpy is +40 kJ for the displayed basis.

A stated ΔH belongs to the reaction as written. Reversing the equation changes its sign; multiplying coefficients multiplies ΔH. A per-mole label must specify per mole of which species or reaction extent. Do not transfer a numerical enthalpy to a differently scaled equation unchanged.

If A→B has ΔH=−50 kJ per written mole conversion, 2A→2B has −100 kJ and B→A has +50 kJ under matching conditions.

Pause and explain

What happens to ΔH when the equation is reversed?

Check your reasoning after answering

Its sign reverses because the products/reactants energy difference is reversed, provided conditions and species states match.

Part 4 · Keep energy and reaction rate separate

An activation barrier separates reactant and product states along a modeled pathway. A catalyst provides another pathway with a lower barrier but does not change the reactant/product endpoint difference for the same reaction conditions. A reaction can therefore be thermodynamically favored yet slow. Reaction coordinate is a schematic progress description, not elapsed time or distance traveled by a molecule across a real hill. Distinguish endpoint balance, barrier height and measured rate before explaining a temperature or catalyst effect.

A favorable energy difference can coexist with an activation barrierA favorable energy difference can coexist with an activation barrierEnergy (relative units)010203040506001234Reaction coordinate (schematic)Uncatalyzed pathCatalyzed path
Original qualitative path curves in arbitrary energy units, not a measured potential-energy surface or a rate-versus-time graph.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

What remains unchanged between the two selected paths despite the lower catalytic peak?

Visual reasoning — after your attempt

The starting and final energy levels—and therefore the endpoint difference—remain unchanged in the selected account.

A favorable or energy-releasing reaction can be slow because of an activation barrier. A catalyst changes pathway and rate, not the thermodynamic difference between the same states. Energy release alone does not establish safe conditions, self-sustaining operation, or complete conversion.

A reaction may require initiation and lose energy to surroundings faster than it maintains a useful temperature. Thermodynamic and kinetic questions need different evidence.

Pause and explain

Does a negative ΔH establish a fast reaction?

Check your reasoning after answering

No. Rate depends on pathway, activation barriers, concentrations, temperature, and other conditions, not just net enthalpy.

Apply the whole unit · Interpret and scale a reaction energy record

Illustrative equation: A→B,ΔH=−80.0 kJ per 1 mol A converted under stated constant-pressure conditions. In the model 0.250 mol A converts completely.

Your task

Calculate reaction-system and ideal surroundings heat changes, reverse and double the equation’s enthalpy, and explain why neither the sign nor size establishes the reaction speed.

What your response should show

  • Choose the appropriate chemical model or relationship and state its conditions.
  • Show substitutions, units, particle or charge counts, and intermediate reasoning as relevant.
  • Use supplied evidence to justify the conclusion; distinguish observation from inference.
  • Identify a meaningful limitation, uncertainty, or next measurement.
Response guidance — after your attempt
  1. Scale: 0.250×(−80.0)=−20.0 kJ for the reaction system.

  2. With no other energy destinations, surroundings gain +20.0 kJ.

  3. B→A has +80.0 kJ per written mole; 2A→2B has −160 kJ.

The energy changes are tied to the specified equation amount, states, and conditions. The surroundings result assumes a complete limited energy account. Rate and initiation require kinetic evidence; an exothermic label is not a proof of fast, complete, or self-sustaining conversion.

Scientific references and source-model foundations

Parent / teacher teaching notes

Have students label equation amount and system boundary before signs. Require a sentence distinguishing activation energy from net enthalpy. Ask the learner to explain each particle symbol, axis, unit and arrow before calculating. Distinguish hypothetical models and calculated curves from measured records. Public OpenSciEd excerpts here are selected foundation prompts, not complete high-school teacher editions or an endorsement. All required advanced explanations and practice are provided locally.

Potential-Energy Diagram (Exothermic)Reaction progress →EaΔHReactantsProducts
Selected exothermic path with lower product enthalpy. Forward activation energy is the barrier height above the reactant level, not the absolute peak coordinate. Reaction coordinate is schematic rather than elapsed time; rate and net energy are distinct.

The key idea

A reaction energy account needs a system, defined states and amount. Bond breaking requires energy, product formation can offset it, and reaction enthalpy is distinct from activation barrier and rate. Calorimetry uses a complete heat-capacity/boundary account.

Heat Transfer (Calorimetry)

q = mcΔT

q is heat energy in joules (J); m is mass in grams; c is the specific heat (4.18 J/g°C for liquid water); ΔT = T final − T initial in °C.

Enthalpy from Bond Energies

ΔH = (energy to break bonds) − (energy to form bonds)

a negative ΔH means the reaction releases energy overall (exothermic); a positive ΔH means it absorbs energy overall (endothermic).

Worked examples

Example 1

How much heat (in joules) is absorbed when 200. g of water is heated from 20.0°C to 50.0°C? The specific heat of water is 4.18 J/g°C.
  1. Identify the values: m = 200 g, c = 4.18 J/g°C, ΔT = T final − T initial = 50.0 − 20.0 = 30.0°C.
  2. Apply q = mcΔT = 200 × 4.18 × 30.0.
  3. Multiply: 4.18 × 30.0 = 125.4, and 125.4 × 200 = 25,080 J.
Answer: 25,080 J (about 25.1 kJ) absorbed

Example 2 · Worked application

A reaction has ΔH=−80 kJ per stated reaction amount. Interpret direction and reverse-reaction value.
  1. Negative ΔH means the system's enthalpy decreases and heat is released at constant pressure under the model.
  2. Reversing the reaction reverses the sign.
  3. The magnitude refers to the stated stoichiometric amount.
Answer: Forward releases 80 kJ; reverse ΔH=+80 kJ.
Check the reasoning

Do not omit the reaction-amount basis when scaling.

Example 3

For the reaction H₂ + Cl₂ → 2HCl, the bond energies are H–H = 436 kJ/mol, Cl–Cl = 242 kJ/mol, and H–Cl = 431 kJ/mol. Calculate ΔH and state whether the reaction is exothermic or endothermic.
  1. Energy to break the reactant bonds: one H–H (436) + one Cl–Cl (242) = 678 kJ absorbed.
  2. Energy released forming the product bonds: two H–Cl = 2 × 431 = 862 kJ released.
  3. ΔH = (bonds broken) − (bonds formed) = 678 − 862 = −184 kJ/mol. The negative sign means energy is released.
Answer: ΔH = −184 kJ/mol; the reaction is exothermic

Example 4 · Find and fix the mistake

Context: A reaction has ΔH=−80 kJ per stated reaction amount. Interpret direction and reverse-reaction value. A student claims: “A negative enthalpy means no activation energy is required.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: Do not omit the reaction-amount basis when scaling.
  2. Heat release and activation barrier are different properties; an exothermic reaction may still need initiation.
Answer: Heat release and activation barrier are different properties; an exothermic reaction may still need initiation.
Check the reasoning

Do not omit the reaction-amount basis when scaling.

Example 5 · Reason from the visual model

Reaction enthalpy belongs to the equation’s stated amount and directionReaction enthalpy belongs to the equation’s stated amount and directionA → B ΔH = −40 kJ per equation amount2A → 2B ΔH = −80 kJB → A ΔH = +40 kJScale coefficients and energy together; reversal changes the sign.
Original hypothetical transformation values, not real thermochemical data or an assertion about rate.
What is wrong with reversing A→B while keeping the same negative ΔH sign?
  1. Enthalpy is a state function, and a thermochemical reaction change is associated with a defined transformation and amount basis. Multiplying every coefficient scales the enthalpy change by the same factor; reversing the reaction reverses its sign. A number labeled kJ/mol must specify mol of what—product, reactant or reaction extent. Phase labels also matter because liquid and vapor have different enthalpy states. Keep these details when using a reference value in stoichiometry.
  2. It reverses the physical energy change without reversing the account’s sign; the corresponding B→A enthalpy is +40 kJ for the displayed basis.
Answer: It reverses the physical energy change without reversing the account’s sign; the corresponding B→A enthalpy is +40 kJ for the displayed basis.
Check the reasoning

Original hypothetical transformation values, not real thermochemical data or an assertion about rate.

Avoid these mistakes

Check your understanding

Breaking costs 500kJ and forming releases 650kJ. Find modeled ΔH.

Discuss the answer

ΔH=500−650=−150kJ for the represented amount; exothermic. Average bond values are approximate.

Return to the phenomenon

Return to the initial case. How can a reaction release energy if breaking its reactant bonds requires energy? Revise your drawing or explanation using two named ideas and one stated limitation.

Compare explanations after your attempt

Bond breaking costs energy, while formation can release more. Net change depends on all species and conditions, with a separate activation-barrier question for rate.

What should we investigate next?

Which comparison would test a remaining uncertainty? State what you would change, keep comparable and measure.

Investigate, calculate and revise

Keep a first model and an evidence-supported revision. Attempt each task before opening guidance; all required explanations and supplied-data routes are available locally.

Activity 1 · Return to the opening case

Assigned reading and preparation

Use the opening phenomenon, unit definitions and explained Parts 1–4.

Your task

Return to the initial case. How can a reaction release energy if breaking its reactant bonds requires energy? Revise your drawing or explanation using two named ideas and one stated limitation.

Success criteria

  • Use the stated observations and appropriate units.
  • Connect a labeled model with the chemical mechanism.
  • State assumptions and an evidence limitation.
  • Explain a substantive revision or next test.
Hint

Keep species identity, material transfer and energy account distinct.

Response guidance — discuss after your attempt

Bond breaking costs energy, while formation can release more. Net change depends on all species and conditions, with a separate activation-barrier question for rate.

Activity 2 · Transfer to a changed case

Assigned reading and preparation

Cover the worked answer and use the explained models, relationships and notebook.

Your task

A selected reaction absorbs 720 kJ in the bond-breaking account and releases 880 kJ on product formation. Estimate net enthalpy, then predict the corresponding value when the entire equation is doubled.

Success criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
Hint

Name known quantities and conditions, show intermediate steps and check conservation.

Response guidance — discuss after your attempt

ΔH≈720−880=−160 kJ for the selected equation amount. Doubling all coefficients gives approximately −320 kJ. Average bond energies are an approximate full-reaction estimate, not proof about spontaneity or rate.

Words to know

enthalpy change (ΔH)
The heat absorbed or released by a reaction at constant pressure; negative for reactions that release heat, positive for reactions that absorb it.
exothermic reaction
A reaction that releases energy to its surroundings; its ΔH is negative and the surroundings warm up.
endothermic reaction
A reaction that absorbs energy from its surroundings; its ΔH is positive and the surroundings cool down.
bond energy
The energy needed to break one mole of a particular chemical bond; the same amount is released when that bond forms.
activation energy (Ea)
The minimum energy colliding particles must have for a reaction to occur — the 'hump' reactants must climb before they can become products.
specific heat (c)
The energy needed to raise the temperature of 1 gram of a substance by 1°C; for liquid water it is 4.18 J/g°C.

Lavoisier's ice calorimeter: measuring heat with a melting snowball

Long before electronic sensors, Antoine Lavoisier and mathematician Pierre-Simon Laplace built a clever device in the 1780 s to measure the heat a reaction releases. They nested a reacting sample inside a chamber packed with ice; the heat given off melted a measurable amount of that ice, and the mass of meltwater told them exactly how much energy had flowed out. In one famous run they even placed a live guinea pig inside and showed that respiration warms an animal by the same kind of slow combustion that burns charcoal — an early hint that the chemistry of a candle and the chemistry of a living body are cousins. Every modern calorimeter, and the equation q = mcΔT you use with it, descends directly from that icy experiment.

The misconception that 'exothermic' means 'starts on its own'

It is tempting to assume that because an exothermic reaction releases energy, it must happen spontaneously the moment the reactants touch. But gasoline can sit safely in a can beside oxygen for years, and a log will not burst into flame just because burning is exothermic. The reason is the activation energy — the hump every reaction must climb before it can release its energy — so a spark, a flame, or a hot surface is needed to push those first molecules over the barrier. Once over, the energy released can supply the activation energy for the next molecules, which is why a fire, once lit, sustains itself. Exothermic tells you where a reaction ends up, not whether it will start without a push.

Where the Calories on a food label come from

The 'Calories' printed on a cereal box are literally combustion measurements. Food scientists burn a dried sample inside a sealed bomb calorimeter submerged in water, then use q = mcΔT to convert the water's temperature rise into energy. One food Calorie (capital C) is actually a kilocalorie — 1000 of the small calories used in chemistry, and about 4184 joules. So the same equation that sizes a power-plant cooling system also decides whether a snack is labeled 100 Calories or 300, connecting the abstract idea of enthalpy to the very concrete question of how much energy your dinner will give you.

Self-heating meals and instant cold packs

Engineers put endothermic and exothermic chemistry to work in your hands. A flameless ration heater tucked into a soldier's or camper's meal uses the exothermic reaction of magnesium metal with water to boil a pouch of food without a stove. An instant cold pack does the reverse: snapping its inner barrier lets ammonium nitrate dissolve endothermically, pulling heat out of a sprained ankle within seconds. Both are designed around ΔH — chemists deliberately chose reactions with the right sign and size of energy change so the product warms or cools by just the amount a person needs.

Why ΔH is only half the story

A common surprise for chemistry students is that some endothermic reactions happen readily anyway — an instant cold pack works without any push, even though it absorbs energy. Energy release is not the only thing driving a reaction; nature also favors an increase in disorder (called entropy). When a solid dissolves into freely moving ions, the jump in disorder can be enough to make an energy-absorbing process go forward on its own. Chemists combine both factors — the energy change ΔH and the disorder change — into a single quantity called free energy, which you will meet in a later course. For now, remember that ΔH tells you about the heat, but it is only one of the two forces steering whether a reaction actually proceeds.

In the real world

Chemical engineers use calorimetry and ΔH to design everything from safe rocket propellants to the flameless self-heating pouches that warm a soldier's or a camper's meal.

Exit check

Breaking costs 500kJ and forming releases 650kJ. Find modeled ΔH.

Check your explanation after answering

ΔH=500−650=−150kJ for the represented amount; exothermic. Average bond values are approximate.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Calorimetry, Hess’s Law & Enthalpy Calculations

Learning goals

Readings for this unit

Before this unit

Energy transfer, q=mcΔT, moles, and signed numbers.

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Start with something to explain

Does a measured temperature rise by itself give a reaction enthalpy?

Illustrative evidence case. Two cups show the same temperature rise but contain different water masses.

A thermometer measures a response used to infer heat transferA thermometer measures a response used to infer heat transferSample + surrounding waterWater: 100.0 gΔT = +5.00°Cqwater = 100.0 × 4.18 × 5.00 = +2090 JReaction heat also accounts for apparatus and losses.
Original selected water-response calculation. The apparatus is schematic and the arrow is qualitative energy transfer, not a calibrated sensor.

Notice and wonder

Record two observations using the stated quantities or relationships. Keep observations separate from possible causes. Write one question that a new measurement could help answer.

Does a measured temperature rise by itself give a reaction enthalpy?

Your first model

Track thermal mass, the cup contribution and the amount reacted.

Build the language from the idea

calorimeter heat capacity
Energy needed to raise the apparatus temperature by one degree.
state function
A property determined by state rather than path.
Hess’s law
Reaction enthalpies add when equations add.

Calorimetry estimates transferred energy from a measured temperature change. In a simplified insulated cup, qsolution=m c ΔT and qreaction≈−qsolution. A warmer solution gains heat; the reaction loses it and is exothermic. This sign distinction follows the chosen system boundary.

A better model includes the cup and thermometer: qreaction=−(m c ΔT+CcalΔT), where Ccal is the calorimeter heat capacity in J/°C. Heat exchanged with room air is another correction. Report assumptions before treating the calculated energy as an exact reaction enthalpy.

A thermometer measures a response used to infer heat transferA thermometer measures a response used to infer heat transferSample + surrounding waterWater: 100.0 gΔT = +5.00°Cqwater = 100.0 × 4.18 × 5.00 = +2090 JReaction heat also accounts for apparatus and losses.
Original selected water-response calculation. The apparatus is schematic and the arrow is qualitative energy transfer, not a calibrated sensor.

To express enthalpy per mole, divide reaction heat by moles of the specified reacting substance or the reaction extent. For a balanced thermochemical equation, ΔH belongs to the equation as written. Doubling every coefficient doubles ΔH; reversing the reaction reverses its sign.

Normalize measured heat by the actual reacting amountNormalize measured heat by the actual reacting amountqreaction ≈ −2.09 kJReacting amount = 0.0500 molΔH per reacting mol ≈ −2.09/0.0500= −41.8 kJ/mol on this stated basis
Original selected heat normalization using a supplied inferred reaction heat, not a validated calorimeter measurement.

Hess’s law follows from enthalpy being a state function. Add known reaction steps to obtain a target equation and add their corresponding ΔH values. Cancel intermediates. This allows indirect calculation without assuming that a real reaction follows the artificial sequence used for bookkeeping.

Hess’s law combines state changes while canceling intermediatesHess’s law combines state changes while canceling intermediatesA → B ΔH₁ = −30 kJB → C ΔH₂ = +12 kJA → C ΔH = −18 kJCancel intermediates and add the corresponding energy changes.
Original hypothetical two-step enthalpy cycle with stated values and compatible species states assumed.

Using standard formation enthalpies, ΔH°reaction=ΣνΔH°f(products)−ΣνΔH°f(reactants). Coefficients ν multiply tabulated values. Elements in their defined standard reference states have formation enthalpy zero by convention, not because those substances contain no energy.

Formation values combine through coefficients and reference statesFormation values combine through coefficients and reference statesΔH°reaction = ΣνΔH°f(products) − ΣνΔH°f(reactants)Selected modelΔH°f (kJ/mol)A(g)−20B(g)−702A(g) → B(g)−70 − 2(−20) = −30 kJMultiply each formation value by its equation coefficient.
Original hypothetical A/B formation values for arithmetic, not real species or a claim of atom conservation without their composition being specified.

Bond-energy estimates use energy required to break reactant bonds minus energy released forming product bonds. Average bond energies are approximations and often gas-phase values, so their result need not equal a precise tabulated reaction enthalpy. Compare method assumptions when answers differ.

Build your understanding

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Part 1 · Translate a temperature rise into measured heat

Calorimetry infers an energy transfer from measured changes and a defined heat-capacity model. Water mass, specific heat and temperature rise give qwater, but the reaction’s heat is not automatically exactly its negative. Include the calorimeter, other solution components and environmental transfer as appropriate. A thermometer reads temperature, not joules directly. Record the initial/final states, mass basis and thermal boundary before using qreaction≈−qsurroundings as an approximation.

A thermometer measures a response used to infer heat transferA thermometer measures a response used to infer heat transferSample + surrounding waterWater: 100.0 gΔT = +5.00°Cqwater = 100.0 × 4.18 × 5.00 = +2090 JReaction heat also accounts for apparatus and losses.
Original selected water-response calculation. The apparatus is schematic and the arrow is qualitative energy transfer, not a calibrated sensor.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

What extra term may be needed if the calorimeter cup also warms substantially?

Visual reasoning — after your attempt

Its heat-capacity contribution, such as CcalΔT, belongs in the surroundings account, along with relevant losses.

For a stated single-phase sample, q=mcΔT uses its mass and specific heat. A calorimeter can also absorb energy, and environmental exchange may matter. The solution’s q is not automatically the reaction’s q until an energy boundary and assumptions connect them.

If a solution warms, qsolution is positive. Under an ideal insulated reaction/solution model, qreaction≈−qsolution; include calorimeter heat if its constant is supplied.

Pause and explain

Why does a measured temperature rise not directly give reaction ΔH without assumptions?

Check your reasoning after answering

Mass, heat capacity, calorimeter absorption, losses, pressure conditions, and reacting amount are needed to relate the measured warming to reaction enthalpy.

Part 2 · Normalize by reaction amount

An inferred molar reaction enthalpy divides the appropriate reaction-system heat by the amount that actually reacted on the stated stoichiometric basis. Use the limiting amount rather than automatically the total solution moles or whichever reactant was weighed first. The sign follows the system convention, and uncertainty in temperature, heat capacity, amount and loss corrections affects the result. “Per mole” without naming the reaction basis is incomplete, especially when coefficients differ from one.

Normalize measured heat by the actual reacting amountNormalize measured heat by the actual reacting amountqreaction ≈ −2.09 kJReacting amount = 0.0500 molΔH per reacting mol ≈ −2.09/0.0500= −41.8 kJ/mol on this stated basis
Original selected heat normalization using a supplied inferred reaction heat, not a validated calorimeter measurement.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why could dividing by the initial amount of an excess reactant give the wrong molar enthalpy?

Visual reasoning — after your attempt

Only part of that excess may react; normalization must use the actual extent or the specified reacting amount.

After finding total reaction heat, divide by the appropriate reacted mole amount to obtain a molar enthalpy for the specified equation scale. Use the limiting or actually reacted amount rather than automatically the total supplied reagent amount. Keep joules versus kilojoules explicit.

−2090 J from 0.0500 mol modeled conversion corresponds to −41.8 kJ/mol. The mole denominator must refer to the stated reaction amount.

Pause and explain

What is wrong with dividing by moles of an unrelated spectator?

Check your reasoning after answering

That denominator does not represent reaction extent. It would report a number with no appropriate molar reaction interpretation.

Part 3 · Add equations using Hess’s law

Hess’s law uses the state-function character of enthalpy: the overall change depends on initial and final states rather than which conceptual route is added. Scale or reverse component equations as necessary, cancel shared intermediates and apply the same operations to their enthalpies. Intermediate B can disappear from the net equation without implying it was never involved in a real mechanism. The algebraic route need not be the actual laboratory pathway, and phases must match when canceling a species.

Hess’s law combines state changes while canceling intermediatesHess’s law combines state changes while canceling intermediatesA → B ΔH₁ = −30 kJB → C ΔH₂ = +12 kJA → C ΔH = −18 kJCancel intermediates and add the corresponding energy changes.
Original hypothetical two-step enthalpy cycle with stated values and compatible species states assumed.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why can B cancel while the +12 kJ second step must still be included?

Visual reasoning — after your attempt

B is an intermediate in the summed transformation. Its associated state-change energy remains part of the overall endpoint balance.

Enthalpy is a state function, so matching steps can be added to obtain a target reaction. Reverse or scale each equation and its ΔH together. Cancel intermediate species algebraically, checking states and conditions, rather than adding energies from unrelated processes.

A→B and B→C add to A→C. The intermediate B cancels when its amount matches on both sides.

Pause and explain

Why can mismatched species states prevent simple cancellation?

Check your reasoning after answering

Aqueous, gaseous, liquid, or solid states have different enthalpies. A phase-change step may be needed to make the energy account consistent.

Part 4 · Use formation enthalpies with coefficients

A standard formation enthalpy refers to forming one mole of a specified substance from elements in their reference states under the stated standard conditions. The reaction sum uses products minus reactants with all coefficients included. Elements in their defined reference states have zero formation enthalpy by convention, not zero total internal energy. Standard pressure does not by itself define every temperature; read the table’s temperature and phase labels. Consistent references are essential for a valid cancellation.

Formation values combine through coefficients and reference statesFormation values combine through coefficients and reference statesΔH°reaction = ΣνΔH°f(products) − ΣνΔH°f(reactants)Selected modelΔH°f (kJ/mol)A(g)−20B(g)−702A(g) → B(g)−70 − 2(−20) = −30 kJMultiply each formation value by its equation coefficient.
Original hypothetical A/B formation values for arithmetic, not real species or a claim of atom conservation without their composition being specified.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why is the A contribution multiplied by two for 2A→B?

Visual reasoning — after your attempt

Two moles of A occur per displayed reaction amount; enthalpy is extensive and follows that coefficient.

A standard reaction enthalpy can be calculated as ΣνΔHf°(products)−ΣνΔHf°(reactants), with correct coefficients and states. Elements in their standard reference states have zero standard formation enthalpy by convention, not zero total energy.

A table value must be read for the correct phase. Water liquid and vapor have different formation enthalpies and cannot be substituted casually.

Pause and explain

Does ΔHf°=0 mean an element contains no energy?

Check your reasoning after answering

No. It is a reference convention for its standard-state formation enthalpy, not a claim that the substance has zero absolute energy.

Apply the whole unit · Calculate a calorimetric molar enthalpy

Illustrative record: 100.0 g solution warms from 20.0°C to 25.0°C during 0.0500 mol reaction extent. Use c=4.18 J/g·°C; assume constant pressure, negligible calorimeter absorption and environmental loss.

Your task

Find solution heat, reaction heat, and molar reaction enthalpy, showing signs and units. Identify two omitted effects that could alter an experimental interpretation.

What your response should show

  • Choose the appropriate chemical model or relationship and state its conditions.
  • Show substitutions, units, particle or charge counts, and intermediate reasoning as relevant.
  • Use supplied evidence to justify the conclusion; distinguish observation from inference.
  • Identify a meaningful limitation, uncertainty, or next measurement.
Response guidance — after your attempt
  1. ΔT=5.0°C; qsolution=100.0×4.18×5.0=2090 J.

  2. qreaction≈−2090 J under the stated isolated energy account.

  3. ΔH per reaction extent≈−2090/0.0500=−41800 J/mol=−41.8 kJ/mol before precision rounding.

The model is exothermic. With the temperature-change precision, a final reported value around −42 kJ/mol is appropriate; extra digits show the working calculation. Calorimeter heating, heat loss, different heat capacity, or incomplete reaction can alter the inferred value. The actual reacting amount must correspond to the stated equation extent.

Scientific references and source-model foundations

Parent / teacher teaching notes

Check which part warmed before assigning signs. Require an equation-extent denominator and separate working precision from final reporting. Ask the learner to explain each particle symbol, axis, unit and arrow before calculating. Distinguish hypothetical models and calculated curves from measured records. Public OpenSciEd excerpts here are selected foundation prompts, not complete high-school teacher editions or an endorsement. All required advanced explanations and practice are provided locally.

The key idea

Choose a system, preserve energy signs, and scale enthalpy with the reaction equation.

Worked examples

Example 1

100 g water warms 5.0°C; c=4.18 J/g°C. Estimate reaction heat neglecting cup/loss.
  1. qwater=100×4.18×5=2090 J.
  2. qreaction=−qwater.
Answer: −2.09 kJ

Example 2 · Worked application

A 100 g water sample warms 5.0°C with c=4.18 J/(g·°C). Find water heat and ideal reaction heat.
  1. q_water=100×4.18×5.0=2090 J.
  2. If the reaction is the only source and all heat enters water, q_reaction=−q_water.
  3. Real calorimeter and surroundings may also absorb energy.
Answer: Water gains about 2.1 kJ; reaction loses about 2.1 kJ in the ideal model.
Check the reasoning

System and surroundings have opposite signs in this boundary.

Example 3

A→B has ΔH=+40 kJ; B→C has ΔH=−70 kJ. Find A→C.
  1. Add equations and cancel B.
  2. Add enthalpies 40−70.
Answer: −30 kJ

Example 4 · Find and fix the mistake

Context: A 100 g water sample warms 5.0°C with c=4.18 J/(g·°C). Find water heat and ideal reaction heat. A student claims: “A warmer solution means the reaction absorbed positive heat from it.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: System and surroundings have opposite signs in this boundary.
  2. The solution gained heat; the supplying reaction released heat under the stated model.
Answer: The solution gained heat; the supplying reaction released heat under the stated model.
Check the reasoning

System and surroundings have opposite signs in this boundary.

Example 5 · Reason from the visual model

Hess’s law combines state changes while canceling intermediatesHess’s law combines state changes while canceling intermediatesA → B ΔH₁ = −30 kJB → C ΔH₂ = +12 kJA → C ΔH = −18 kJCancel intermediates and add the corresponding energy changes.
Original hypothetical two-step enthalpy cycle with stated values and compatible species states assumed.
Why can B cancel while the +12 kJ second step must still be included?
  1. Hess’s law uses the state-function character of enthalpy: the overall change depends on initial and final states rather than which conceptual route is added. Scale or reverse component equations as necessary, cancel shared intermediates and apply the same operations to their enthalpies. Intermediate B can disappear from the net equation without implying it was never involved in a real mechanism. The algebraic route need not be the actual laboratory pathway, and phases must match when canceling a species.
  2. B is an intermediate in the summed transformation. Its associated state-change energy remains part of the overall endpoint balance.
Answer: B is an intermediate in the summed transformation. Its associated state-change energy remains part of the overall endpoint balance.
Check the reasoning

Original hypothetical two-step enthalpy cycle with stated values and compatible species states assumed.

Avoid these mistakes

Check your understanding

Explain the sign of ΔH for a warming cup reaction.

Discuss the answer

The solution gains heat, so the reaction releases heat and has negative ΔH under the stated model.

Return to the phenomenon

Return to the initial case. Does a measured temperature rise by itself give a reaction enthalpy? Revise your drawing or explanation using two named ideas and one stated limitation.

Compare explanations after your attempt

Heat depends on heat capacity and temperature change, and molar enthalpy additionally needs the reaction amount and boundary corrections. Equal thermometer changes need not mean equal energy transfers.

What should we investigate next?

Which comparison would test a remaining uncertainty? State what you would change, keep comparable and measure.

Investigate, calculate and revise

Keep a first model and an evidence-supported revision. Attempt each task before opening guidance; all required explanations and supplied-data routes are available locally.

Activity 1 · Return to the opening case

Assigned reading and preparation

Use the opening phenomenon, unit definitions and explained Parts 1–4.

Your task

Return to the initial case. Does a measured temperature rise by itself give a reaction enthalpy? Revise your drawing or explanation using two named ideas and one stated limitation.

Success criteria

  • Use the stated observations and appropriate units.
  • Connect a labeled model with the chemical mechanism.
  • State assumptions and an evidence limitation.
  • Explain a substantive revision or next test.
Hint

Keep species identity, material transfer and energy account distinct.

Response guidance — discuss after your attempt

Heat depends on heat capacity and temperature change, and molar enthalpy additionally needs the reaction amount and boundary corrections. Equal thermometer changes need not mean equal energy transfers.

Activity 2 · Transfer to a changed case

Assigned reading and preparation

Cover the worked answer and use the explained models, relationships and notebook.

Your task

A reaction heats 50.0 g water by 8.00°C. Use c=4.18 J/(g·°C), neglect apparatus/losses, and assume 0.0200 mol reacts. Estimate reaction heat and molar enthalpy on that basis.

Success criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
Hint

Name known quantities and conditions, show intermediate steps and check conservation.

Response guidance — discuss after your attempt

qwater=50.0×4.18×8.00=1672 J. qreaction≈−1.672 kJ. Dividing by 0.0200 mol gives approximately −83.6 kJ/mol on the specified reacting-amount basis, subject to the neglected terms.

Words to know

calorimeter heat capacity
Energy needed to raise the apparatus temperature by one degree.
state function
A property determined by state rather than path.
Hess’s law
Reaction enthalpies add when equations add.

In the real world

Use the chapter investigation to connect this unit to measured evidence and a practical decision.

Exit check

Explain the sign of ΔH for a warming cup reaction.

Check your explanation after answering

The solution gains heat, so the reaction releases heat and has negative ΔH under the stated model.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Entropy, Free Energy & Reaction Feasibility

Learning goals

Readings for this unit

Before this unit

Energy signs, kelvin temperature, and algebra.

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Start with something to explain

Can a process absorb heat yet be thermodynamically favored?

Illustrative evidence case. A selected transformation has positive ΔH and a sufficiently positive ΔS at its stated temperature.

Entropy needs an energy-and-constraint account beyond a disorder sloganEntropy needs an energy-and-constraint account beyond a disorder sloganConstrained distributionMore accessible arrangementsEntropy concerns accessible microstates under specified constraints.
Original qualitative distribution comparison; dot arrangements are examples, not a counted thermodynamic microstate dataset.

Notice and wonder

Record two observations using the stated quantities or relationships. Keep observations separate from possible causes. Write one question that a new measurement could help answer.

Can a process absorb heat yet be thermodynamically favored?

Your first model

Compare the enthalpy term with TΔS using compatible units and a defined system.

Build the language from the idea

entropy
A measure related to accessible microscopic arrangements and energy dispersal.
Gibbs free energy
A thermodynamic potential useful for constant-temperature, constant-pressure processes.
spontaneous
Thermodynamically favored under stated conditions; not necessarily rapid.

Enthalpy alone does not determine whether a change is thermodynamically favored. Some endothermic processes occur readily because the total entropy of system and surroundings increases. Entropy counts accessible microscopic arrangements and energy dispersal; simply calling it disorder can hide what is being counted.

Entropy needs an energy-and-constraint account beyond a disorder sloganEntropy needs an energy-and-constraint account beyond a disorder sloganConstrained distributionMore accessible arrangementsEntropy concerns accessible microstates under specified constraints.
Original qualitative distribution comparison; dot arrangements are examples, not a counted thermodynamic microstate dataset.

For a system at constant temperature and pressure, Gibbs free-energy change is ΔG=ΔH−TΔS. Negative ΔG indicates a thermodynamic driving tendency in the specified conditions; positive ΔG favors the reverse; zero corresponds to equilibrium. Use temperature in kelvin and matching energy units.

Enthalpy and entropy jointly determine a free-energy changeEnthalpy and entropy jointly determine a free-energy changeΔG = ΔH − TΔSΔH = +20.0 kJ/mol; ΔS = +0.100 kJ/(mol·K)At 300 K: ΔG = 20.0 − 30.0 = −10.0 kJ/molUse kelvin and compatible energy units; state the conditions.
Original hypothetical thermodynamic values with a consistent molar basis, not a real material’s temperature-dependent property dataset.

A larger number of gas particles often increases entropy under comparable conditions, and dispersing a substance or warming it can increase accessible arrangements. These are useful tendencies, not universal replacements for data. Entropy changes in surroundings must also be considered to judge total entropy.

If ΔH<0 and ΔS>0, ΔG is negative at all positive temperatures in the simple constant-value model. If both are positive, sufficiently high temperature can favor the process. The crossover estimate T=ΔH/ΔS assumes those values are approximately constant across the interval.

Thermodynamically favorable does not mean fast. A large activation barrier can make a favored reaction proceed imperceptibly slowly. Catalysts change kinetic pathways but do not change the overall equilibrium constant or reaction ΔG for the same reactants and products.

Thermodynamic driving tendency does not set a reaction timescaleThermodynamic driving tendency does not set a reaction timescaleFree energy (relative units)02040608001234Reaction coordinate (schematic)Lower final free energy can coexist with a large forward barrier.
Original qualitative free-energy profile with arbitrary values, not a measured transition-state landscape or a practical reaction-time prediction.

For independent study, label enthalpy and entropy values as supplied at stated conditions. Convert J to kJ before subtracting. Describe the result as favorability under a model, not a prediction of completion time or a guarantee of laboratory outcome.

Build your understanding

Use the detailed parent plan: two core 50–60-minute sessions per focused unit, with a third assigned for selected calculation/modeling topics. First study the core explanation and Parts 1–2 with their figures/checks; next study Parts 3–4, the whole-unit application, worked cases, varied practice and exit check. Attempt reasoning before opening guidance. Extend time when actual understanding requires it; investigations and chapter assessments have separate sessions.

Part 1 · Explain entropy beyond a disorder slogan

Entropy S is a thermodynamic state quantity connected with the number and distribution of accessible microscopic arrangements. For suitable equal-probability microstate counting, S=kB ln W provides a useful bridge, while macroscopic changes can be evaluated through reversible heat transfer and temperature. “Disorder” is an imperfect analogy, not a measurement procedure. The same particle count can have different accessible arrangements when volume or other constraints change; assess the full system and surroundings rather than judging entropy from a messy-looking drawing.

Entropy needs an energy-and-constraint account beyond a disorder sloganEntropy needs an energy-and-constraint account beyond a disorder sloganConstrained distributionMore accessible arrangementsEntropy concerns accessible microstates under specified constraints.
Original qualitative distribution comparison; dot arrangements are examples, not a counted thermodynamic microstate dataset.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why does a more spread-out dot picture not by itself determine a numerical entropy change?

Visual reasoning — after your attempt

The relevant energy, constraints and accessible microstate model are not specified quantitatively. Appearance alone is insufficient.

Entropy relates to the number of accessible microscopic arrangements and energy dispersal in a thermodynamic description. Gas formation, mixing, and phase changes can influence it, but visual messiness is not a complete definition. Distinguish system entropy from total entropy including surroundings.

A system’s entropy can decrease while surrounding entropy increases sufficiently. Looking only at the system cannot establish the spontaneity of the full process.

Pause and explain

Can a spontaneous process have a negative system entropy change?

Check your reasoning after answering

Yes. A sufficiently positive surroundings contribution can make total entropy increase even if the system’s entropy decreases.

Part 2 · Use free energy under its conditions

At constant temperature and pressure under the appropriate constraints, Gibbs free energy helps assess the thermodynamic direction through ΔG=ΔH−TΔS. A process can be endothermic yet favored when the entropy term is sufficiently positive. Convert entropy units before multiplying by absolute T; joules and kilojoules cannot be subtracted without conversion. The result describes the specified state change under its conditions, not every possible mixture or a measured rate. State any approximation that ΔH and ΔS remain constant over a temperature range.

Enthalpy and entropy jointly determine a free-energy changeEnthalpy and entropy jointly determine a free-energy changeΔG = ΔH − TΔSΔH = +20.0 kJ/mol; ΔS = +0.100 kJ/(mol·K)At 300 K: ΔG = 20.0 − 30.0 = −10.0 kJ/molUse kelvin and compatible energy units; state the conditions.
Original hypothetical thermodynamic values with a consistent molar basis, not a real material’s temperature-dependent property dataset.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why can the selected positive-ΔH transformation have negative ΔG at 300 K?

Visual reasoning — after your attempt

The positive entropy contribution TΔS=30.0 kJ/mol exceeds the 20.0 kJ/mol enthalpy cost.

At constant temperature and pressure, ΔG=ΔH−TΔS provides a feasibility criterion under suitable thermodynamic conditions. Use Kelvin and compatible energy units. Negative ΔG favors forward change for the stated actual conditions; zero corresponds to equilibrium; positive favors the reverse.

If ΔH is in kJ/mol and ΔS in J/mol·K, convert entropy to kJ/mol·K before multiplying by T.

Pause and explain

What common error changes a free-energy calculation by a factor of one thousand?

Check your reasoning after answering

Combining kJ enthalpy with J entropy without conversion. The two terms must use compatible energy units.

Part 3 · Distinguish actual and standard-state favorability

The standard reaction free energy ΔG° refers to a defined reference-state account. The actual driving tendency also depends on mixture composition through Q, the reaction quotient, using consistent dimensionless activities. At equilibrium Q=K and the reaction’s ΔG is zero. A negative ΔG° does not mean every possible starting mixture moves forward, because the RT ln Q contribution can change the actual sign. Concentration-only classroom expressions approximate activities and require an explicitly consistent convention.

Standard-state favorability and the actual mixture are differentStandard-state favorability and the actual mixture are differentΔG = ΔG° + RT ln QAt equilibrium: ΔG = 0 and Q = KΔG° = −RT ln KQ and K use compatible dimensionless activity conventions.
Original thermodynamic relationships; no logarithm of a dimensional raw concentration is intended.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Why can a reaction with negative ΔG° fail to proceed net forward from a very product-rich starting mixture?

Visual reasoning — after your attempt

A sufficiently large Q can make RT ln Q positive enough to change the actual ΔG; the mixture composition matters.

ΔG° describes standard-state conditions, while actual ΔG depends on reaction composition through ΔG=ΔG°+RT ln Q. A positive standard value does not prove no forward conversion can occur at any composition. Equilibrium links ΔG° to K rather than forcing all reactions to stop.

A reaction mixture far from standard ratios can have a different driving direction from the standard-state criterion.

Pause and explain

Why can actual composition change direction without changing ΔG°?

Check your reasoning after answering

The RT ln Q term reflects the mixture’s state. ΔG° is a reference property, while actual ΔG includes current activities.

Part 4 · Separate feasibility from rate

Thermodynamic feasibility and kinetics answer different questions. A lower product free-energy state can be favored while an activation barrier makes conversion slow on the observed timescale. A catalyst changes available pathways and rates without changing equilibrium for the same reaction and conditions. A free-energy curve is a model, not a stopwatch. Evidence for practical performance must include reaction time, pathway, transport and possible competing changes rather than only the endpoint sign.

Thermodynamic driving tendency does not set a reaction timescaleThermodynamic driving tendency does not set a reaction timescaleFree energy (relative units)02040608001234Reaction coordinate (schematic)Lower final free energy can coexist with a large forward barrier.
Original qualitative free-energy profile with arbitrary values, not a measured transition-state landscape or a practical reaction-time prediction.

Read the visual model

Identify the labeled structures and units, then trace the arrows or compare values under the caption’s stated conditions. Separate the displayed evidence from a further inference. Write your reasoning before opening the guidance.

Does a negative reaction free-energy change imply a reaction will finish quickly at room temperature?

Visual reasoning — after your attempt

No. The activation pathway and other kinetic factors can make the change slow even when its direction is thermodynamically favored.

Thermodynamic favorability does not determine how quickly a process occurs. Activation barriers can make a favored reaction slow, and a catalyst can accelerate approach to equilibrium without changing ΔG° or K for the same temperature. State whether a conclusion concerns direction or timescale.

A calculated negative ΔG does not justify a claim of instant conversion or complete product recovery. Kinetics and equilibrium composition still matter.

Pause and explain

Does negative ΔG guarantee a fast process?

Check your reasoning after answering

No. It indicates thermodynamic direction under stated conditions, while rate depends on the kinetic pathway and barriers.

Apply the whole unit · Find a temperature-dependent sign change

Illustrative approximate values: ΔH=+40.0 kJ/mol and ΔS=+100 J/mol·K, treated as constant over the compared range. Compare 300 K and 500 K.

Your task

Calculate ΔG at both temperatures and the zero-crossing temperature, explain the competing terms, and state why the result is not a rate prediction or a universal standard-state/actual-state equivalence.

What your response should show

  • Choose the appropriate chemical model or relationship and state its conditions.
  • Show substitutions, units, particle or charge counts, and intermediate reasoning as relevant.
  • Use supplied evidence to justify the conclusion; distinguish observation from inference.
  • Identify a meaningful limitation, uncertainty, or next measurement.
Response guidance — after your attempt
  1. Convert ΔS to 0.100 kJ/mol·K.

  2. At 300 K: ΔG=40.0−300×0.100=+10.0 kJ/mol.

  3. At 500 K: ΔG=40.0−500×0.100=−10.0 kJ/mol.

  4. Zero crossing: T=ΔH/ΔS=400 K in the constant-value approximation.

The entropy term outweighs the positive enthalpy term above the modeled crossing. The calculation applies to the conditions associated with the supplied changes, with no guarantee they stay constant indefinitely. Standard-state values would describe ΔG° and actual composition adds another term. Neither sign establishes a reaction timescale.

Scientific references and source-model foundations

Parent / teacher teaching notes

Require Kelvin and an explicit J-to-kJ conversion. Ask direction, conditions, and rate as three separate questions. Ask the learner to explain each particle symbol, axis, unit and arrow before calculating. Distinguish hypothetical models and calculated curves from measured records. Public OpenSciEd excerpts here are selected foundation prompts, not complete high-school teacher editions or an endorsement. All required advanced explanations and practice are provided locally.

The key idea

Free energy connects enthalpy and entropy; kinetics determines how quickly change can occur.

Worked examples

Example 1

ΔH=+20kJ/mol, ΔS=+.100kJ/mol·K, T=300 K. Find ΔG.
  1. Use ΔG=ΔH−TΔS.
  2. 20−300(.100)=−10.
Answer: −10 kJ/mol; favored in this model

Example 2 · Worked application

Use ΔH=+10 kJ/mol and ΔS=+50 J/(mol·K) at 300 K to find ΔG.
  1. Convert entropy to 0.050 kJ/(mol·K).
  2. ΔG=ΔH−TΔS=10−300×0.050.
  3. Negative ΔG indicates thermodynamic favorability under the specified state, not rapid reaction.
Answer: ΔG=−5 kJ/mol.
Check the reasoning

Units and absolute temperature must match.

Example 3

ΔH=40kJ/mol and ΔS=.080kJ/mol·K. Find crossover.
  1. At ΔG=0, T=ΔH/ΔS.
  2. 40/.080.
Answer: 500 K, with the constant-value assumption.

Example 4 · Find and fix the mistake

Context: Use ΔH=+10 kJ/mol and ΔS=+50 J/(mol·K) at 300 K to find ΔG. A student claims: “A spontaneous reaction must happen instantly.” Evaluate the claim and write a corrected explanation.
  1. Test the claim against the stated conditions: Units and absolute temperature must match.
  2. Thermodynamic favorability says nothing by itself about kinetic speed; barriers can make favorable changes slow.
Answer: Thermodynamic favorability says nothing by itself about kinetic speed; barriers can make favorable changes slow.
Check the reasoning

Units and absolute temperature must match.

Example 5 · Reason from the visual model

Standard-state favorability and the actual mixture are differentStandard-state favorability and the actual mixture are differentΔG = ΔG° + RT ln QAt equilibrium: ΔG = 0 and Q = KΔG° = −RT ln KQ and K use compatible dimensionless activity conventions.
Original thermodynamic relationships; no logarithm of a dimensional raw concentration is intended.
Why can a reaction with negative ΔG° fail to proceed net forward from a very product-rich starting mixture?
  1. The standard reaction free energy ΔG° refers to a defined reference-state account. The actual driving tendency also depends on mixture composition through Q, the reaction quotient, using consistent dimensionless activities. At equilibrium Q=K and the reaction’s ΔG is zero. A negative ΔG° does not mean every possible starting mixture moves forward, because the RT ln Q contribution can change the actual sign. Concentration-only classroom expressions approximate activities and require an explicitly consistent convention.
  2. A sufficiently large Q can make RT ln Q positive enough to change the actual ΔG; the mixture composition matters.
Answer: A sufficiently large Q can make RT ln Q positive enough to change the actual ΔG; the mixture composition matters.
Check the reasoning

Original thermodynamic relationships; no logarithm of a dimensional raw concentration is intended.

Avoid these mistakes

Check your understanding

Distinguish favorable, fast, and complete.

Discuss the answer

Free energy addresses direction, activation barriers address rate, and equilibrium composition addresses extent.

Return to the phenomenon

Return to the initial case. Can a process absorb heat yet be thermodynamically favored? Revise your drawing or explanation using two named ideas and one stated limitation.

Compare explanations after your attempt

The free-energy balance can be negative despite positive enthalpy. This still needs the actual mixture conditions and a separate kinetic account.

What should we investigate next?

Which comparison would test a remaining uncertainty? State what you would change, keep comparable and measure.

Investigate, calculate and revise

Keep a first model and an evidence-supported revision. Attempt each task before opening guidance; all required explanations and supplied-data routes are available locally.

Activity 1 · Return to the opening case

Assigned reading and preparation

Use the opening phenomenon, unit definitions and explained Parts 1–4.

Your task

Return to the initial case. Can a process absorb heat yet be thermodynamically favored? Revise your drawing or explanation using two named ideas and one stated limitation.

Success criteria

  • Use the stated observations and appropriate units.
  • Connect a labeled model with the chemical mechanism.
  • State assumptions and an evidence limitation.
  • Explain a substantive revision or next test.
Hint

Keep species identity, material transfer and energy account distinct.

Response guidance — discuss after your attempt

The free-energy balance can be negative despite positive enthalpy. This still needs the actual mixture conditions and a separate kinetic account.

Activity 2 · Transfer to a changed case

Assigned reading and preparation

Cover the worked answer and use the explained models, relationships and notebook.

Your task

For a selected process use ΔH=+30.0 kJ/mol and ΔS=+0.150 kJ/(mol·K), treated constant. Find ΔG at 250 K, the modeled crossover temperature and one limit of the prediction.

Success criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.
Hint

Name known quantities and conditions, show intermediate steps and check conservation.

Response guidance — discuss after your attempt

At 250 K, ΔG=30.0−250(0.150)=−7.50 kJ/mol. The modeled crossover is 30.0/0.150=200 K. Actual ΔH/ΔS can vary with temperature and phases, and the calculation does not establish a rate.

Words to know

entropy
A measure related to accessible microscopic arrangements and energy dispersal.
Gibbs free energy
A thermodynamic potential useful for constant-temperature, constant-pressure processes.
spontaneous
Thermodynamically favored under stated conditions; not necessarily rapid.

In the real world

Use the chapter investigation to connect this unit to measured evidence and a practical decision.

Exit check

Distinguish favorable, fast, and complete.

Check your explanation after answering

Free energy addresses direction, activation barriers address rate, and equilibrium composition addresses extent.

Explain your reasoning without notes. If a key idea is missing, revisit the lesson and try again.

Problem 1

A chemical hand-warmer becomes hot once you activate it. Is the reaction inside exothermic or endothermic, and what is the sign of ΔH?
Answer and explanation

Exothermic; ΔH is negative

The pack releases heat into its surroundings (your hands), which is the definition of an exothermic reaction. An exothermic reaction loses energy, so its ΔH is negative.

Problem 2

How much heat (in J) is released when 150. g of water cools from 60.0°C to 40.0°C? (c = 4.18 J/g°C)
Answer and explanation

12,540 J (about 12.5 kJ) released

The water cools by ΔT = 60.0 − 40.0 = 20.0°C, so q = mcΔT = 150 × 4.18 × 20.0 = 12,540 J of heat released.

Problem 3

For a reaction, breaking all the reactant bonds absorbs 620 kJ and forming all the product bonds releases 790 kJ. Calculate ΔH and state whether the reaction is exothermic or endothermic.
Answer and explanation

ΔH = −170 kJ; exothermic

ΔH = (energy to break bonds) − (energy to form bonds) = 620 − 790 = −170 kJ. The negative sign means energy is released overall, so the reaction is exothermic.

Problem 4

Breaking costs 500kJ and forming releases 650kJ. Find modeled ΔH.
Answer and explanation

ΔH=500−650=−150kJ for the represented amount; exothermic. Average bond values are approximate.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 5

Chapter review: A selected reaction absorbs 720 kJ in the bond-breaking account and releases 880 kJ on product formation. Estimate net enthalpy, then predict the corresponding value when the entire equation is doubled.
Answer and explanation

ΔH≈720−880=−160 kJ for the selected equation amount. Doubling all coefficients gives approximately −320 kJ. Average bond energies are an approximate full-reaction estimate, not proof about spontaneity or rate.

ΔH≈720−880=−160 kJ for the selected equation amount. Doubling all coefficients gives approximately −320 kJ. Average bond energies are an approximate full-reaction estimate, not proof about spontaneity or rate.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 6

A reaction releases 3.00 kJ while .050 mol reacts. Find ΔH per mole.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

-60 kJ/mol

−3/.050 =−60.

Problem 7

How does neglected heat loss affect an exothermic cup estimate?
Answer and explanation

Less heat reaches the measured solution, so the estimated release magnitude is typically too small.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 8

Chapter review: A reaction heats 50.0 g water by 8.00°C. Use c=4.18 J/(g·°C), neglect apparatus/losses, and assume 0.0200 mol reacts. Estimate reaction heat and molar enthalpy on that basis.
Answer and explanation

qwater=50.0×4.18×8.00=1672 J. qreaction≈−1.672 kJ. Dividing by 0.0200 mol gives approximately −83.6 kJ/mol on the specified reacting-amount basis, subject to the neglected terms.

qwater=50.0×4.18×8.00=1672 J. qreaction≈−1.672 kJ. Dividing by 0.0200 mol gives approximately −83.6 kJ/mol on the specified reacting-amount basis, subject to the neglected terms.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

Problem 9

Why convert entropy units before calculating ΔG?
Answer and explanation

TΔS must have the same energy-per-mole units as ΔH.

Response criteria

  • State a scientifically accurate conclusion.
  • Show the calculation or mechanism that supports it.
  • Include units, conditions, or limits where relevant.

Problem 10

ΔH=30 kJ/mol, ΔS=.050 kJ/mol·K. Find crossover T.
Hints

Write the relationship first; substitute with consistent units.

Answer and explanation

600 K

30/.050=600.

Problem 11

Chapter review: For a selected process use ΔH=+30.0 kJ/mol and ΔS=+0.150 kJ/(mol·K), treated constant. Find ΔG at 250 K, the modeled crossover temperature and one limit of the prediction.
Answer and explanation

At 250 K, ΔG=30.0−250(0.150)=−7.50 kJ/mol. The modeled crossover is 30.0/0.150=200 K. Actual ΔH/ΔS can vary with temperature and phases, and the calculation does not establish a rate.

At 250 K, ΔG=30.0−250(0.150)=−7.50 kJ/mol. The modeled crossover is 30.0/0.150=200 K. Actual ΔH/ΔS can vary with temperature and phases, and the calculation does not establish a rate.

Response criteria

  • Use the stated measurements or conditions, with correct units.
  • Connect the result to the chemical mechanism or evidence relationship.
  • Identify the assumption, model limit or further evidence requested.

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