Physical Science: Chemistry — Final exam worked answers

Question 1 · 1 point

A 42.0 g sample occupies 15.0 mL. Find density.

Worked answer

2.8 g/mL

42.0/15.0 = 2.80.

1 point for the correct objective answer; no written-method marks for this item.

Question 2 · 3 points

A 50.0 g solid displaces 20.0 mL water. Find density and describe an accuracy check.

Worked answer

2.50 g/mL. Repeated readings test precision; reference comparisons address accuracy.

ρ=m/V=50.0/20.0. Check a calibrated balance or independent volume reference.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 3 · 3 points

Separate salt and sand while preserving both solids. Explain why filtration alone is insufficient.

Worked answer

Filtration removes sand particles; dissolved salt passes through with water.

Dissolve salt in water, filter and dry sand, then recover salt by safe evaporation.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 4 · 1 point

Rutherford's gold-foil experiment, in which a few alpha particles bounced sharply backward, was the direct evidence for which idea?

1. Electrons exist as probability clouds
2. Atoms are indivisible solid spheres
3. An atom's mass and positive charge are concentrated in a tiny nucleus
4. Electrons travel in fixed orbits

Worked answer

An atom's mass and positive charge are concentrated in a tiny nucleus

Most particles passed through (mostly empty space), but the rare sharp deflections showed a small, dense, positively charged nucleus.

1 point for the correct objective answer; no written-method marks for this item.

Question 5 · 3 points

Isotopes at 35 u and 37 u occur in 75% and 25% abundance. Find average mass.

Worked answer

35.5 u.

35(0.75)+37(0.25).

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 6 · 3 points

Compare 400 nm and 800 nm photon energies and explain atomic line spectra.

Worked answer

The 400 nm photon has twice the energy; lines reflect discrete allowed transitions.

E=hc/λ; halving wavelength doubles energy. Allowed atomic level differences select photon frequencies.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 7 · 1 point

Which type of element usually forms a cation by losing electrons?

1. a halogen
2. a metal
3. a nonmetal
4. a noble gas

Worked answer

a metal

Metals hold their few valence electrons loosely and lose them to become positive cations.

1 point for the correct objective answer; no written-method marks for this item.

Question 8 · 3 points

Write aluminum nitrate and count oxygen atoms in two formula units.

Worked answer

Al(NO₃)₃; 18 O atoms.

Al³⁺ balances three NO₃⁻; 2×3×3 oxygen atoms.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 9 · 3 points

Explain why CO₂ is nonpolar while water is polar.

Worked answer

CO₂ is linear with cancelling dipoles; bent water has a nonzero molecular dipole.

Use bond polarity and molecular geometry; compare vector dipole sums.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 10 · 1 point

Two or more simpler substances combine to form a single product, A + B → AB. What type of reaction is this?

1. synthesis
2. decomposition
3. single replacement
4. combustion

Worked answer

synthesis

Several substances combining into one product is the defining pattern of a synthesis (combination) reaction.

1 point for the correct objective answer; no written-method marks for this item.

Question 11 · 3 points

Find an empirical formula from 24 g C and 8 g H using C=12 and H=1 g/mol.

Worked answer

CH₄. Composition alone does not establish every structural detail.

Moles: C=2, H=8; divide both by 2.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 12 · 3 points

Write the net ionic equation when aqueous silver nitrate and sodium chloride produce solid AgCl.

Worked answer

Ag⁺(aq)+Cl⁻(aq)→AgCl(s).

Split aqueous strong electrolytes and cancel Na⁺ and NO₃⁻; check charge.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 13 · 1 point

In the balanced equation N₂ + 3H₂ → 2NH₃, what is the mole ratio of H₂ to NH₃?

1. 3 : 1
2. 3 : 2
3. 1 : 1
4. 2 : 3

Worked answer

3 : 2

The coefficients give H₂ : NH₃ = 3 : 2, read straight from the balanced equation.

1 point for the correct objective answer; no written-method marks for this item.

Question 14 · 3 points

N₂+3H₂→2NH₃ begins with 1 mol N₂ and 2 mol H₂. Find limiting reactant and maximum product.

Worked answer

H₂ limits; maximum 4/3 mol NH₃.

N₂ supports 2 mol product; H₂ supports 2×2/3 mol. Choose the smaller.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 15 · 3 points

What volume of 0.10 M NaOH neutralizes 25 mL of 0.20 M HCl in a supplied-data problem?

Worked answer

50 mL.

Acid amount=0.025×0.20=0.005 mol. The 1:1 ratio gives V=0.005/0.10 L.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 16 · 1 point

According to the kinetic molecular theory, the average kinetic energy of gas particles is directly proportional to the…

1. number of particles
2. Kelvin temperature
3. pressure of the gas
4. volume of the container

Worked answer

Kelvin temperature

A core assumption of KMT is that average kinetic energy is directly proportional to the absolute (Kelvin) temperature.

1 point for the correct objective answer; no written-method marks for this item.

Question 17 · 3 points

Find volume of 1 mol ideal gas at 2 atm and 300 K with R=0.0821 L·atm/(mol·K).

Worked answer

12.315 L, about 12.3 L.

V=nRT/P=24.63/2.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 18 · 3 points

Melt 10 g ice at 0°C and warm the liquid to 10°C. Use Lf=334 J/g and c=4.18 J/(g·°C).

Worked answer

3758 J. Phase change still absorbs energy during a temperature plateau.

Melting needs 3340 J; warming needs 418 J; add them.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 19 · 1 point

In a solution of sugar dissolved in water, which part is the solvent?

1. the sugar
2. the water
3. the sweetness
4. the glass

Worked answer

the water

The solvent does the dissolving and is present in the larger amount — here, the water.

1 point for the correct objective answer; no written-method marks for this item.

Question 20 · 3 points

Find molality for 0.20 mol sugar in 0.50 kg water and ideal freezing depression with i=1, Kf=1.86.

Worked answer

0.40 mol/kg and 0.744°C depression.

b=0.20/0.50=0.40; ΔTf=iKfb.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 21 · 3 points

Why can salt water conduct while a sugar solution conducts poorly?

Worked answer

Dissolved salt supplies mobile ions; neutral sugar molecules do not supply comparable ion amounts.

Identify which dissolved species can carry charge.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 22 · 1 point

An Arrhenius acid produces which ion when dissolved in water?

1. hydrogen ion, H⁺ (as H₃O⁺)
2. sodium ion, Na⁺
3. chloride ion, Cl⁻
4. hydroxide, OH⁻

Worked answer

hydrogen ion, H⁺ (as H₃O⁺)

Arrhenius acids release H⁺ ions, which combine with water to form hydronium, H₃O⁺.

1 point for the correct objective answer; no written-method marks for this item.

Question 23 · 3 points

A buffer has pKa=4.8 and equal conjugate acid/base amounts. Estimate pH and state a limitation.

Worked answer

About 4.8; sufficiently large additions exhaust buffer capacity.

pH≈pKa+log(1); both species must remain appreciable.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 24 · 3 points

Estimate pH for 0.010 M strong monoprotic acid at 25°C. Compare hydronium with pH 4.

Worked answer

pH 2; 100 times the hydronium concentration in the introductory approximation.

pH=−log(0.010)=2; factor=10^(4−2).

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 25 · 1 point

In an endothermic reaction, the sign of ΔH is…

1. negative
2. positive
3. always zero
4. impossible to determine

Worked answer

positive

An endothermic reaction absorbs energy into the system, so ΔH is positive.

1 point for the correct objective answer; no written-method marks for this item.

Question 26 · 3 points

A reaction warms 100 g water by 5°C. Use c=4.18 and neglect cup heat and losses. Find reaction heat.

Worked answer

−2.09 kJ.

Water gains 100×4.18×5=2090 J; reaction heat has opposite sign.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 27 · 3 points

For ΔH=+20 kJ/mol, ΔS=+0.100 kJ/(mol·K), T=300 K, find ΔG. Does it determine rate?

Worked answer

−10 kJ/mol; favored does not mean fast.

ΔG=20−300(0.100); rate also depends on activation pathway.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 28 · 1 point

For a reaction whose rate increases with this reactant’s concentration, which change usually speeds it up while other conditions stay fixed?

1. removing the catalyst
2. cooling the reactants
3. using large chunks instead of a fine powder
4. increasing the concentration of a reactant

Worked answer

increasing the concentration of a reactant

Increasing that reactant’s concentration can increase rate under the stated conditions. Concentration effects depend on the actual reaction and rate law; this is not a universal rule for every reaction.

1 point for the correct objective answer; no written-method marks for this item.

Question 29 · 3 points

For A⇌B, K=4 and current Q=0.5. Predict net direction and state the catalyst effect.

Worked answer

Net forward; equilibrium constant stays unchanged.

Q<K favors forward adjustment. A catalyst changes kinetics, not K at fixed temperature.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 30 · 3 points

Concentration falls from 0.80 to 0.20 M in 30 s. Find average disappearance rate.

Worked answer

0.020 M/s.

Use (0.80−0.20)/30 with a positive disappearance-magnitude convention.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 31 · 1 point

Find nitrogen oxidation number in NO₃⁻ with O=−2.

Worked answer

5

x−6=−1, x=+5.

1 point for the correct objective answer; no written-method marks for this item.

Question 32 · 3 points

Cathode and anode reduction potentials are +0.34 and −0.76 V. Find standard cell voltage and external electron direction.

Worked answer

1.10 V; electrons travel from anode to cathode through the wire.

E°cell=0.34−(−0.76); oxidation supplies electrons at the anode.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 33 · 3 points

A 96 g parent isotope has half-life 5 years. Find parent after 15 years and state alpha-decay count changes.

Worked answer

12 g parent; daughter mass number decreases 4 and atomic number decreases 2.

Three half-lives leave 96/8 g; alpha carries A=4 and Z=2.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 34 · 1 point

How many H atoms are in acyclic alkane C₆H…?

Worked answer

14 H atoms

2×6+2=14.

1 point for the correct objective answer; no written-method marks for this item.

Question 35 · 3 points

Give the formula of a five-carbon acyclic alkane. Explain how ethanol and dimethyl ether can share a formula but differ in properties.

Worked answer

C₅H₁₂; ethanol has an O–H donor while the ether does not.

CnH₂n+₂ gives C₅H₁₂; different connectivity changes functional groups and intermolecular interactions.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.

Question 36 · 3 points

Reusable production impact is 120 units plus 1/use; disposable is 5/use. Find break-even and two model limits.

Worked answer

Equal at 30 uses; reusable lower afterward under the assumptions.

Solve 120+n=5n; assess lifespan and washing/end-of-life boundary.

Marking criteria

• 1 point: select a valid relationship, mechanism, or model.
• 1 point: show correct calculation or evidence-based reasoning.
• 1 point: give a correct conclusion with units and stated conditions.