Long Free-Response Practice长题综合训练

~50 min

Learning goals

  • Finish a 10-point long FRQ in about 22 minutes, budgeting time across its parts
  • Understand how long questions are built, with one scenario, several units and links between parts
  • Score your work against the scoring points and find where points were lost

Before you start

  • Time management (4.1.3)
  • How to read scoring guidelines (4.3.1)
  • Showing work on calculations (4.3.2)

What a long question looks like

The first three questions of Section II are long questions worth 10 points each. A long question usually centers on one scenario (a reaction or an experiment) and splits into seven or eight parts that span several units: equations and stoichiometry, gases, thermochemistry, equilibrium, structure, and so on. It often opens with a data table that later parts draw on, and results from early parts are often needed later.

Five steps for a long question

  1. Read it all (1–2 minutes). Read every part, circle the data and units, and work out what each part asks for.
  2. Answer part by part, labeled (a), (b), …, each in its own space.
  3. If stuck, skip ahead or carry on with an assumed value, stating it: “Assume the answer to (c) is ….”
  4. Write every calculation in four lines (4.3.2): equation, substitution with units, result, answer to the question.
  5. Keep 1–2 minutes to check units, signs, significant figures, and whether every part was actually answered.

Splitting by points gives about 22 minutes per long question and 9 per short one (4.1.3). Use the timer below for timed practice:

FRQ timer: give each question a time limit by points
22:00

Example: a complete long question

Propane, C₃H₈, is a common fuel. Standard enthalpies of formation at 25 °C (OpenStax Appendix G):

SubstanceΔfH° (kJ/mol)
C₃H₈(g)−103.8
O₂(g)0
CO₂(g)−393.51
H₂O(l)−285.83

(a) Write the balanced equation for the complete combustion of propane (forming liquid water).

(b) Use the table to calculate ΔH° for this reaction.

(c) A student burns 0.250 g of propane under a can holding 400.0 g of water, and the water warms by 6.10 °C (specific heat of water 4.18 J/(g·°C)). Calculate the heat absorbed by the water.

(d) From (c), calculate the heat released per mole of propane and write the experimental ΔH.

(e) How does the experimental value compare with (b)? Give one reason.

(f) Calculate the volume of O₂ at 25 °C and 1.00 atm needed to burn 0.250 g of propane.

(g) Draw the Lewis structure of CO₂ and state the molecule’s shape and polarity.

Try it yourself first with a 22-minute timer, then step through the solution:

Step-by-step solution
  1. (a) (1 point) Balance the equation. Balance C and H first, then O:

    CX3HX8(g)+5 OX2(g)→3 COX2(g)+4 HX2O(l)\begin{aligned} &\ce{C3H8(g) + 5O2(g)} \\ &\quad \ce{-> 3CO2(g) + 4H2O(l)} \end{aligned}
  2. (b) (2 points: 1 for the setup, 1 for the value and sign) ΔH° from enthalpies of formation.

    ΔH∘=[3(−393.51)+4(−285.83)]−[(−103.8)+5(0)]=−2323.85+103.8=−2220.1 kJ/mol\begin{aligned} \Delta H^\circ &= [3(-393.51) + 4(-285.83)] \\ &\quad - [(-103.8) + 5(0)] \\ &= -2323.85 + 103.8 \\ &= \boxed{-2220.1\ \text{kJ/mol}} \end{aligned}
  3. (c) (1 point) Heat absorbed by the water.

    q=mcΔT=(400.0)(4.18)(6.10)=1.02×104 J=10.2 kJ\begin{aligned} q &= mc\Delta T = (400.0)(4.18)(6.10) \\ &= 1.02 \times 10^{4}\ \text{J} = 10.2\ \text{kJ} \end{aligned}
  4. (d) (2 points: 1 for the moles, 1 for ΔH with its negative sign) ΔH per mole.

    n(CX3HX8)=0.25044.10=5.67×10−3 molΔH=−10.2 kJ5.67×10−3 mol=−1.80×103 kJ/mol\begin{aligned} n(\ce{C3H8}) &= \frac{0.250}{44.10} = 5.67 \times 10^{-3}\ \text{mol} \\ \Delta H &= -\frac{10.2\ \text{kJ}}{5.67 \times 10^{-3}\ \text{mol}} \\ &= \boxed{-1.80 \times 10^{3}\ \text{kJ/mol}} \end{aligned}

    Combustion releases heat, and the water’s heat comes from the reaction, so ΔH is negative.

  5. (e) (1 point) Compare and give a reason. The experimental magnitude is only 1800 ÷ 2220 ≈ 81% of the theoretical value. Reasons include: some heat escapes to the air or warms the can instead of the water; or combustion is incomplete (forming CO or soot), releasing less heat.

  6. (f) (2 points: 1 for moles of O₂, 1 for the volume) Volume of O₂. From the equation, n(O₂) = 5 n(C₃H₈):

    n(OX2)=5×5.669×10−3=0.02834 molV=nRTP=(0.02834)(0.08206)(298.15)1.00=0.693 L\begin{aligned} n(\ce{O2}) &= 5 \times 5.669 \times 10^{-3} = 0.02834\ \text{mol} \\ V &= \frac{nRT}{P} = \frac{(0.02834)(0.08206)(298.15)}{1.00} \\ &= \boxed{0.693\ \text{L}} \end{aligned}
  7. (g) (1 point) Structure of CO₂. O=C=O, with a double bond from C to each O and two lone pairs on each O; C has two electron domains, so the molecule is linear (180°). The two C=O bond dipoles are equal and opposite and cancel, so CO₂ is nonpolar.

Practice: on a long question, what’s the best move in each situation?
  1. Part (c) needs your answer to (b), which you’ve already found
  2. Part (d) needs your answer to (c), and (c) has had you stuck for 5 minutes
  3. Part (e) is an explanation you know
  4. Part (b) needs an enthalpy of formation you can’t find for a moment
  5. You’ve spent 25 minutes on this long question, with two parts left
  6. Part (a) only asks for a balanced equation
  7. Part (f) needs a method you have no idea about
  8. You calculated a molar mass of 0.08 g/mol, which is clearly unreasonable

Common mistakes

Mistake 1: “A long question has to be done straight from (a) to the end.” The parts are linked, but many can be done on their own. Skip a part you’re stuck on, or carry on with an assumed value, instead of letting one part hold up the whole question.

Mistake 2: “The parts are independent, so there’s no need to read the whole question first.” Later parts often use earlier results and the data at the top. Reading it all first tells you that (b)’s result will be needed in (d), so you’ll keep an extra digit.

Mistake 3: “When I’ve finished, I’m done; no need to check.” One or two minutes checking units, signs and significant figures often recovers a point or two; writing a positive ΔH for an exothermic reaction, for example, costs a point.

Quick check

How many points is one long Section II question worth?

Splitting time by points, about how long does one long question get?

When first reading a long question, what matters most?

In the example, the experimental |ΔH| is smaller than the theoretical value. What is the most likely reason?

Part (d) needs your answer to (c); you wrote “Assume (c) is 10.0 kJ” and carried on. How is (d) usually scored?

Which of these is NOT on the final checklist for a long question?

AP-style practice

AP-style free response

A key step in making sulfuric acid by the contact process is 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), run industrially at about 700 K with a V₂O₅ catalyst. Data at 25 °C, with ΔfH° in kJ/mol and S° in J/(mol·K) (OpenStax Appendix G):

SubstanceΔfH°S°
SO₂(g)−296.83248.2
O₂(g)0205.2
SO₃(g)−395.72256.76

(a) Calculate ΔH° for the reaction.

(b) Predict the sign of ΔS° with a reason, then calculate ΔS°.

(c) Calculate ΔG° and the equilibrium constant K at 25 °C.

(d) Assuming ΔH° and ΔS° don’t change with temperature, estimate the temperature above which the reaction becomes unfavorable under standard conditions.

(e) K is enormous at 25 °C. Why is the industrial process run at about 700 K, and why is a catalyst used?

(f) At constant temperature, the reaction vessel is compressed to half its volume. Use the relationship between Q and K to predict which way the equilibrium shifts.

Model answer and scoring

(a) ΔH° = 2(−395.72) − [2(−296.83) + 0] = −791.44 + 593.66 = −197.8 kJ/mol rxn. (1 point)

(b) Negative: 3 mol of gaseous reactants become 2 mol of gaseous product, so there are fewer gas molecules and less dispersal. ΔS° = 2(256.76) − [2(248.2) + 205.2] = 513.52 − 701.6 = −188.1 J/(mol·K). (2 points: 1 for the sign and reason, 1 for the calculation)

(c) ΔG° = ΔH° − TΔS° = −197.8 − 298.15 × (−0.1881) = −141.7 kJ/mol; ln K = −ΔG°/(RT) = 141,700 ÷ (8.314 × 298.15) = 57.2, so K ≈ 7 × 10²⁴. (2 points)

(d) ΔG° = 0 when T = ΔH°/ΔS° = (−197,800 J) ÷ (−188.1 J/K) ≈ 1.05 × 10³ K. Above about 1050 K, ΔG° > 0 and the reaction is unfavorable under standard conditions. (1 point)

(e) At 25 °C the reaction is very favorable thermodynamically but has a high activation energy, so it is extremely slow (kinetic control). Heating to about 700 K speeds it up, and 700 K is still below 1050 K, so K is still greater than 1. The V₂O₅ catalyst lowers the activation energy so the reaction is fast enough at this temperature; a catalyst speeds up the forward and reverse reactions equally and doesn’t change K. (2 points)

(f) Halving the volume doubles every partial pressure, so Q = P(SO₃)² ÷ [P(SO₂)² × P(O₂)] becomes 2² ÷ (2² × 2) = 1/2 of its value. Then Q < K, so the reaction proceeds forward, forming more SO₃ (toward fewer gas molecules). (2 points)

Scoring (10 points): (a) 1; (b) 2; (c) 2; (d) 1; (e) 2; (f) 2.

Summary

  • A long question: one scenario, seven or eight parts across several units, with parts often linked; about 22 minutes each.
  • Five steps: read it all and circle the data → answer each labeled part → skip or assume a value when stuck → four-line calculations → keep 1–2 minutes to check.
  • Afterward, score yourself point by point against the scoring points and note why each point was lost.

AP tip: Before the exam, do at least one complete timed long question a week (a released question or this site’s mock exam) and score it against the guidelines right away. After a few weeks, 22 minutes will start to feel like enough.

Sources: ΔfH° and S° from OpenStax Chemistry 2e Appendix G.

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