2024 AP Chemistry Free-Response Questions

Directions: Questions 1–3 are long free-response questions that require about 23 minutes each to answer and are worth 10 points each. Questions 4–7 are short free-response questions that require about 9 minutes each to answer and are worth 4 points each. For each question, show your work for each part in the space provided after that part. Examples and equations may be included in your responses where appropriate. For calculations, clearly show the method used and the steps involved in arriving at your answers. You must show your work to receive credit for your answer. Pay attention to significant figures. C₃H₆O₃(aq) + NaOH(aq) → NaC₃H₅O₃(aq) + H₂O(l) 1. A student is studying the reaction between lactic acid, C₃H₆O₃, and sodium hydroxide, NaOH, as represented in the balanced equation above. (a) The structural formula of lactic acid is shown in the following diagram. Circle the hydrogen atom that most readily participates in the chemical reaction with sodium hydroxide. Structural formula diagram: H₃C–C(H)(OH)–C(=O)–O–H. (b) The student begins the experiment by dissolving 10.22 g of sodium hydroxide (molar mass 40.00 g/mol) in enough water to produce 500. mL of solution. Calculate the molarity of the sodium hydroxide solution. The student uses the sodium hydroxide solution from part (b), a buret, a pH meter, and a 100 mL Erlenmeyer flask to titrate a 25.0 mL sample of lactic acid solution. The student’s data are shown in the following graph. (c) Use the information in the graph to determine the approximate pKₐ of lactic acid. (d) The preceding diagram represents the relative amounts of major species in a sample of the solution in the flask at one point during the titration. (Note that water molecules are omitted.) Species diagram legend: ● = Na⁺; ○–● = C₃H₆O₃; ● = C₃H₅O₃⁻. [The diagram shows two Na⁺ ions, two C₃H₆O₃ molecules, and four C₃H₅O₃⁻ ions.] (i) Draw an X on the preceding titration curve at a point in the titration where the reaction mixture would be represented by this diagram. (ii) Justify your answer. (iii) The student repeats the experiment but uses a solution of NaOH(aq) with twice the concentration, as shown in the preceding table. On the following graph, draw the titration curve that would be expected for experiment 2. | Experiment | Mass of NaOH(s) (grams) | Volume of Solution (mL) | Titration Curve | | 1 | 10.22 | 500. | Already shown on graph | | 2 | 20.44 | 500. | ? | (e) In a third experiment, the student investigates the enthalpy of the reaction between lactic acid and sodium hydroxide. The student combines 100.0 mL of a 0.500 M lactic acid solution at 20.0°C with 100.0 mL of a 0.500 M NaOH solution at 20.0°C in a calorimeter. The final temperature of the resulting combined solution is 23.2°C. Assume that the density of each solution before combining is 1.00 g/mL and that the specific heat capacity of the combined solution is 4.2 J/(g · °C). (i) Calculate the quantity of heat produced in the reaction, in J. (ii) Calculate the molar enthalpy of reaction, in kJ/mol₍rxn₎. Include the sign in your answer. (iii) The student claims that if heat is lost from the calorimeter to the surrounding air during the reaction, then the experimental value of the molar enthalpy of reaction will be smaller in magnitude than the actual value. Do you agree or disagree with the student’s claim? Justify your answer.

2. A chemical reaction between maleic acid (H₂C₄H₂O₄) and sodium bicarbonate (NaHCO₃) occurs in the presence of water to produce carbon dioxide and sodium maleate (Na₂C₄H₂O₄), as represented by the following equation. H₂C₄H₂O₄(aq) + 2 NaHCO₃(aq) → 2 CO₂(g) + 2 H₂O(l) + Na₂C₄H₂O₄(aq) (a) A student combines equal masses of H₂C₄H₂O₄(s) chunks and NaHCO₃(s) chunks with sufficient water at 20.0°C. The student determines that 0.0114 mol of CO₂(g) is produced after the reaction goes to completion. (i) Calculate the number of grams of CO₂(g) produced. (ii) The CO₂(g) produced from the reaction at 20.0°C was collected and found to have a pressure of 1.25 atm. Calculate the volume of CO₂(g), in liters. (b) The student performs a second experiment that is identical to the first except that the student grinds the chunks of H₂C₄H₂O₄(s) and NaHCO₃(s) into powder before combining the powder with water. (i) What happens to the surface area of the reactants when the student grinds the chunks into powder? (ii) The rate-determining step for the overall reaction is the dissolving of the solids. Would the time required for the dissolving of the solids in the second experiment be longer than, shorter than, or the same as the time required in the first experiment? Justify your answer based on the collisions between particles. (iii) When the reaction is complete, will the volume of CO₂(g) at the end of the second experiment be greater than, less than, or equal to the volume at the end of the first experiment? Justify your answer. The student conducts additional trials of the experiment and produces the following data table. | Trial | Mass of H₂C₄H₂O₄ (grams) | Mass of NaHCO₃ (grams) | Moles of CO₂ Produced (mol) | |---|---:|---:|---:| | 3 | 1.543 | 1.251 | 0.01489 | | 4 | 1.543 | 1.686 | 0.02007 | (c) Based on the student’s data, identify the limiting reactant in trial 3. Justify your answer. (d) The reaction has a value of ΔS° greater than zero. Using particle-level reasoning, explain why the entropy increases as the reaction progresses. The student notices that the temperature of the reaction mixture decreases as the reaction takes place and correctly determines that the reaction is endothermic. (e) The student claims that the reaction is thermodynamically favorable at all temperatures because ΔS°rxn > 0 and the reaction is endothermic. Do you agree or disagree with the student’s claim? Justify your answer. Next, the student investigates the acid-base behavior of maleic acid. The student notes that maleic acid is a diprotic acid. The two acid dissociation processes that occur are represented by the following equations. H₂C₄H₂O₄ + H₂O ⇌ HC₄H₂O₄⁻ + H₃O⁺ Kₐ₁ = 1.5 × 10⁻² HC₄H₂O₄⁻ + H₂O ⇌ C₄H₂O₄²⁻ + H₃O⁺ Kₐ₂ = 8.5 × 10⁻⁷ (f) Calculate the pKₐ₂ value for the HC₄H₂O₄⁻ ion. (g) A buffer solution with a pH of 7.00 is prepared using C₄H₂O₄²⁻ and HC₄H₂O₄⁻. Calculate the ratio [C₄H₂O₄²⁻]/[HC₄H₂O₄⁻] in this solution.

3. Sterling silver is an alloy that is commonly used to make jewelry and consists of 92.5% silver and 7.5% other metals, such as copper, by mass. Over time, the alloy can form a tarnish of Ag₂S(s) when it reacts with hydrogen sulfide, as represented by the following equation. 2 Ag(s) + H₂S(g) → Ag₂S(s) + H₂(g) (a) What are the oxidation numbers of silver in Ag(s) and Ag₂S(s)? Ag(s) ________ Ag₂S(s) ________ (b) The following table contains the atomic radii for silver and copper. | Element | Silver (Ag) | Copper (Cu) | |---|---:|---:| | Atomic radius (pm) | 165 | 145 | (i) Explain why sterling silver is better classified as a substitutional alloy than as an interstitial alloy. (ii) Using principles of atomic structure and Coulomb’s law, explain why silver has a larger atomic radius than copper does. The Ag₂S tarnish on sterling silver can be removed until only sterling silver remains. A student weighs a tarnished sterling silver sample both before and after removing the Ag₂S(s) (molar mass 247.80 g/mol) and records the data in the following table. | | Before Tarnish Removal | After Tarnish Removal | |---|---:|---:| | Mass | 409.21 g | 398.94 g | (c) Assuming that only Ag₂S(s) is removed, calculate the number of moles of silver atoms removed. Rhodium plating is a process used to protect sterling silver from tarnishing. This involves electroplating (depositing) solid rhodium, Rh(s), onto the surface of the metal from an acidified solution of Rh₂(SO₄)₃(aq). Oxygen gas is produced during this process. (d) A table of half-reactions related to the overall reaction is provided. | Half-Reaction | E° (V) | |---|---:| | Rh³⁺(aq) + 3 e⁻ → Rh(s) | +0.80 | | O₂(g) + 4 H⁺(aq) + 4 e⁻ → 2 H₂O(l) | +1.23 | (i) Write the balanced net ionic equation for plating Rh(s) from the acidified Rh₂(SO₄)₃(aq) solution. (ii) Calculate the value of E°cell for the reaction in part (d)(i). (iii) Based on your answer to part (d)(ii), explain why this process requires the use of an external power source. (e) Calculate the length of time, in seconds, required to plate 2.8 g of Rh(s) onto a piece of sterling silver if 2.0 C/s of current is applied.

Begin your response to QUESTION 4 on this page. 4. A student performs an experiment to determine the specific heat capacity of a metal. The student places a cube of the metal in boiling water so its temperature will be 100.0°C. The student then places the metal cube into a calorimeter that contains water and records the highest temperature of the water. A data table and a diagram of the thermometer at the highest temperature are shown. Data table: Mass of metal cube — 98.1 g Mass of water — 52.0 g Initial temperature of metal cube — 100.0°C Initial temperature of water — 25.0°C Highest temperature of water — ? (a) What should the student report as the highest temperature of the water? ________ (b) A particle-level representation of water molecules in the calorimeter before and after the metal cube was added is shown. The length of the arrows in the Before diagram represents the speed of the water molecules in the system. In the After diagram, draw an arrow for each molecule to indicate how the speed of each of the molecules changes after the metal cube is added. The diagrams are labeled “Before” and “After.” The Before diagram shows three water-molecule dots with arrows of different lengths; the After diagram shows three water-molecule dots without arrows.

5. Hydrogen gas and iodine gas react to form hydrogen iodide at an elevated temperature, as represented by the following equation. H₂(g) + I₂(g) ⇌ 2 HI(g)  ΔH_rxn = −12.19 kJ/mol_rxn (a) Write the expression for the equilibrium constant, Kc, for this reaction. (b) H₂(g) and I₂(g) are added to a previously evacuated container and allowed to react. (i) At a certain time, the value of the reaction quotient, Q, is 0.67. The following particle diagram is an incomplete representation of the system at this time. The diagram shows the relative number of H₂(g) and I₂(g) molecules, but the HI(g) molecules are not included. Draw the number of HI(g) molecules needed to complete the diagram so that it accurately represents the system. [Particle diagram: a container showing three H₂ molecule pairs and two I₂ molecule pairs. Legend: an unshaded circle represents an H atom; a shaded circle represents an I atom.] (ii) A student monitors the number of moles of HI(g) over time. Hypothesize an experimental change that could have been applied to the system in the rigid container at time t to result in the change in the number of moles of HI(g) shown in the graph. Assume that the student did not add more HI(g) to the system. [Graph: moles of HI(g) versus time. The curve rises to an equilibrium plateau, remains constant until time t, then rises to a higher plateau.] (iii) After equilibrium is established, the mixture is transferred to a larger container at constant temperature. As a result, would the number of moles of HI(g) increase, decrease, or remain the same? Justify your answer.

6. At elevated temperatures, NO₂ undergoes decomposition in the gas phase, forming NO and O₂ as represented by the following equation. 2 NO₂ → 2 NO + O₂ A scientist measures the change in [NO₂] over the first 100. s of the reaction at 546°C. The scientist uses the data collected from the experiment to generate the following two graphs. The first graph plots ln[NO₂] versus time (seconds), with plotted values approximately (0, −8.6), (20, −9.15), (40, −9.5), (60, −9.75), (80, −9.98), and (100, −10.1). The second graph plots 1/[NO₂] versus time (seconds), with plotted values approximately (0, 5,000), (20, 9,000), (40, 13,500), (60, 17,000), (80, 21,000), and (100, 25,000). Based on these data, the scientist makes the claim that the rate law for the reaction is rate = k[NO₂]². (a) Explain how the graphs indicate that the reaction is second order with respect to NO₂. (b) At a certain point in the reaction, the rate of disappearance of NO₂ is determined to be 6.52 × 10⁻⁷ M/s. Determine the rate of appearance, in M/s, of O₂ at this same point in the reaction. (c) NO₂ is a molecule that contains an odd number of electrons and can be oxidized to form the NO₂⁺ ion. In NO₂, the unpaired electron is presumed to be localized on the nitrogen atom, as shown in the Lewis diagram in the box on the left. [Left Lewis diagram: O=N−O, with the unpaired electron on nitrogen and lone-pair electrons shown on the oxygen atoms.] [Right box: [ O N O ]⁺] (i) In the box on the right, complete the Lewis diagram for NO₂⁺. Be sure to show all bonding and nonbonding electrons. (ii) A student makes the claim that the bond angles in NO₂ and NO₂⁺ are different from each other. Do you agree or disagree with the student’s claim? Justify your answer.

7. A student conducts a chromatography experiment and needs to prepare 100.0 mL of 0.340 M NaCl(aq) to use as the solvent. (a) Calculate the mass of solid NaCl (molar mass 58.44 g/mol) needed to prepare the 100.0 mL of 0.340 M NaCl(aq). (b) In the following table, briefly list the additional steps necessary to prepare the 100.0 mL of 0.340 M NaCl(aq) solution using only materials selected from the choices given. Assume that all appropriate safety measures are already in place. Not all materials in the list may be needed. Choices: • Solid NaCl • Distilled water • Weighing paper and scoop • Balance • 100.0 mL volumetric flask • 50.0 mL graduated cylinder • Pipet • 150 mL beakers • Chromatography paper Table: Step | Step Description and Materials Used 1. | Use the weighing paper and scoop to measure the correct mass of solid NaCl on the balance. 2. | 3. | Swirl the mixture to dissolve the solid NaCl. 4. | 5. | Stopper and invert the mixture several times to ensure that the mixture is homogeneous. The student uses the NaCl(aq) solvent to separate a mixture of compounds X and Y in a chromatography experiment. After 30 minutes, the student removes the chromatography paper from the chamber. The results of the experiment are shown. Diagram labels: Solvent Front; Compound Y; Compound X; Start Line. The diagram shows Compound Y above Compound X, with both compounds between the Start Line and Solvent Front. (c) A second student conducts the same chromatography experiment but removes the chromatography paper from the chamber after 15 minutes instead of 30 minutes. Predict the effect, if any, this would have on the separation distance between compounds X and Y in the new experiment. Explain your reasoning.