2024 Free Response

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 (Lewis) formula of lactic acid: a chain H—C—C—C(=O)—O—H, drawn as: Top row: H, H, O(double bond) The first carbon bears an H above, an H below, and a bond to the second carbon. The second carbon bears an OH group below it (O bonded down to an H). The third carbon is a carbonyl carbon (C=O, double bond to O above) bonded to an —O—H (single-bonded hydroxyl oxygen then H) on the right. Full skeleton:

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. The student's data are shown in the following graph.

[Graph: titration curve of pH vs. Volume of NaOH(aq) Added (mL); x-axis 0 to 34 mL in increments of 2, y-axis pH 0 to 14 in increments of 2. Curve starts near pH 2-3 at V=0, rises slowly/gradually (buffer region) from about V=2 to V=14, then shows a steep equivalence-point jump between about V=15 and V=17 (pH rising sharply from about 4 to about 11-12), then levels off and rises slowly to about pH 13 by V=34.]

Use the information in the graph to determine the approximate p$K_a$ of lactic acid. ___________

[Particle diagram box showing the relative amounts of major species in a sample of the solution in the flask at one point during the titration. Water molecules are omitted. Key: solid black circle = $\text{Na}^+$; circle half-white/half-gray (with a small white circle attached) = $\text{C}_3\text{H}_6\text{O}_3$; circle half-black/half-gray (with a small white circle attached) = $\text{C}_3\text{H}_5\text{O}_3^-$. The box contains 2 large gray/white two-tone circles (labeled as $\text{C}_3\text{H}_6\text{O}_3$-type), 2 large gray/black two-tone circles (labeled as $\text{C}_3\text{H}_5\text{O}_3^-$-type), and 2 small solid black circles ($\text{Na}^+$), with small white circles attached to some of the larger circles.]

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.)

Draw an X on the preceding titration curve at a point in the titration where the reaction mixture would be represented by this diagram.

Justify your answer.

The following table shows two experiments:

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.

[Blank graph titled "Experiment 1" with a faint curve of Experiment 1 shown as reference (pH vs. Volume of NaOH(aq) Added (mL), x-axis 0 to 34 mL, y-axis pH 0 to 14); student draws the Experiment 2 curve on the same axes.]

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 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).

Calculate the quantity of heat produced in the reaction, in J.

Calculate the molar enthalpy of reaction, in kJ/mol$_{rxn}$. Include the sign in your answer.

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.

A student combines equal masses of $\text{H}_2\text{C}_4\text{H}_2\text{O}_4(s)$ chunks and $\text{NaHCO}_3(s)$ chunks with sufficient water at 20.0°C. The student determines that 0.0114 mol of $\text{CO}_2(g)$ is produced after the reaction goes to completion.

Calculate the number of grams of $\text{CO}_2(g)$ produced.

The $\text{CO}_2(g)$ produced from the reaction at 20.0°C was collected and found to have a pressure of 1.25 atm. Calculate the volume of $\text{CO}_2(g)$, in liters.

The student performs a second experiment that is identical to the first except that the student grinds the chunks of $\text{H}_2\text{C}_4\text{H}_2\text{O}_4(s)$ and $\text{NaHCO}_3(s)$ into powder before combining the powder with water.

What happens to the surface area of the reactants when the student grinds the chunks into powder?

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.

When the reaction is complete, will the volume of $\text{CO}_2(g)$ 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.

Based on the student's data, identify the limiting reactant in trial 3. Justify your answer.

The reaction has a value of $\Delta S^\circ$ 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.

The student claims that the reaction is thermodynamically favorable at all temperatures because $\Delta S^\circ_{rxn} > 0$ 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.

Calculate the p$K_{a_2}$ value for the $\text{HC}_4\text{H}_2\text{O}_4^-$ ion.

A buffer solution with a pH of 7.00 is prepared using $\text{C}_4\text{H}_2\text{O}_4^{2-}$ and $\text{HC}_4\text{H}_2\text{O}_4^-$. Calculate the ratio

in this solution.

What are the oxidation numbers of silver in $\text{Ag}(s)$ and $\text{Ag}_2\text{S}(s)$?

$\text{Ag}(s)$__________ $\text{Ag}_2\text{S}(s)$__________

The following table contains the atomic radii for silver and copper.

Explain why sterling silver is better classified as a substitutional alloy than as an interstitial alloy.

Using principles of atomic structure and Coulomb's law, explain why silver has a larger atomic radius than copper does.

The $\text{Ag}_2\text{S}$ 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 $\text{Ag}_2\text{S}(s)$ (molar mass 247.80 g/mol) and records the data in the following table.

Assuming that only $\text{Ag}_2\text{S}(s)$ 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, $\text{Rh}(s)$, onto the surface of the metal from an acidified solution of $\text{Rh}_2(\text{SO}_4)_3(aq)$. Oxygen gas is produced during this process.

A table of half-reactions related to the overall reaction is provided.

Write the balanced net ionic equation for plating $\text{Rh}(s)$ from the acidified $\text{Rh}_2(\text{SO}_4)_3(aq)$ solution.

Calculate the value of $E^\circ_{cell}$ for the reaction in part (d)(i).

Based on your answer to part (d)(ii), explain why this process requires the use of an external power source.

Calculate the length of time, in seconds, required to plate 2.8 g of $\text{Rh}(s)$ onto a piece of sterling silver if 2.0 C/s of current is applied.

What should the student report as the highest temperature of the water? ___________

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.

[Two circular "particle diagram" boxes side by side, each drawn as a beaker/pot shape with a magnifying circle showing 3 dots (water molecules) inside. "Before" box: 3 dots, each with an arrow attached showing velocity — one dot has a short leftward arrow, one dot has a short arrow pointing down-left, one dot has a longer arrow pointing up-right (varying arrow lengths representing different molecular speeds). "After" box: the same 3 dots shown with no arrows drawn yet — student is to add arrows on each dot to indicate the (expected higher/more uniform) speed after the metal cube is added.]

Assuming the metal transfers 2940 J of thermal energy to the water, calculate the specific heat of the metal in J/(g·°C).

In a second experiment, 2940 J of thermal energy is transferred from 98.1 g of aluminum, which has a specific heat capacity of 0.897 J/(g·°C). Explain how the magnitude of the temperature change of the aluminum, $\Delta T_{Al}$, compares with the magnitude of the temperature change of the metal in the original experiment.

Write the expression for the equilibrium constant, $K_c$, for this reaction.

$\text{H}_2(g)$ and $\text{I}_2(g)$ are added to a previously evacuated container and allowed to react.

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 $\text{H}_2(g)$ and $\text{I}_2(g)$ molecules, but the $\text{HI}(g)$ molecules are not included. Draw the number of $\text{HI}(g)$ molecules needed to complete the diagram so that it accurately represents the system.

[Rectangular particle-diagram box containing: 2 pairs of bonded circles representing $\text{I}_2$ molecules — one pair (2 gray/shaded circles bonded together) upper-left, one pair (2 white/open circles bonded together) upper-right; 2 pairs of bonded circles representing $\text{H}_2$ molecules — one pair (2 small white circles bonded) center, one pair (2 gray circles bonded) lower-middle-right, one more pair (2 small white circles bonded) lower-left. A legend to the right of the box: open/white circle = H atom, gray/shaded circle = I atom. Molecule counts shown: 2 $\text{I}_2$ molecules (one gray-gray pair, one white-white pair — actually representing $\text{I}_2$ and possibly another diatomic), plus H2-type pairs — the diagram shows a total of 3 diatomic pairs that are H-containing and 2 that are I-containing among the 5 total pairs drawn, matching an $\text{H}_2$: $\text{I}_2$ ratio consistent with $Q = 0.67$. Student must add the correct number of HI molecules (single white-gray bonded pairs) to complete the diagram.]

A student monitors the number of moles of $\text{HI}(g)$ 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 $\text{HI}(g)$ shown in the graph. Assume that the student did not add more $\text{HI}(g)$ to the system.

[Graph: y-axis "Moles of HI(g)" (unlabeled scale), x-axis "Time"; curve rises steeply from the origin, levels off into a plateau, then at a dashed vertical line marked $t$ the curve jumps up abruptly to a new, higher level and levels off again into a second plateau.]

After equilibrium is established, the mixture is transferred to a larger container at constant temperature. As a result, would the number of moles of $\text{HI}(g)$ increase, decrease, or remain the same? Justify your answer.

Explain how the graphs indicate that the reaction is second order with respect to $\text{NO}_2$.

At a certain point in the reaction, the rate of disappearance of $\text{NO}_2$ is determined to be $6.52 \times 10^{-7}\ M/\text{s}$.

Determine the rate of appearance, in $M/\text{s}$, of $\text{O}_2$ at this same point in the reaction.

$\text{NO}_2$ is a molecule that contains an odd number of electrons and can be oxidized to form the $\text{NO}_2^+$ ion. In $\text{NO}_2$, the unpaired electron is presumed to be localized on the nitrogen atom, as shown in the Lewis diagram in the box on the left.

[Two boxes side by side. Left box: Lewis structure of $\text{NO}_2$ — $\text{O}$ (with two lone pairs) double-bonded on the left to a central N (bearing an unpaired dot, single electron, above it), N single-bonded on the right to another $\text{O}$ (bearing three lone pairs, i.e., a negative-type oxygen with full octet): $\ddot{\text{O}}=\dot{\text{N}}-\ddot{\text{O}}:$ with all lone pairs shown as dots. Right box: empty bracket template $\left[\ \text{O}\quad \text{N}\quad \text{O}\ \right]^+$ for the student to complete with the Lewis structure of $\text{NO}_2^+$, showing atoms O, N, O in a row inside square brackets with a superscript plus charge, currently drawn with no bonds or lone pairs (blank template for the student to fill in).]

In the box on the right, complete the Lewis diagram for $\text{NO}_2^+$. Be sure to show all bonding and nonbonding electrons.

A student makes the claim that the bond angles in $\text{NO}_2$ and $\text{NO}_2^+$ are different from each other. Do you agree or disagree with the student's claim? Justify your answer.

Calculate the mass of solid NaCl (molar mass 58.44 g/mol) needed to prepare the 100.0 mL of 0.340 $M$ NaCl($aq$).

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.

Materials available: 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.

Fill in steps 2 and 4.

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: a rectangular chromatography-paper strip inside a chamber. From top to bottom: a horizontal line labeled "Solvent Front" near the top; below it, two spot markers close together labeled with arrows — the upper spot labeled "Compound Y" and, just below it, the lower spot labeled "Compound X"; near the bottom, a horizontal line labeled "Start Line".]

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.