Kinetics

2.a. The particle-level representation of the equimolar mixture of NO(g) and $NO_2(g)$ in the flask at the completion of the reaction between NO(g) and $O_2(g)$ is shown below in the box on the right. In the box below on the left, draw the particle-level representation of the reactant mixture of NO(g) and $O_2(g)$ that would yield the product mixture shown in the box on the right. In your drawing, represent oxygen atoms and nitrogen atoms as indicated below.

2.b. The student reads in a reference text that NO(g) and $NO_2(g)$ will react as represented by the equation below. Thermodynamic data for the reaction are given in the table below the equation.

$NO(g) + NO_2(g) \rightleftharpoons N_2O_3(g)$

Calculate the value of the equilibrium constant, K, for the reaction at 298 K.

2.c. $N_2O_3(g)$ reacts with water to form nitrous acid, $HNO_2(aq)$, a compound involved in the production of acid rain. The reaction is represented below.

$N_2O_3(g) + H_2O(l) \rightarrow 2 HNO_2(aq)$

The skeletal structure of the $HNO_2$ molecule is shown in the box below.

2.c.i. Complete the Lewis electron-dot diagram of the $HNO_2$ molecule in the box below, including any lone pairs of electrons.

H O N O

2.c.ii. Based on your completed diagram above, identify the hybridization of the nitrogen atom in the $HNO_2$ molecule.

2.d. To produce an aqueous solution of $HNO_2$, the student bubbles $N_2O_3(g)$ into distilled water. Assume that the reaction goes to completion and that $HNO_2$ is the only species produced. To determine the concentration of $HNO_2(aq)$ in the resulting solution, the student titrates a 100. mL sample of the solution with 0.100 M $KOH(aq)$. The neutralization reaction is represented below.

$HNO_2(aq) + OH^-(aq) \rightarrow NO_2^-(aq) + H_2O(l)$

The following titration curve shows the change in pH of the solution during the titration.

Use the titration curve and the information above to

2.d.i. determine the initial concentration of the $HNO_2(aq)$ solution

2.d.ii. estimate the value of p$K_a$ for $HNO_2(aq)$

2.e. During the titration, after a volume of 15 mL of 0.100 M $KOH(aq)$ has been added, which species, $HNO_2(aq)$ or $NO_2^-(aq)$, is present at a higher concentration in the solution? Justify your answer.

6.a. The graph of 1/[$NO_2$] vs time is linear, which indicates that the reaction is second order.

6.b. Rate = k[$NO_2$]$^2$

6.c.i. Yes, the rate law for mechanism I is consistent with the rate law in part (b). The rate law for the slow step is Rate = k[$NO_2$]$^2$, which is the same as the overall rate law.

6.c.ii. Yes, the rate law for mechanism II is consistent with the rate law in part (b). The rate law for the slow step is Rate = k[$N_2O_4$]. Since $N_2O_4$ is formed from the fast equilibrium step, the rate law can be rewritten as Rate = k[$NO_2$]$^2$.

A sample of pure $N_2O_5(g)$ is placed in an evacuated container and allowed to decompose at a constant temperature of 300 K. The concentration of $N_2O_5(g)$ in the container is measured over a period of time, and the measurements are recorded in the following table.

5.a. Determine the value of the rate constant, $k$, for the reaction. Include units in your answer.

The reaction is first order. The half-life is 1.67 hr. $t_{1/2} = \frac{0.693}{k}$, so $k = \frac{0.693}{1.67} = 0.415 , hr^{-1}$

5.b. The following mechanism is proposed for the decomposition of $N_2O_5(g)$.

Step 1: $N_2O_5(g) \rightarrow NO_2(g) + NO_3(g)$

Step 2: $NO_2(g) + NO_3(g) \rightarrow NO_2(g) + NO(g) + O_2(g)$

Step 3: $N_2O_5(g) + NO(g) \rightarrow 3NO_2(g)$

5.b.i. Identify which step of the proposed mechanism (1, 2, or 3) is the rate-determining step. Justify your answer in terms of the rate law given.

Step 1 is the rate-determining step. The rate law is rate = $k[N_2O_5]$, so the rate-determining step must only involve one molecule of $N_2O_5$.

5.c. If this experiment was repeated at the same temperature but with twice the initial concentration of $N_2O_5$, would the value of $k$ increase, decrease, or remain the same? Explain your reasoning.

The value of $k$ would remain the same. The rate constant, $k$, is temperature dependent but is independent of concentration.

3.a) Write the balanced net ionic equation for the reaction.

3.b) The student correctly identifies that trial 5 is inconsistent with the other trials. Explain why the student’s claim is correct using the data in the table. 3.c) Based on the reaction conditions and the collisions that occur between particles, explain the reason for the difference in the reaction times for trial 2 and trial 3. 3.d) The student claims that the reaction is zero order with respect to HCl($aq$). Do you agree or disagree with the student’s claim? Justify your answer using the student’s data. 3.e) The HCl($aq$) was present in excess in all trials of the experiment. Determine the molarity of the HCl($aq$) in the beaker after the reaction is complete in trial 2. Assume that the volume of the mixture remains constant at 50.0 mL throughout the trial. (The molar mass of CaCO$_3$ is 100.09 g/mol.)

3.f) Is the reaction endothermic or exothermic? Justify your answer using the information in the table. 3.g.i) Calculate the magnitude of heat transfer, q, in joules. 3.g.ii) Calculate the enthalpy of reaction in units of kJ/mol$_{rxn}$. Include the algebraic sign on your answer.

2.a) A student combines equal masses of $H_2C_4H_2O_4(s)$ chunks and $NaHCO_3(s)$ chunks with sufficient water at 20.0°C. The student determines that 0.0114 mol of $CO_2(g)$ is produced after the reaction goes to completion.

2.a.i) Calculate the number of grams of $CO_2(g)$ produced.

2.a.ii) The $CO_2(g)$ produced from the reaction at 20.0 °C was collected and found to have a pressure of 1.25 atm. Calculate the volume of $CO_2(g)$, in liters.

2.b) The student performs a second experiment that is identical to the first except that the student grinds the chunks of $H_2C_4H_2O_4(s)$ and $NaHCO_3(s)$ into powder before combining the powder with water.

2.b.i) What happens to the surface area of the reactants when the student grinds the chunks into powder?

2.b.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.

2.c) When the reaction is complete, will the volume of $CO_2(g)$ 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.

2.d) The student conducts additional trials of the experiment and produces the following data table.

2.d.i) Based on the student’s data, identify the limiting reactant in trial 3. Justify your answer.

2.d.ii) The reaction has a value of Δ$S$° greater than zero. Using particle-level reasoning, explain why the entropy increases as the reaction progresses.

2.e) 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 Δ$S_{rxn}$ > 0 and the reaction is endothermic. Do you agree or disagree with the student’s claim? Justify your answer.

2.f) 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.

$H_2C_4H_2O_4 + H_2O \rightleftharpoons HC_4H_2O_4^- + H_3O^+$ $K_{a1}$ = 1.5 × 10⁻²

$HC_4H_2O_4^- + H_2O \rightleftharpoons C_4H_2O_4^{2-} + H_3O^+$ $K_{a2}$ = 8.5 × 10⁻⁷

2.f.i) Calculate the p$K_a$ value for the $HC_4H_2O_4^-$ ion.

2.f.ii) A buffer solution with a pH of 7.00 is prepared using $C_4H_2O_4^{2-}$ and $HC_4H_2O_4^-$. Calculate the ratio $\frac{[C_4H_2O_4^{2-}]}{[HC_4H_2O_4^-]}$ in this solution.

6.a) Explain how the graphs indicate that the reaction is second order with respect to $NO_2$.

6.b) At a certain point in the reaction, the rate of disappearance of $NO_2$ is determined to be 6.52 × 10⁻⁷ $M$/s. Determine the rate of appearance, in $M$/s, of $O_2$ at this same point in the reaction.

6.c) $NO_2$ is a molecule that contains an odd number of electrons and can be oxidized to form the $NO_2^+$ ion. In $NO_2$, the unpaired electron is presumed to be localized on the nitrogen atom, as shown in the Lewis diagram in the box on the left.

6.c.i) In the box on the right, complete the Lewis diagram for $NO_2^+$. Be sure to show all bonding and nonbonding electrons.

6.c.ii) A student makes the claim that the bond angles in $NO_2$ and $NO_2^+$ are different from each other. Do you agree or disagree with the student’s claim? Justify your answer.