CHEM 1442: Exam 2 Practice Questions (ch. 13,14)

Consider the following reaction mechanism. A chemist proposed that the first step is slow compared to the second step. Step 1: H2O2(aq) + I-(aq) → H2O(l) + IO-(aq) Step 2: H2O2(aq) + IO- (aq) → H2O(l) + O2(g) + I-(aq) Select all the correct statements. If none of them are correct, select "None." (I) I- and IO- are intermediates. (II) I- is a catalyst. (III) According to the proposed mechanism, the rate of the overall reaction is equal to k [H2O2]2, where k is the rate constant.

(II) only

The following reaction follows first-order kinetics with a half-life of 0.321 s. A → B + C Initially, a vessel contains only A, and the initial concentration is 1.63 M. Determine A's concentration (in M) after 1.30 seconds. Round your answer to two significant figures.

0.098 M

13.9 A chemical reaction that is first order in A is observed to have a rate constant of 1.2 × 10‒2 s ‒1 at a particular temperature. If the initial concentration is 2.0 M, what is the concentration of A after 200. s?

0.18 M

Consider the following reaction. 2 NO(g) ⇌ N2(g) + O2(g) KP = 874 at 2150 K A chemist prepares a 50.0-L reaction chamber with NO(g) at a pressure of 0.650 atm. The system was allowed to come to equilibrium at 2150 K. What was the partial pressure of N2(g) of the equilibrium mixture? Round your answer to three significant figures.

0.320 atm

Consider the following chemical reaction. 2 NO2(g) ⇌ 2 NO(g) + O2(g) A chemist pace 1.55 moles of NO2(g) in a 2.00-L sealed container. When the reaction reaches equilibrium at a particular temperature, she finds that the concentration of NO2 is 0.311 M. Determine the value of KC for this reaction at this temperature.

0.516

Example #1. The rate constant for a certain first-order reaction, A products, is 𝒌 = 𝟐. 𝟑𝟖 × 𝟏𝟎 −𝟑 𝒔 −𝟏 at 500 °C. If the initial concentration of A is 1.50 M, what will the concentration be after 215 s?

0.899 M

A chemist measures chlorine gas's molarity in a reaction vessel during a particular chemical reaction. When the reaction begins, the molarity of Cl2 is 0.173 M. After 750.0 s, the molarity of Cl2 drops to 0.0582 M. Determine the average rate of consumption of chlorine gas during the first 750.0 seconds of the reaction. Round your answer to two significant figures.

1.5 × 10-4 M/s

Consider the following chemical reaction. 4 NH3(g) + 7 O2(g) → 4 NO2(g) + 6 H2O(g) Determine the rate of formation of NO2 when the rate of consumption of O2 is 2.75 M/s.

1.57 M/s

A chemist finds that a particular reaction follows first-order kinetics. She finds that the rate constants of the reaction are 6.12 × 10-3 s-1 at 195.0°C and 8.82 × 10-2 s-1 at 225.0°C. Calculate the activation energy for this reaction. Round your answer to three significant figures.

172 kJ/mol

13.2 Write a balanced equation for the gas phase reaction with the following reaction rate: 𝑟𝑎𝑡𝑒 = − 1/2 ∆[𝑁𝑂]/∆𝑡 = − 1/2 ∆[𝐻2 ]/∆𝑡 = ∆[𝑁2 ]/∆𝑡 = 1/2 ∆[𝐻2𝑂]/∆𝑡

2 NO(g) + 2 H2(g) → N2(g) + 2 H2O(g)

13.12 A particular reaction, A → products, is found to be second order with a rate constant of 2.55 × 10‒3 M‒1 s ‒1 at a particular temperature. If the initial concentration of A is 2.95 M, what will its concentration be after 20.0 s?

2.56 M

Consider the following reaction 2 H2O(g) + O2(g) ⇌ 2 H2O2(g) KP = ? Determine the value of KP for the reaction by using the following data. H2(g) + O2(g) ⇌ H2O2(g) KP = 2.3 × 106 2 H2(g) + O2(g) ⇌ 2 H2O(g) KP = 1.8 × 1037

2.9 × 10-25

Consider the following reaction. X(g) + 3 Y(g) ⇌ 2 Z(g) The reaction has a KC value of 0.0339 at 337 K. Determine KP at 337 K. Round your answer to three significant figures.

4.43 × 10-5

Example #2: In the balanced equation below, if the rate of formation of NO2 is 2.75 M∙s⁻¹ , what is the rate of consumption of O2?

4.81 mol O₂/L∙s

13.11 The reaction A → products was found to be first order. If the half-life of this reaction is 30.0 min, how long (in min) would it take for 62.5% of A to react?

42.5 min

Example #3. The half-life of a particular first-order process, A → products, is 142 s at 100 °C. How long would it take for 90.0% of A to react at this temperature?

472 s

A reaction obeys the following rate law: Rate = k [A]2 (k = 0.00813 M-1 s -1) Initially, a vessel contains A at a concentration of 2.40 M. Determine how long it takes for the concentration of A to decrease by 58.0%. (that is, 58.0% of A are consumed.) Round your answer to two significant figures.

71 s

The decomposition reaction of a substance follows first-order kinetics. A chemist finds that 39% of the substance decomposes in 55.0 min. Determine the half-life of this reaction. Round off your answer to three significant figures.

77.1 min

Example #2. A particular compound decomposes in a first-order process. If it takes 13.0 min for 10.0% of this substance to decompose at a certain temperature, what is the half-life at this temperature?

85.5 min

13.10 Consider the first-order reaction: A → products. If 25% of A disappears in 36 s, what is the halflife of the reaction?

87 s

14.21 Consider the following reaction at a particular temperature: Ni(s) + 4 CO(g) ⇌ Ni(CO)4(g) An equilibrium mixture contains 0.72 mol Ni, 0.0083 mol CO, and 0.0036 mol Ni(CO)4, all in a 5.00 L container. What is the value of Kc for this reaction at this temperature?

9.5 × 10⁷

13.3 Consider the Haber process for the production of ammonia: N2(g) + 3 H2(g) 2 NH3(g) If hydrogen is being consumed at a rate of 14.7 M∙s⁻¹ , what is the rate of production of ammonia?

9.80 M∙s-1

14.18 Consider the following reaction: Cl2(g) + 2 NO(g) ⇌ 2 ClNO(g) Kc = 1.0 × 10¹⁰ at 200. °C What is/are the predominant species present in an equilibrium mixture at 200. °C?

ClNO is the predominant species present at equilibrium.

13.16 A particular reaction has Ea = 75 kJ/mol and ΔHrxn = ‒21 kJ/mol. What is the activation energy for the reverse reaction?

Ea = 96 kJ/mol

Consider the equilibrium system established in a closed vessel by the following reaction. 3 Fe(s) + 4 H2O(g) ⇌ Fe3O4(s) + 4H2(g) Select all the changes that shift the equilibrium to the right. If none of them will shift the equilibrium to the right, select "None." I. Addition of H2O(g) II. Use of a catalyst. III. Removal of H2(g) IV. Addition of Ar(g)

I and III

Consider the equilibrium system established in a closed vessel by the following reaction. N2(g) + O2(g) ⇌ 2NO(g) ΔH = 90.29 kJ Select one correct statement. If the temperature increases, the equilibrium shifts to the left, and the pressure of N2 will go up. If the temperature increases, the equilibrium shifts to the right, and the pressure of N2 will go down. Temperature change does not affect the position of equilibrium for this reaction.

If the temperature increases, the equilibrium shifts to the right, and the pressure of N2 will go down.

Consider the equilibrium system established in a closed vessel by the following reaction. 4NH3(g) + 3O2(g) ⇌ 2N2(g) + 6H2O(g) Select one correct statement. Assume that the temperature stays constant. The volume change will not affect the position of equilibrium for this reaction. If the vessel's volume increases, the equilibrium shifts to the left, and the pressure of NH3 will go up. If the vessel's volume increases, the equilibrium shifts to the right, and the pressure of NH3 will go down.

If the vessel's volume increases, the equilibrium shifts to the right, and the pressure of NH3 will go down.

Example #3. The vapor pressure of water at 35 °C is 42.2 torr. Determine the values of KP and Kc for the following equilibrium at 35 °C: H2O(l) ⇌ H2O(g)

KP = 0.0555; Kc = 2.20 × 10‒3

14.17 The vapor pressure of water at 50.0 °C is 92.5 torr. Determine the values of KP and Kc at 50.0 °C for the reaction shown. H2O(g) ⇌ H2O(l)

KP = 8.22 at 50.0 °C; Kc = 218 at 50.0 °C

Example #1. Consider the reaction: N2(g) + 3 H2(g) ⇌ 2 NH3(g) An equilibrium mixture of these gases at a certain temperature contains [N2] = 3.75 M, [H2] = 2.88 M, and [NH3] = 4.18 M. What is the value of Kc at this temperature?

Kc = 0.195

14.19 Consider the following equilibria, all at 400. K: H2(g) + Cl2(g) ⇌ 2 HCl(g) Kc1 = 4.3 × 10¹² H2(g) ⇌ 2 H(g) Kc2 = 2.1 × 10‒40 Cl2(g) ⇌ 2 Cl(g) Kc3 = 8.3 × 10‒13 Use this information to determine the value of Kc (at the same temperature) for the following reaction: H(g) + Cl(g) ⇌ HCl(g) Kc = ?

Kc = 1.6 × 1032

14.22 1.55 mol of NO2(g) was placed in a 2.00 L container. When the reaction shown below had reached equilibrium at a particular temperature, the concentration of NO2 was found to be 0.203 mol/L. What is the value of Kc for this reaction at this temperature? 2 NO2(g) ⇌ 2 NO(g) + O2(g

Kc = 2.27

Example #4. Consider the following reaction: 4 Fe(s) + 3 O2(g) ⇌ 2 Fe2O3(s) At 575 K, an equilibrium mixture contains 2.00 mol Fe, 0.125 mol O2, and 3.00 mol Fe2O3, all in a 2.00 L container. Determine the values of Kc and KP at 575 K for this reaction.

Kc = 4.10 × 10³ ; KP = 0.0390

14.24 KP for the reaction below is 0.0112 at 0.0°C. What is Kc for this reaction at 0.0 °C? SO2Cl2(g) ⇌ SO2(g) + Cl2(g)

Kc = 5.00 × 10⁻⁴

Example #5. Consider the following equilibrium: 2 NOCl(g) ⇌ 2 NO(g) + Cl2(g) Kc = 1.65 × 10‒4 at 200 °C Determine the value of Kc' for the reaction shown: 6 NO(g) + 3 Cl2(g) ⇌ 6 NOCl(g) Kc' = ???

Kc' = 2.23 × 10¹¹

Consider the following reaction. A + B → C + D Using the following kinetics data, determine the units of the rate constant in the rate law for this reaction. Experiment / [A] (M) / [B] (M) / Initial Rate (M/s) 1 / 0.340 / 0.380 / 0.0216 2 / 0.340 / 1.06 / 0.169 3 / 0.510 / 0.380 / 0.0324

M-2 s-1

13.6 The experimentally determined rate law for a particular reaction is: 𝑟𝑎𝑡𝑒 = 𝑘[𝐴][𝐵]² What are the units of the rate constant 𝑘?

M‒2 s ‒1

Consider the following reaction. N2 (g) + 3H2 (g) ⇌ 2NH3 (g) The equilibrium constant for the reaction is 6.0 × 10⁶ at 25°C. Select one correct statement when the reaction reaches equilibrium, assuming that the temperature is 25°C. Please note that "predominate" = be greater in amount. Reactants predominate. Either products or reactants could predominate depending on initial concentrations. Roughly equal amounts of products and reactants are present. Products predominate.

Products predominate.

Consider the following rate law. Rate = k [A]3 [B] How does the rate changes if the concentration of A is doubled while everything else stays the same? Rate increases by a factor of 9 (that is, 9 times faster). Rate increases by a factor of 8 (that is, 8 times faster). Rate increases by a factor of 16 (that is, 16 times faster). Rate remains unchanged. Rate increases by a factor of 6 (that is, 6 times faster). Rate doubles (that is, 2 times faster).

Rate increases by a factor of 8 (that is, 8 times faster).

13.17 Consider two reactions. Reaction #1 has an activation energy of 122 kJ/mol, and reaction #2 has an activation energy of 108 kJ/mol. All other factors being equal, which reaction occurs at a higher rate at a given temperature?

Reaction #2 is faster at a given temperature. The lower the activation energy, the faster the reaction

13.14 The following reaction occurs in one elementary, bimolecular step. What is the mechanism, and what is the rate law for this reaction? 2 NO2(g) → O2(g) + N2O2(g)

Since this reaction occurs in one elementary step, the mechanism of the reaction is the same as the overall balanced equation. Mechanism: NO2 + NO2 → O2 + N2O2 The rate law for this reaction is therefore: 𝑟𝑎𝑡𝑒 = 𝑘[𝑁𝑂2 ]²

Consider the following reaction: A + B → C + D A chemist determines that the reaction is second order in A and second order overall. Select the reaction mechanism which supports her observation. If none of them support the observation, select "None." In this question, the symbols (A, B, C, D, X, and Y) represent chemical substances. Step 1: A → C (slow) Step 2: B → D (fast) Step 1: A + A → C + X (slow) Step 2: B + X → A + D (fast) Step 1: A + A → C + X (slow) Step 2: B + X → D (fast) None Step 1: A + X → C + Y (slow) Step 2: B + Y → D + X (fast)

Step 1: A + A → C + X (slow) Step 2: B + X → A + D (fast)

Example #1. Consider the Haber process for the synthesis of ammonia: N2(g) + 3H2(g) ⇌ 2 NH3(g) ΔH° = ‒91.8 kJ Which of the following would increase the equilibrium yield of ammonia? a) increasing the total pressure by compressing the system b) increasing the partial pressure of N2 c) decreasing the partial pressure of H2 d) increasing the total pressure by addition of He(g) e) addition of a catalyst f) increasing the temperature

The equilibrium yield of ammonia would be increased by (a) and (b) only

The equilibrium constant, KP, is 4.2 × 10-4 at a specific temperature for the following reaction. N2(g) + O2(g) ⇌ 2 NO(g) A chemist measures the partial pressure of each substance in the container as follows. Pressure for N2 = 0.11 atm Pressure for O2 = 1.5 atm Pressure for NO = 0.030 atm Select one correct statement, and select "None" if none of the statements are correct. The system is not at equilibrium. The reaction will shift to the right for the system to reach equilibrium. The concentrations of the substances are required to determine if the system is at equilibrium. The system is at equilibrium. No net reaction takes place. None. The system is not at equilibrium. The reaction will shift to the left for the system to reach equilibrium.

The system is not at equilibrium. The reaction will shift to the left for the system to reach equilibrium.

Example #2. Consider the reaction and its rate law, shown below: 2 NO(g) + 2 H2(g) → N2(g) + 2 H2O(g) 𝒓𝒂𝒕𝒆 = 𝒌[𝑵𝑶]²[𝑯𝟐] What is the order of this reaction with respect to NO(g)? What is the order with respect to H2? What is the overall order of this reaction?

Therefore, this reaction is third order overall.

14.25 Consider the following equilibrium: A(g) + B(g) ⇌ 2 C(g) Kc = 6.55 at 100. °C Suppose that 2.00 mol of A and 2.00 mol of B were placed in a 5.00 L container. What would be the equilibrium concentration of each gas once the system reached equilibrium at 100. °C?

[A]eq = 0.176 mol/L; [B]eq = 0.176 mol/L; [C]eq = 0.449 mol/L

Example #1. Consider the following equilibrium: A(g) + 2 B(g) ⇌ 3 C(g) + D(g) Suppose that 1.00 mol each of A, B, C, and D were placed in a 5.00 L container. When the system reached equilibrium at a particular temperature, 1.22 mol of B were present in the equilibrium mixture. Determine the equilibrium concentrations of A, B, C, and D, and determine the value of Kc at this particular temperature.

[A]eq = 0.222 M; [B]eq = 0.244 M; [C]eq = 0.134 M; [D]eq = 0.178 M; Kc = 0.0324

Example #2. At a given temperature, the equilibrium constant Kc is 0.195 for the reaction shown: N2(g) + 3 H2(g) ⇌ 2 NH3(g) Kc = 0.195 An equilibrium mixture contains 1.62 mol/L of N2 and 2.08 mol/L NH3. What is the concentration of H2 in this mixture?

[H2] = 2.39 mol/L

Example #3. The equilibrium constant for the reaction N2O4(g) ⇌ 2 NO2(g) is Kc = 17.4 at 200. °C. Suppose that 1.00 mol of NO2 is placed in a 10.0 L container at 200. °C and allowed to reach equilibrium. What is the equilibrium concentration of N2O4?

[N2O4]eq = 5.62 × 10‒4 M

Determine the equilibrium constant expression (KC) for the following reaction. Zn(s) + 2Ag+(aq) ⇌ Zn2+(aq) + 2Ag(s) You do not need to use subscript "eq" in the expression.

[Zn²⁺]/[Ag⁺]²

Example #4. A particular reaction was found to be exothermic with the following equilibrium constant: Kc = 1.0 × 10‒3 at 400. K Which response below best describes the value of Kc at 500. K? a) Kc < 1.0 × 10‒3 b) Kc = 1.0 × 10‒3 c) Kc > 1.0 × 10‒3 d) There is not enough information given to decide

a

c) Suppose that a particular reaction is third order in A and third order overall. What will happen to the rate if the concentration of A doubles? If the concentration of A increases by a factor of 3.00? If the concentration of A increases by a factor of 1.25?Example #4. a) Suppose that a particular reaction has the rate law: 𝒓𝒂𝒕𝒆 = 𝒌[𝑨] What will happen to the rate if the concentration of A increases by a factor of 3.00? What will happen to the rate if the concentration of A increases by a factor of 1.25? b) Suppose that a particular reaction is second order in A and second order overall. What will happen to the rate if the concentration of A increases by a factor of 3.00? by a factor of 1.25? c) Suppose that a particular reaction is third order in A and third order overall. What will happen to the rate if the concentration of A doubles? If the concentration of A increases by a factor of 3.00? If the concentration of A increases by a factor of 1.25?

a) In a first-order reaction, such as this, the rate is directly proportional to the concentration of A. Therefore, if the concentration of A increases by a factor of 3.00, the rate of the reaction will also increase by a factor of 3.00. If the concentration increases by a factor of 1.25, the rate will also increase by a factor of 1.25. b) In a second-order reaction, the rate is directly proportional to the square of the concentration. Therefore, if the concentration of A increases by a factor of 3.00, the rate will increase by a factor of 3.002 = 9.00. If the concentration of A increases by a factor of 1.25, the rate will increase by a factor of 1.252 = 1.56. c)The rate is directly proportional to the concentration of A cubed. Therefore, if the concentration of A doubles, the rate increases by a factor of 23 = 8. If the concentration of A increases by a factor of 3.00, the rate will increase by a factor of 3.003 = 27.0. If the concentration of A increases by a factor of 1.25, the rate will increase by a factor of 1.253 = 1.95.

14.20 Consider the following equilibrium: NH4SH(s) ⇌ NH3(g) + H2S(g) a) 2.00 mol of NH4SH were placed in an evacuated 10.0 L container. When the system reached equilibrium at 250. °C, the partial pressure of NH3 was found to be 72.9 torr. What is the value of KP at 250. °C? b) What is the value of Kc for this reaction at 250. °C? c) In which direction will the equilibrium shift if 1.00 mol of NH4SH is added to the equilibrium system?

a) KP = 9.20 × 10‒3 (Hint: When calculating KP, all partial pressures must be in units of atm.) b) Kc = 4.99 × 10‒6 c) The equilibrium will not change. Adding a solid to a heterogeneous equilibrium does not affect the equilibrium position.

14.23 Consider the following equilibrium: A(g) ⇌ B(g) + C(g) KP = 3.50 × 103 at 500. °C The three gases, A, B, and C, were placed in a reaction vessel with these initial partial pressures: PA = 2.50 atm PB = 15.0 atm PC = 18.0 atm a) Determine the value of QP for the initial conditions. Will the reaction proceed in a forward direction or reverse direction at 500. °C? b) Determine the equilibrium partial pressures of these three gases.

a) QP = 108; therefore, QP < KP, and the forward reaction will occur. b) PA = 0.10 atm; PB = 17.4 atm; PC = 20.4 atm

Example #4. Consider the following reaction: A(g) + 2 B(g) ⇌ C(g) + 3 D(g) Kc = 300. Suppose we have the following mixtures. In which direction will each reaction proceed in order to reach equilibrium? a) A 2.0 L container containing 1.0 mol A, 1.0 mol B, 5.0 mol C, and 4.0 mol D b) A 2.0 L container containing 0.80 mol A, 0.80 mol B, 6.0 mol C, and 8.0 mol D c) A 2.0 L container contains 1.0 mol A, 1.0 mol B, 1.0 mol C, and 0.0 mol D. d) A 2.0 L container contains 0.0 mol A, 1.0 mol B, 1.0 mol C, and 1.0 mol D. e) A 2.0 L container contains 0.0 mol A, 1.0 mol B, 0.0 mol C, and 1.0 mol D.

a) Qc < Kc, and the reaction will proceed in the forward direction b): Qc > Kc; therefore, the reaction will proceed in the reverse direction. c) Qc < Kc; therefore, the forward reaction will occur d) The reverse reaction will occur e) Neither the forward nor the reverse reaction occurs

Example #2. Consider the equilibrium shown: CaCO3(s) ⇌ CaO(s) + CO2(g) This is an endothermic reaction. Suppose that the system is at equilibrium. How does the equilibrium shift in response to a) decreasing the total pressure by expansion b) increasing the partial pressure of CO2 c) increasing the pressure by addition of He(g) d) increasing the temperature e) increasing the mass of CaCO3

a) The equilibrium shifts to the right. b) The equilibrium shifts to the left. c) No change. d) The equilibrium shifts to the right. e) No change

Example #1. The complete mechanism for a particular reaction is believed to occur in two steps: step 1: A + B → C + D (slow) step 2: A + C → B + E (fast) a) Write the overall balanced equation for this reaction. b) What is the role of B in this reaction? c) What is the role of C in this reaction? d) What is the rate law for this reaction?

a) The overall balanced equation is obtained by adding the two reactions and canceling any species that are present on both sides. The overall balanced equation is: 2A → D + E b) B is a catalyst. It is consumed in one step and regenerated in a subsequent step. c) C is an intermediate. It is produced in one step and then consumed in a later step. d) The rate law for a reaction is determined from the slow step of the mechanism. The first step, in which A collides with B, is the slow step. If the concentration of A increases, then the probability of collision increases. If the concentration of B increases, the probability of collision also increases. Therefore, the rate law is first order with respect to A and first order with respect to B.

14.14 In which direction will each of the following equilibria shift if the total pressure is increased by compressing the system? a) H2(g) + Cl2(g) ⇌ 2 HCl(g) b) Fe2O3(s) + 3 CO(g) ⇌ 2 Fe(s) + 3 CO2(g) c) NH4Br(s) ⇌ NH3(g) + Br2(g)

a) There will be no change to the equilibrium position. (The number of moles of gas on both the reactant and product sides is the same.) b) The equilibrium position does not change, since there are three moles of gas on both the reactant and product sides. c) The equilibrium will shift to the left

14.16 The following reaction is used in the refining of nickel are: NiO(s) + CO(g) ⇌ Ni(s) + CO2(g) Kc = 4295 at 1000. K Kc = 1472 at 1100. K Describe how each of the following would affect the equilibrium yield of Ni? a) Increase the temperature. b) Increase the partial pressure of CO(g). c) Decrease the partial pressure of CO2(g). d) Increase the total pressure by addition of He(g). e) Increase the total pressure by compression. f) Increase the mass of NiO(s).

a) This would lower the equilibrium yield of Ni. Notice that as the temperature increases, the magnitude of Kc decreases. That means that the reaction is an exothermic reaction. Increasing the temperature of an exothermic reaction will cause the equilibrium to shift to the left. b) This would increase the equilibrium yield of Ni. c) This would increase the equilibrium yield of Ni. d) He is a nonparticipating substance. Therefore, the addition of He would have no effect on the equilibrium yield of Ni. e) There would be no effect on the equilibrium yield of Ni. Both the reactant and product sides contain the same number of moles of gas. Therefore, changing the total pressure by expansion or compression will not affect the equilibrium position. f) Increasing the mass of NiO will not affect the equilibrium yield of Ni. A heterogeneous reaction cannot be driven in one direction or another by addition of a solid.

14.27 Consider the equilibrium below: A(g) ⇌ 2 B(g) Kc = 10.0 at 525 K Determine the equilibrium concentrations of A and B at 525 K from each of the initial concentrations shown below. a) [A]0 = 10.00 M; [B]0 = 0.00 M b) [A]0 = 0.00 M; [B]0 = 10.00 M c) [A]0 = 5.00 M; [B]0 = 7.50 M

a) [A]eq = 6.10 M; [B]eq = 7.81 M b) [A]eq = 2.50 M; [B]eq = 5.00 M c) [A]eq = 5.16 M; [B]eq = 7.18 M

14.26 Consider the following equilibrium: 2 SO2(g) + O2(g) ⇌ 2 SO3(g) a) When the temperature of this reaction is increased, the equilibrium yield of O2(g) increases. Is this an endothermic or exothermic reaction? b) If the total pressure of this reaction were increased by compression, what would happen to the equilibrium yield of O2(g)?

a) exothermic b) The equilibrium yield of O2(g) would decrease

Example #6. What are the units of the rate constant (a) for a first-order reaction? (b) for a second-order reaction? (c) for a zero-order reaction?

a) s⁻¹ b) M⁻¹s⁻¹ c) Ms⁻¹

14.13 Consider the following reaction: A(g) + B(g) ⇌ 2 C(g) A particular equilibrium mixture of these three gases consists of 2.00 mol of A, 2.00 mol of B, and 1.00 mol of C in a 1.00 L flask. a) What is the value of Kc for this reaction at this particular temperature? b) Suppose an additional 2.00 mol of C is added to the equilibrium mixture. What is the value of the reaction quotient, Qc? Will the equilibrium shift to the left or to the right? c) Determine the new equilibrium concentrations of A, B, and C after equilibrium has been restored.

a) 𝐾𝑐 = [𝐶]²/[𝐴][𝐵] = (1.00)²/(2.00)(2.00) = 0.250 b) 𝑄𝑐 = [𝐶]²/[𝐴][𝐵] = (3.00)²/(2.00)(2.00) = 2.25 𝑄𝑐 > 𝐾𝑐 and the equilibrium shifts to the left. c) [𝐴]𝑒𝑞 = [𝐵]𝑒𝑞 = 2.80 𝑀; [𝐶]𝑒𝑞 = 1.40 M

13.5 The reaction A + B → C + D has been found to be first order in A and second order in B. In experiment #1, the initial concentrations of both A and B were 0.10 M. Experiment #2 was performed at the same temperature, but this time the concentrations of both A and B were 0.30 M. a) Write the rate law. b) Determine the ratio of the rate of the reaction in experiment #2 to the rate in experiment #1, 𝑟𝑎𝑡𝑒2/𝑟𝑎𝑡𝑒1

a) 𝑟𝑎𝑡𝑒 = 𝑘[𝐴][𝐵]² b) 𝑟𝑎𝑡𝑒2/𝑟𝑎𝑡𝑒1 = 27

14.15 Consider the following equilibrium: NH4NO3(s) ⇌ N2O(g) + 2 H2O(g) KP = 5.21 at 750 K This is an endothermic reaction. Which statement below best describes the value of KP at 1000 K? a) KP = 5.21 b) KP < 5.21 c) KP > 5.21

c) KP > 5.21

Example #2. Consider the following hypothetical reaction: A + B → C + D Suppose that this reaction is known to be second order in A and second order overall. Which of the following is a valid mechanism for this reaction? a) A + X C + Y (slow) B + Y D + X (fast) b) A + A C + X (slow) B + X D (fast) c) A C (slow) B D (fast) d) A + B C + D e) A + A C + X (slow) B + X A + D (fast)

e

13.7 The rate law for a particular reaction was determined experimentally. If the value of the rate constant is 0.0592 min⁻¹ at 150 °C, what is the order of the reaction?

first order (Hint: look at the units of the rate constant.)

13.18 A particular first-order reaction has an activation energy of 45.5 kJ/mol. The rate constant for this reaction is 8.72 × 10⁻⁴ s⁻¹ at 35 °C. What is the rate constant at 65 °C?

k = 4.22 × 10⁻³ s⁻¹

The reaction is second order in N2 and first order in H2. Select the correct rate law expression.

rate = k [N2]² [H2]

13.8 Determine the rate law for the reaction below, given the initial rate data, all collected at the same temperature. O2(g) + 2 NO(g) → 2 NO2(g) Experiment / [O2]₀ / [NO]₀ / rate (-𝛥[𝑂2]/𝛥𝑡) #1 / 0.0350 M / 0.0240 M / 0.143 M∙s‒1 #2 / 0.0350 M / 0.0150 M / 0.0559 M∙s‒1 #3 / 0.0450 M / 0.0240 M / 0.184 M∙s‒1

rate = 𝑘 [O2][NO]²

Consider the following reaction. A + B → C + D Using the following kinetics data, determine the rate law for this reaction. Experiment / [A] (M) / [B] (M) / Initial Rate (M/s) 1 / 0.050 / 0.010 / 5.0 × 10-4 2 / 0.050 / 0.040 / 2.0 × 10-3 3 / 0.100 / 0.010 / 1.0 × 10-3

rate=k [A] [B]

13.4 The rate law for the reaction 2 NO(g) + Br2(g) → 2 NOBr(g) is 𝑟𝑎𝑡𝑒 = 𝑘[𝑁𝑂]²[𝐵𝑟2] What is the order of this reaction with respect to each reactant? What is the overall order of the reaction?

second order in NO; first order in Br2; third order overall

Determine the molecularity of the following elementary reaction. O3 → O2 + O

unimolecular

Example #1. Write the Kc and KP equations for each of the following equilibria. a) NH4Cl(s) ⇌ NH3(g) + HCl(g) b) MgO(s) + CO2(g) ⇌ MgCO3(s)

𝐾𝑐 = [𝑁𝐻3 ][𝐻𝐶𝑙] 𝑎𝑛𝑑 𝐾𝑃 = 𝑃𝑁𝐻3 × 𝑃𝐻𝐶l 𝐾𝑐 = 1/[𝐶𝑂2 ] 𝑎𝑛𝑑 𝐾𝑃 = 1/𝑃𝐶𝑂2

Example #2. The equilibrium constant for the reaction 2 NO(g) ⇌ N2(g) + O2(g) is KP = 874 at 2150 K. A 50.0 L reaction chamber was loaded with NO(g) at a partial pressure of 0.600 atm. The system was allowed to come to equilibrium at 2150 K. What was the partial pressure of N2(g) and what was the total pressure of the equilibrium mixture?

𝑃𝑁2 is 0.295 atm. The total pressure of the equilibrium mixture is 0.600 atm

13.1 Express the rate of the following reaction in terms of the changes in concentration of each reactant and product. 4 NH3(g) + 5 O2(g) → 4 NO(g) + 6 H2O(g)

𝑟𝑎𝑡𝑒 = − 1 4 ∆[𝑁𝐻3 ] ∆𝑡 = − 1 5 ∆[𝑂2 ] ∆𝑡 = 1 4 ∆[𝑁𝑂] ∆𝑡 = 1 6 ∆[𝐻2𝑂]

Example #1. Express the rate of the following reaction in terms of the changes in concentration of each reactant and product: 4 PH3(g) → P4(g) + 6 H2(g)

𝑟𝑎𝑡𝑒 = − 1/4 (∆[𝑃𝐻3 ]/∆𝑡) = (∆[𝑃4 ]/∆𝑡) = 1/6 (∆[H2]/∆𝑡)

Example #4. Assume that a reaction occurs by the two-step mechanism below: step 1: A + B ⇌ C (fast, rapid equilibrium) step 2: C → D (slow, rate-determining step) Write the overall balanced equation, and determine the rate law for this reaction.

𝑟𝑎𝑡𝑒 = 𝑘[𝐴][𝐵]

Example #3. The reaction 2 A + B → products is first order in A and second order in B. What is the rate law for this reaction?

𝑟𝑎𝑡𝑒 = 𝑘[𝐴][𝐵]²

Example #1. Consider the balanced equation shown below. What is the rate law for this reaction? 2A + B → C

𝑟𝑎𝑡𝑒 = 𝑘[𝐴]^m[𝐵] ^n[𝐶]^p

Example #5. Consider the following reaction: A + 2 B + C products It was found that doubling the concentration of A caused the rate to quadruple, doubling the concentration of B caused the rate to double, and doubling the concentration of C resulted in no change in the reaction rate. What is the rate law for this reaction?

𝑟𝑎𝑡𝑒 = 𝑘[𝐴]²[𝐵]

13.13 Consider the following reaction: H2(g) + 2 ICl(g) → 2 HCl(g) + I2(g) The mechanism for this reaction is believed to be: step 1: H2 + ICl → HCl + HI (slow) step 2: ICl + HI → HCl + I2 (fast) What rate law is consistent with this mechanism?

𝑟𝑎𝑡𝑒 = 𝑘[𝐻2 ][𝐼𝐶𝑙]

13.15 Ozone in the upper atmosphere decomposes in the following reaction: 2 O3(g) → 3 O2(g) One proposed mechanism for this reaction is: step 1: O3 ⇌ O2 + O (fast, rapid equilibrium) step 2: O + O3 → 2 O2 (slow, rate-determining step) What rate law is consistent with this mechanism? (Hint: a rate law cannot contain a reactive intermediate, but it can contain reactants and even products.)

𝑟𝑎𝑡𝑒 = 𝑘[𝑂3 ]²[𝑂2 ]⁻¹

Example #4. The rate law for the reaction A products is: rate = k[A]2 with a rate constant 𝒌 = 𝟔. 𝟓𝟓 × 𝟏𝟎 −𝟑 𝑴−𝟏𝒔 ‒𝟏 at 250 °C. How long would it take for the concentration of A to decrease from 1.250 M to 0.750 M?

𝑡 = 81.4 s