Homework 8: Kinetics

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These homework problems are suggested and will not be turned in for review. However, answers will be available for them the following week by your class TAs. For more homework feel free to go to the Homework page.

Q1

In the following decomposition reaction,

\[2 N_2O_5 → 4 NO_2 + O_2\]

oxygen gas is produced at the average rate of 9.1 × 10^-4 mol · L^-1 · s^-1. Over the same period, what is the average rate of the following:

the production of nitrogen dioxide
the loss of nitrogen pentoxide

Q2

Consider the following reaction:

N₂(g) + 3 H₂(g) → 2 NH₃(g)

If the rate of loss of hydrogen gas is 0.03 mol · L^-1· s^-1, what is the rate of production of ammonia?

Q3

Nitrogen monoxide reacts with hydrogen gas to produce nitrogen gas and water vapor. The mechanism is believed to be:

Step 1:	2 NO → N₂O₂
Step 2:	N₂O₂ + H₂ → N₂O + H₂O
Step 3:	N₂O + H₂ → N₂ + H₂O

For this reaction find the following:

the overall balanced equation
any reaction intermediates

Q4

Give two reasons why most molecular collisions do not lead to a reaction.

Q5

An important function for managers is to determine the rate-determining steps in their business processes. In a certain fast-food restaurant, it takes 3 minutes to cook the food, 1.5 minutes to wrap the food, and 5 minutes to take the order and make change. How would a good manager assign the work to four employees?

Q6

For the hypothetical reaction

\[2A + 3B → 3C + 2D\]

the following rate data were obtained in three experiments at the same temperature:

Initial [A]	Initial [B]	Initial rate
(mole liter^-1)	(mole liter^-1')	(moles of A consumed liter^-1‘ sec^-1)
0.10	0.10	0.10
0.20	0.10	0.40
0.20	0.20	0.40

Determine the experimental rate equation for the reaction.
Calculate the specific rate constant, k.
What is the rate of this reaction when [A] =0.30M and [B] = 0.30M?

Q7

For the hypothetical reaction

\[2A + B → 2C\]

the following data were collected in three experiments at 25°C:

Initial [A]	Initial [B]	Initial rate
(mole liter^-1)	(mole liter^-1)	(moles of A consumed liter^-1 sec^-1)
0.10	0.20	300
0.30	0.40	3600
0.30	0.80	14400

What is the experimental rate equation for this reaction?
Calculate the specific rate constant for this reaction.

Q8

In the reaction

\[2NO + Cl_2 → 2NOCl\]

the reactants and products are gases at the temperature of the reaction. The following rate data were measured for three experiments:

Initial p{NO}	Initial p{Cl₂}	Initial rate
(atm)	(atm)	(moles of A consumed atm sec^-1)
0.50	0.50	5.1 x 10^-3
1.0	1.0	4.0 x 10^-2
0.50	1.0	1.0 x 10^-2

From these data, write the rate equation for this gas reaction. What order is the reaction in NO, Cl₂, and overall?
Calculate the specific rate constant for this reaction.

Q9

The reaction 2NO + O₂ → 2NO₂ is first order in oxygen pressure and second order in the pressure of nitric oxide. Write the rate expression.

Q10

The reaction

\[A + B + C → D + F\]

was found to be zero order with respect to A. A solution of reactants A, B, and C was prepared with the following initial concentrations: 0.2M of A, 0.4M of B, and 0.6M of G. The concentration of A in this solution dropped to essentially zero in 5 min. A second solution was prepared with the following initial concentrations: 0.03M of A, 0.4M of B, and 0.6M of C. How long will it take for A to disappear?

Q11

For the reaction

\[2NO + H_2 → N_2O + H_2O\]

the following experimental rate data are collected in three successive experiments at the same temperature:

Initial [NO]	Initial [H₂]	Initial rate
(mole liter^-1)	(mole liter^-1')	(moles of A consumed liter^-1‘ sec^-1)
0.60	0.37	0.18
1.20	0.37	0.72
1.20	0.74	1.44

Using these experimental data, write the rate expression for the reaction.

Q12

The reaction

2HCrO₄^- + 3HSO₃^- + 5H⁺ → 2Cr³⁺ + 3SO₄^2- + 5HQO

follows the rate equation

Rate = k[HCrO₄^-][HSO₃^-]^₂[H⁺]

Why isn’t the rate proportional to the numbers of ions of each kind that are shown by the equation?

Q13

The reaction SO₂Cl₂ —> SO₂ + Cl₂ is a first-order reaction with the rate constant k = 2.2 x 10^-5 sec^-1 at 320°C. What fraction of SO₂CI₂ is decomposed on heating at 320°C for 90 min?

Q14

It often is said that, near room temperature, a reaction rate doubles if the temperature is increased by 10°C. Calculate the activation energy of a reaction whose fate exactly doubles between 27°C and 37°C.

Q15

What is the activation energy for a reaction for which an increase in temperature from 20°C to 30°C exactly triples the rate constant?

Q16

The following data give the temperature dependence of the rate constant for the reaction N₂O₄ → 2NO₂ → 1/2O₂. Plot the data and calculate the activation energy of the reaction.

T(K) k (sec^-1)
273 7.87 x 10^-7
298 3.46 x 10^-5
308 1.35 x 10^-4
318 4.98 x 10^-4
328 1.50 x 10^-3
338 4.87 x 10^-3

Q17

Consider the reaction

CH₄ + Cl₂ → CH₃Cl + HCl (occurs under light)

The mechanism is a chain reaction involving Cl atoms and CH₃ radicals. Which of the following steps does not terminate this chain reaction?

CH₃ + Cl → CH₃CI
CH₃ + HCl → CH₄ + Cl
CH₃ + CH₃ → C₂H₂
Cl + Cl → Cl₂