14.1.3 Determining the Form of a Rate Law

Question 1

Determining the Form of a Rate Law

Answer 1

• The orders of the reactants in the rate law do not necessarily relate to the stoichiometric coefficients in the balanced equation.
• The orders of the reactants in the rate law can be found by converting initial rates of reaction into ratios.
• The value of the rate constant (k) can be calculated once the orders of the reactants are known.

Question 2

note

Answer 2

• The orders of the reactants (m and n) in the rate law can be found by converting initial rates of reaction into ratios.
• For example, four experiments are run for the reaction of nitrogen monoxide (NO) with oxygen (O 2 ) to produce nitrogen dioxide (NO 2 ). The initial concentrations of NO and O 2 are varied over the four experiments, and the initial rate of each is measured.
• To find m, first the initial concentrations and rates from the first two experiments (where [O 2 ] is held constant) are plugged into the rate law. Next, the ratio of these two rate laws is taken, and m is determined to be 2.
• The same process can be used to solve for n, using the data from the first and third experiments (where [NO] is held constant). Using data from the second and forth experiment would yield the same result, n = 1.
• The value of the rate constant (k) can be calculated once the orders of the reactants are known.
• The data from one of the four experiments is plugged into the rate law, and the rate constant is determined to be 1.42 x 10 4 M –2 · s –1 . Since the units on the rate are M/s and the units on the concentrations are M, the units on k are M –2 · s –1 .

Question 3

Suppose you are studying the following reaction.
A + B → 2C
You gather the following initial rate data for the reaction.
Experiment [A]0, M [B]0, M Initial rate, M / s
1 0.50 0.50 5.66 × 10−2
2 1.00 0.50 1.13 × 10−1
3 1.00 1.00 1.60 × 10−1
What is the rate law for this reaction?

Answer 3

rate = (0.16 M −1/2s−1 ) [A] [B]1/2

Question 4

Chlorine dioxide reacts with hydroxide ions according to the following equation
2ClO2(aq) + 2OH-(aq) -> ClO3-(aq) + ClO2-(aq) + H2O(l)
A scientist gathers the following initial rate data for the reaction
Experiment 1 2 3
[ClO2]t0, M 0.025 0.050 0.025
[OHY=]t0, M 0.030 0.030 0.010
Initial, M/s 4.310^-3 1.7210^-2 1.4*10^-3
What is the overall order of the reaction?

Answer 4

third

Question 5

Cyclobutane decomposes to ethylene according to the following equation:

C4H8 → 2C2H4

A scientist gathers the following initial rate data for the reaction:

For what initial concentration of C4H8 will the initial rate of the reaction be equal to 10.0 M / s?

Answer 5

0.11 M

Question 6

Suppose you are studying the following reaction:

2A → B + C

What is the minimum number of initial rate experiments that you would need to perform to determine the rate law of the reaction, including the value of the rate constant?

Answer 6

2

Question 7

hylene (C2H4 ) reacts with bromine gas according to the following equation:

C2H4(g) + Br2(g) → C2H4Br2(g)

The rate of this reaction is first order in [C2H4 ] and third order overall. If the initial concentrations of the reactants are doubled, the rate of the reaction will increase by what factor?.

Answer 7

8

Question 8

Suppose you are studying the following reaction.

2A + B → 2C + D

You gather the following initial rate data for the reaction:

Experiment [A]0, M [b]0, M Initial rate, M/s
1 0.050 0.050 6.6010^-2
2 0.025 0.050 1.6510^-2
3 0.050 0.025 6.60*10^-2

What will be the rate of formation of C when [A] is 0.040 M and [B] is 0.040 M?

Answer 8

0.084 M / s

Question 9

The compound 2-bromo-2-methylpropane (CH3 )3CBr) reacts with hydroxide ions according to the following equation:

(CH3 )3CBr + OH − → (CH3 )3COH + Br−

A scientist gathers the following initial rate data for the reaction:

Experiment [(CH3)3CBr]0, M [OH-]0, M Initial rate, M/s
1 0.015 0.015 1.510^-4
2 0.030 0.015 3.010^-4
3 0.015 0.030 1.5*10^-4

Based on this data, which of the following conclusions can you draw about the rate law of the reaction?

Answer 9

The rate law does not depend on the concentration of OH −

Question 10

Suppose you are studying the following reaction:

2A + 2B → C + 2D

You find that when you double the concentration of A while keeping the concentration of B fixed, the rate of the reaction increases by a factor of 2. What conclusion can you draw about the rate law of this reaction?

Answer 10

The rate law is first order in [A]

Question 11

Permanganate ions react with oxalic acid and hydrogen ions according to the following equation:
2MnO4− (aq) + 5H2C2O4(aq) + 6H + (aq) → 2Mn2+ (aq) + 10CO2(g) + 8H2O(l)

A scientist gathers the following initial rate data for the reaction:

Exp	[ MnO4− ]0 	[H2C2O4 ]0 	[H + ]0 	Initial
rate
1	0.010	0.030	0.020	0.60
2	0.020	0.020	0.020	1.6
3	0.020	0.030	0.020	2.4
4	0.020	0.030	0.010	2.4

What is the order of this reaction in H2C2O4?

Answer 11

1

Question 12

Nitrogen monoxide reacts with chlorine gas according to the following equation.

2NO(g) + Cl2(g) → 2NOCl(g)

This reaction is second order in [ NO] and first order in [Cl2 ]. If the rate constant at a particular temperature is 180 M −2 s−1, what is d [ NOCl] / dt when the initial concentration of NO is 0.35 M and the initial concentration of Cl2 is 0.15 M?

Answer 12

6.6 M / s