Physical Chemistry Third Edition

11.3 Forward Reactions with More Than One Reactant 499

equal to 696 s. Find the order of the reaction and the value

of the rate constant.

11.11A certain reaction with a single reactant is found to be
fourth order and to have at a certain temperature a half-life
of 10.00 s with an initial concentration of 0.100 mol L−^1.
a.Find the concentration of the reactant after a reaction
time of 15.00 s for the same initial concentration and
temperature.
b.Find the concentration after a reaction time of 30.00 s.

11.12The following data were taken for the gas-phase
dimerization of butadiene at some fixed temperature.

Time/min P/atm Time/min P/atm

0 0.8315 55.08 0.6450

3. 25 0.8138 68.05 0.6244

8. 02 0.7886 90.05 0.5954

12. 18 0.7686 119.00 0.5694

17. 30 0.7464 176.67 0.5332

24. 55 0.7194 259.50 0.5013

33. 00 0.6944 373.00 0.4698

42. 50 0.6701

a.Assuming ideal gas behavior, show that

PB 2 P−PB(0)

wherePBis the partial pressure of butadiene andPis

the observed pressure.

b.Find the order of the reaction and the value of the rate

constant at this temperature.

11.13For a reaction of a single reactant at a certain fixed

temperature, the following data were presented:

Time/s [A]/mol L−^1

01. 000

30 0. 7912

60 0. 6415

90 0. 5306

120 0. 4462

150 0. 3804

180 0. 3283

210 0. 2860

Assume that the reverse reaction can be neglected. Show

that the order of the reaction is 3/2 and find the value of

the rate constant at this temperature.

11.14The gas-phase dimerization of butadiene,

2C 4 H 6 −→C 8 H 12

follows second-order kinetics. At timet0, pure

butadiene is introduced into a vessel at 599 K and

0.832 atm. At timet 60 .9 minutes, the total pressure is

0.635 atm. Assume that both gases are ideal and that no

back reaction occurs.

a.Find the partial pressure of butadiene at this time.

b.Find the value of the second-order rate constant at this

temperature.

c.Find the half-life of the reaction under these

conditions.

d.Find the partial pressure of butadiene and the total

pressure att 100 .0 minutes.

11.3 Forward Reactions with More Than One

Reactant

Reactions with more than one reactant are somewhat more complicated than reactions

with a single reactant.

Integration of the Rate Law

Consider a reaction that is first order in each of two reactants:

aA+bB−→products (11.3-1)