Physical Chemistry Third Edition

11.7 The Experimental Study of Fast Reactions 515

PROBLEMS

Section 11.6: Competing Reactions

11.36Consider the competing reactions with significant reverse
reactions:

(1) A
F

(2) A
G

Assume that all of the reactions are first order.

a.Write a computer program using Euler’s method to

integrate the rate differential equations for the case

that the initial concentration of A is nonzero and those

of F and G are zero.

b.Run the program for several sets of rate constants.

11.7 The Experimental Study of Fast Reactions

The “classical” method of studying reaction rates is to mix the reactants and then to

determine the concentration of some reactant or product as a function of time. This

method is clearly inadequate if the reaction time is comparable to or shorter than the

time required to mix the reactants.

Flow Techniques

There are two common flow methods that can be used to speed up the mixing of

liquids or gases. In thecontinuous-flow method, two fluids are forcibly pumped into a

chamber where they are rapidly mixed. The newly mixed fluid passes into a transparent

tube of uniform diameter. The flow rates into the mixing chamber are kept constant

so that the distance along the tube is proportional to the elapsed time after mixing.

The concentration of a reactant or product is determined spectrophotometrically as a

function of position along the tube, using the tube as a spectrophotometer cell.

In thestopped-flow method, two fluids are forced into a mixing chamber as in the

continuous-flow method. After a steady state is attained the flow of solutions into

the chamber is suddenly stopped and the concentration of a product or reactant is

determined spectrophotometrically as a function of time as the system approaches

equilibrium. The mixing chamber is used as a spectrophotometer cell. Figure 11.7

schematically shows a stopped-flow apparatus. Flow systems have been designed that

can mix two liquids in a tenth of a millisecond, so that reactions with half-lives ranging

from 1 millisecond to 1 second can be studied by either of the two flow methods.

Spectrophotometers can be built that record concentrations very quickly, so the response

of the spectrophotometer does not limit this method.

Relaxation Techniques

Relaxation techniques do not rely on mixing, but use the fact that equilibrium compo-

sitions can depend on temperature and pressure. The experiment begins with a system

at equilibrium. The temperature or the pressure of the system is suddenly changed so

that it is no longer at equilibrium and the relaxation of the system to its new equilibrium

state is then monitored.

The Shock-Tube Method

In theshock-tube methoda reaction vessel is constructed with two chambers separated

by a diaphragm that can be ruptured suddenly. On one side is a mixture of gaseous