The Chemistry Maths Book, Second Edition

92 Chapter 3Transcendental functions

wheref 1 = 1 γpis the fugacity and γis the fugacity coefficient. Express pas an explicit

function of the other variables.

42.In a first-order decomposition reaction, A 1 → 1 products, the amount of substance A at

time tis

x(t) 1 = 1 x(0)e

−kt

wherex(0)is the initial amount of A, and kis the rate constant. The time taken for the

amount of A to fall to half of its initial value is called the half-life, τ

122

, of the reaction.

Find the half-life for rate constants: (i)k 1 = 1 3 s

− 1

, (ii)k 1 = 110

− 5

s

− 1

.

Section 3.8

43.As in Example 3.30, sketch (i)x

2

, e

−x

, x

2

e

−x

, (ii)x

− 2

, e

x

, x

− 2

e

x

.