Question

Analyse the statements :

Statement 1: “Half life of every reactions depend upon the initial amount.’’

Statement 2 : “Half life depends on the initial amount except in the case of first order reactions.”

1. Which statement is correct?

2. Give the expressions for half life of a rst order reaction. State how it is related to the initial concentration.

3. Show that t_1/2 of zero order reaction depends on initial amount?

Answer 1

1. Statement 2.

2. t_1/2 = \(\frac{0.693}{k}\) 

t_1/2 of a first order reaction is independent of the initial concentration of the reacting species.

3. For a zero order reaction,

\(k=\frac{[R]_0\,-\,[R]}{t}\)

When t = t_1/2, [R] = [R]₀/2

\(k=\frac{[R]_0\,-\,[R]_0/2}{t}\)

\(k=\frac{[R]_0/2}{t_{1/2}}\) 

t_{1/2 =} \(\frac{[R]_0}{2k}\)

Where [R]₀ is the initial amount. i.e., t_1/2 of zero order reaction is directly proportional to the initial amount.