# Decomposition of X exhibits a rate constant of

Question:

Decomposition of X exhibits a rate constant of $0.05 \mu \mathrm{g} /$ year. How many years are required for the decomposition of $5 \mu \mathrm{g}$ of X into $2.5 \mu \mathrm{g}$ ?

1. 50

2. 25

3. 20

4. 40

Correct Option: 1

Solution:

Rate constant of decomposition of $X=0.05 \mathrm{mg} /$ year.

Unit of rate constant confirms that the decomposition of $X$ is a zero order reaction.

For zero order kinetics,

$[\mathrm{X}]=[\mathrm{X}]_{0}-k t$

$k t=[\mathrm{X}]_{0}-[\mathrm{X}]$

$t=\frac{[X]_{0}-[X]}{k}$

$t=\frac{5-2.5}{0.05}$

$=\frac{2.5}{0.05}=50$ years