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 $2.5 \mu \mathrm{g}$ ?
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
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