# Time required to decompose

Question:

Time required to decompose SO2Cl2 to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

Solution:

We know that for a 1st order reaction,

$t_{1 / 2}=\frac{0.693}{k}$

It is given that t1/2 = 60 min

$\therefore k=\frac{0.693}{t_{1 / 2}}$

$=\frac{0.693}{60}$

$=0.01155 \mathrm{~min}^{-1}$

$=1.155 \mathrm{~min}^{-1}$

Or $k=1.925 \times 10^{-4} \mathrm{~s}^{-1}$