Q.The half life of the homogeneous gaseous reaction $SO_2Cl_2 \rightarrow SO_2+Cl_2$ which obeys first order kinetics is 8.0 minutes. How long will it take for the concentration of $SO_2Cl_2$ to be reduced to 1% of the initial value?

Step 1. $k=\dfrac{0.693}{t_{1/2}}=\dfrac{0.693}{8.0}=0.08663\ \text{min}^{-1}$.

Step 2. '1% of the initial value remaining' means $[A]_0/[A]=100/1=100$.

Step 3. $t=\dfrac{2.303}{k}\log100=\dfrac{2.303}{0.08663}\times2=26.59\times2=53.15\ \text{minutes}$. …

Convert the given half life into a rate constant, then use the first order time formula with the ratio $[A]_0/[A]= …

• Using $[A]_0/[A]=1$ or $99$ instead of the correct $100$ (since 'reduced to 1% of the initial value' means only 1 part in 100 …