Question
A first order reaction is half-completed in 45 minutes. How long does it need for $$99.9\% $$ of the reaction to be completed ?
A.
$$20\,{\text{hours}}$$
B.
$$10\,{\text{hours}}$$
C.
$$7\frac{1}{2}\,{\text{hours}}$$
D.
$$5\,{\text{hours}}$$
Answer :
$$7\frac{1}{2}\,{\text{hours}}$$
Solution :
$$\eqalign{
& {\text{k = }}\frac{{0.693}}{{45}}{\text{further}} \cr
& t = \frac{{2.303}}{{0.693}} \times 45\,\log \frac{{100}}{{100 - 99.9}} \cr
& = \frac{{2.303 \times 45 \times 3}}{{0.693}} \cr
& = 7\frac{1}{2}hours. \cr} $$