Question

The rate constant of a first order reaction is 6.9 × 10^–3 s^–1. How much time will it take to reduce the initial concentration to its 1/8^thvalue?

• A. 100 s
• B. 200 s
• C. 300 s
• D. 400 s

Answer 1

Answer: (C)

300 s

Answer 2

t_1/2 = $\frac{0.693}{K}$ = $\frac{0.693}{6.9 \times 10^{–3}}$ = 100 sec

1M $\overset{\quad t_{1/2}\quad}{\rightarrow}\frac{1}{2}M$ $\xrightarrow { \mathrm { t } _ { 1 / 2 } } \frac { 1 } { 4 } \mathrm { M }$ $\overset{\quad t_{1/2}\quad}{\rightarrow}\frac{1}{8}M$,

$3t_{1/2}$ = 300 sec