Question

What is the two third life of a first order reaction having $k=5.48\times 10^{-14}{s}^{-1}$

• A. $2.01\times 10^{11}s$
• B. $2.01\times 10^{13}s$
• C. $8.08\times 10^{13}s$
• D. $16.04\times 10^{11}s$

Answer 1

Answer: (B)

For two-third of a reaction:
$[A{]}_0=a,[A]=a-\frac{2}{3}a=\frac{a}{3}$
$t_{2/3}=\frac{2.303}{k}\log \frac{[A{]}_0}{[A]}$
$=\frac{2.303}{k}\log \frac{a}{\frac{a}{3}}=\frac{2.303}{k}\log 3$
$t_{2/3}=\frac{2.303\times 0.4771}{5.48\times 10^{-14}}$
$=2.01\times 10^{13}s$