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 $
$t_{2 / 3}=\frac{2.303 \times 0.4771}{5.48 \times 10^{-14}}$
$=2.01 \times 10^{13} s$