Question

A first-order reaction was started with a decimolar solution of the reactant, $8$ minutes and $20$ seconds later its concentration was found to be $M/100.$ So the rate of the reaction is

• A. $2.303 \times 10^{-5} sec^{-1}$
• B. $2.303 \times 10^{-4} sec^{-1}$
• C. $4.606 \times 10^{-3} sec^{-1}$
• D. $2.606 \times 10^{-5} sec^{-1}$

Answer 1

Answer: (C)

For first order reaction$K=\frac{2.303}{t}log\frac{a}{a-x}$
Given $a=\frac{1}{10}=1m$
$a-x=\frac{1}{100}=0.1m;t=500sec$
$\therefore K=\frac{2.303}{500}log \frac{10}{01}=\frac{2.303}{500}log 10$
$=\frac{2.303}{500}=0.004606=4.6\times10^{-3}sec^{-1}$