Question

A substance reacts according to 1${}^{st}$ order kinetic and rate constant for the reaction is $1\times {10}^{-2}se{c}^{-1}$. If the initial concentration is 1 M. Rate of the reaction after 1 minute is:

• A. $5.49\times {10}^{-3}mollitr{e}^{-1}se{c}^{-1}$
• B. $5.55\times {10}^{-3}mollitr{e}^{-1}se{c}^{-1}$
• C. $7.49\times {10}^{-3}mollitr{e}^{-1}se{c}^{-1}$
• D. None of these

Answer 1

The correct option is A $5.49\times {10}^{-3}mollitr{e}^{-1}se{c}^{-1}$

$K=\frac{2.303}{t}log\frac{a}{(a-X)}$

$\therefore {10}^{-2}=\frac{2.303}{1\times 60}log\frac{1}{(1-X)}(\because t=1minute=60sec)$

$\therefore (1-X)=0.549$

Therefore, rate after 1 minute $=K[1-X{]}^1$

$={10}^{-2}\times \left(0.549\right)=5.49\times {10}^{-3}mol{L}^{-1}se{c}^{-1}$

Hence, the correct option is $A$