Question

A first order reaction has a rate constant $23\times {10}^{-3}{s}^{-1}$. How long will it take to reduce $5.0\text{g}$ of the reactant to $3.0\text{g}$?

(Given: $log2=0.3,log3=0.5,log5=0.7$)

• A. 20 seconds
• B. 30 seconds
• C. 40 seconds
• D. 50 seconds

Answer 1

The correct option is A 20 seconds

Applying the first order rate equation
$k=\frac{2.303}{t}log\frac{a}{(a-n)}$
Where, $k=$ rate constant,
$a=$ initial amount of the reactant,
$a-n=$ amount of the reactant left after the reaction
$\therefore t=\frac{2.303}{23\times {10}^{-3}}log\frac{5}{3}\approx 20$ seconds