Question

Rate constant $k=2.303{\text{min}}^{-1}$ for a particular reaction. The initial concentration of the reaction is $1{\text{mol litre}}^{-1}$, then the rate of reaction after $1$ minute is:

• A. $2.303{\text{Mmin}}^{-1}$
• B. $0.2303{\text{Mmin}}^{-1}$
• C. $0.1{\text{Mmin}}^{-1}$
• D. None of these

Answer 1

The correct option is B $0.2303{\text{Mmin}}^{-1}$

Since the unit of rate constant is ${\text{min}}^{-1}$, thus it is a first order reaction.
For a first order reaction,
$k=\frac{2.303}{t}log\left(\frac{C_{A_0}}{C_A}\right)$
$2.303\times 1=2.303$log$\left(\frac{C_{A_0}}{C_A}\right)$
$\Rightarrow \frac{C_{A_0}}{C_A}=10$
$\therefore C_A=\frac{1}{10}=0.1M$
$\therefore$Rate after $1$ min
$r_1=k.C_A=2.303\times 0.1=0.2303{\text{Mmin}}^{-1}$