Question

The rate of a first-order reaction is $0.04mol{L}^{-1}{s}^{-1}$ at $10seconds$ and $0.03mol{L}^{-1}{s}^{-1}$ at $20seconds$ after initiation of the reaction. The half-life period of the reaction is :

• A. $24.1s$
• B. $34.1s$
• C. $44.1s$
• D. $54.1s$

Answer 1

Answer: (A)

Let the rate $=k\left[A\right]$

At $t=10seconds$

$0.04=k\left[A_1\right]$

At $t=20seconds$

$0.03=k\left[A_2\right]$

$\therefore$, in $10$ seconds concentration of $A$ decreases by $\frac{0.01}{k}\left[M\right]$

Using first order kinetics equation,

$10\times k=ln\left(\frac{0.04/k}{0.03/k}\right)$

$10\times k=0.028$

$k=0.028$

Half life of first order reaction $=\frac{ln2}{k}$

$t_{1/2}=\frac{ln2}{0.028}=24.1seconds$