Question

For a first order reaction $A\to \text{Products}$
The concentration of A changes from $0.1M$ to $0.025M$ in 40 minutes. The rate of reaction when the concentration of A is $0.01M$ is:

• A. $3.46mol{L}^{-1}mi{n}^{-1}$
• B. $3.46\times {10}^{-4}mol{L}^{-1}mi{n}^{-1}$
• C. $0.52\times {10}^{-2}mol{L}^{-1}mi{n}^{-1}$
• D. $5.2mol{L}^{-1}mi{n}^{-1}$

Answer 1

The correct option is B $3.46\times {10}^{-4}mol{L}^{-1}mi{n}^{-1}$

For a first order reaction:
$A\to \text{Products}$
$\left[A\right]=[A{]}_0{e}^{-kt}$
Here
$[A{]}_0=0.1M$ is the intial concentration
$\left[A\right]=0.025M$ is the concentration at time t=40 minutes
$k$ is the first order rate constant.

$0.025=0.1\times e^{-k\times 40}\ln 4=k\times 40k=\frac{\ln 4}{40}mi{n}^{-1}\approx 0.0346mi{n}^{-1}$
For a first order reaction:
$A\to \text{Products}$
$\text{Rate}=k\left[A\right]$
At, $\left[A\right]=0.01M$
$\text{Rate}=0.0346\times 0.01mol{L}^{-1}mi{n}^{-1}\text{Rate}=3.46\times {10}^{-4}mol{L}^{-1}mi{n}^{-1}$