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  • For a first order reaction A → Products The concentration of A changes from 0.1 M to 0.025 M in 40 minutes. The rate of reaction when the concentratio

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

Option: 1

3.46 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}


Option: 2

3.46 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}


Option: 3

0.52 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}


Option: 4

5.2 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}


Answers (1)

best_answer

For a first order reaction:
A → Products
\mathrm{[A]=[A]_0 e^{-k t}}
Here
\mathrm{ [A]_0=0.1 M } is the intial concentration
\mathrm{[A]=0.025 M }  is the concentration at time t=40 minutes k is the first order rate constant.
\mathrm{ 0.025=0.1 \times e^{-k \times 40} }

\mathrm{\ln 4=k \times 40}

\mathrm{k=\frac{\ln 4}{40} min ^{-1} \approx 0.0346 \mathrm{~min}^{-1}}
For a first order reaction:
A → Products
Rate =k[A]
At, [A]=0.01 M
Rate \mathrm{=0.0346 \times 0.01 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}}
Rate \mathrm{=3.46 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}}

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