Question

The concentration of a reactant X decreases from $0.1 M$ to $0.005 M$ in $40 min$. If the reaction follows first order kinetics, the rate of the reaction when the concentration of X is $0.01 M$ will be:

• A. $1.73 \times 10^{4} M\cdot min^{-1}$
• B. $3.47 \times 10^{4} M\cdot min^{-1}$
• C. $3.47 \times 10^{-5} M\cdot min^{-1}$
• D. $7.5 \times 10^{-4} M\cdot min^{-1}$

Hint:

Rate for 1st order $= k \times \text{Concentration}$.

Answer 1

The Correct Option is D

Step 1: Concept
First order rate constant $k = \frac{2.303}{t} \log \frac{A_{0}}{A}$.
Step 2: Analysis
$k = \frac{2.303}{40} \log \frac{0.1}{0.005} = \frac{2.303}{40} \log 20 = 0.075$.
Rate $= k[X] = 0.075 \times 0.01$.
Step 3: Conclusion
Rate $= 7.5 \times 10^{-4} M\cdot min^{-1}$.
Final Answer: (D)