Question

The rate of reaction $A \rightarrow P$ is $1.25 \times 10^{-2}$ mol dm$^{-3}$ s$^{-1}$ when $[A] = 0.5$ M. Calculate the rate constant if the reaction is second order in A.

• A. 0.05
• B. 0.04
• C. 0.03
• D. 0.01

Hint:

For $n^{th}$ order reactions, the units of $k$ are (mol dm$^{-3}$)$^{1-n}$ s$^{-1}$. For $n=2$, it is mol$^{-1}$ dm$^{3}$ s$^{-1}$.

Answer 1

The Correct Option is A

Step 1: Concept
For a second-order reaction, the rate law is expressed as Rate $= k[A]^{2}$, where $k$ is the rate constant and $[A]$ is the molar concentration of the reactant.

Step 2: Meaning
We are given:
Rate $= 1.25 \times 10^{-2}$ mol dm$^{-3}$ s$^{-1}$
$[A] = 0.5$ M (which is $0.5$ mol dm$^{-3}$)

Step 3: Analysis
Substitute the given values into the rate law equation:
$1.25 \times 10^{-2} = k \times (0.5)^{2}$
$1.25 \times 10^{-2} = k \times 0.25$
$k = \frac{1.25 \times 10^{-2}}{0.25}$
$k = 5 \times 10^{-2}$

Step 4: Conclusion
$k = 0.05$ mol$^{-1}$ dm$^{3}$ s$^{-1}$. Comparing this with the options, the value is 0.05. Final Answer: (A)