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: Understanding the Concept:
The rate of a chemical reaction is proportional to the concentration of reactants raised to their stoichiometric coefficients in the rate law.
For a second-order reaction involving a single reactant A, the rate expression is given by \(r = k[A]^2\).
Step 2: Key Formula or Approach:
The formula to be used is:
\[ \text{Rate} = k[A]^2 \]
Where:
\(k\) is the rate constant.
\([A]\) is the concentration of reactant A.
Step 3: Detailed Explanation:
Given values from the problem:
Rate (\(r\)) = \(1.25 \times 10^{-2}\text{ mol dm}^{-3}\text{ s}^{-1}\)
Concentration (\([A]\)) = \(0.5\text{ M} = 0.5\text{ mol dm}^{-3}\)

Substitute these values into the second-order rate equation:
\[ 1.25 \times 10^{-2} = k \times (0.5)^2 \]
\[ 1.25 \times 10^{-2} = k \times 0.25 \]
To find \(k\), divide the rate by the square of the concentration:
\[ k = \frac{1.25 \times 10^{-2}}{0.25} \]
\[ k = \frac{0.0125}{0.25} \]
\[ k = 0.05 \]
Step 4: Final Answer:
The rate constant for the reaction is 0.05.