Question

The rate of reaction \(A \rightarrow P\) is \(1.25 \times 10^{-2}\ \text{mol dm}^{-3}\text{s}^{-1}\) when \([A] = 0.5\ \text{M}\). 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 reaction orders:
• First order: \[ \text{Rate} = k[A] \]
• Second order: \[ \text{Rate} = k[A]^2 \]
• Third order: \[ \text{Rate} = k[A]^3 \] Always substitute concentration carefully before solving for \(k\).

Answer 1

The Correct Option is A

Concept: The rate law for a reaction relates the rate of reaction to the concentration of reactants. For a reaction that is second order with respect to reactant \(A\): \[ \text{Rate} = k[A]^2 \] where:
• \(k\) = rate constant
• \([A]\) = concentration of reactant
• Rate = rate of reaction To find the rate constant, we rearrange the equation: \[ k = \frac{\text{Rate}}{[A]^2} \]

Step 1: Writing the given data.
Given: \[ \text{Rate} = 1.25 \times 10^{-2}\ \text{mol dm}^{-3}\text{s}^{-1} \] \[ [A] = 0.5\ \text{M} \] Reaction order with respect to \(A = 2\)

Step 2: Writing the rate law equation.
Since the reaction is second order: \[ \text{Rate} = k[A]^2 \] Substituting the given values: \[ 1.25 \times 10^{-2} = k(0.5)^2 \]

Step 3: Calculating \((0.5)^2\).
\[ (0.5)^2 = 0.25 \] Thus: \[ 1.25 \times 10^{-2} = k(0.25) \]

Step 4: Finding the value of rate constant \(k\).
\[ k = \frac{1.25 \times 10^{-2}}{0.25} \] \[ k = 5 \times 10^{-2} \] \[ k = 0.05 \]

Step 5: Final conclusion.
Therefore, the value of the rate constant is: \[ \boxed{0.05} \] Hence, the correct answer is: \[ \boxed{(1)\ 0.05} \]