Question

\(A \rightarrow B\) is a first order reaction. What is the concentration of reactant A after 28.8 seconds if the initial concentration of A is 0.1 M and rate constant \(k = 0.0693\,s^{-1}\)? (Given \(e = 2.718\))

• A. \(0.1/e\) M
• B. \(0.1/e^2\) M
• C. \(0.1/e^3\) M
• D. \(0.1/e^4\) M

Hint:

For first-order reactions, always remember: \([A] = [A]_0 e^{-kt}\), so \(kt\) directly gives the power of \(e\).

Answer 1

The Correct Option is B

Step 1: Integrated rate law for first-order kinetics.
[A] = [A]₀ e^(-kt).

Step 2: Substituting the given parameters.
[A]₀ = 0.1 M, k = 0.0693 s⁻¹, t = 28.8 s.

Step 3: Computing the exponent.
kt = 0.0693 × 28.8 ≈ 1.994 ≈ 2, so e^(-kt) ≈ e⁻².

Step 4: Final concentration.
[A] = 0.1 × e⁻² = 0.1/e² M.

Step 5: Interpretation.
The reactant amount decays exponentially, dropping to 1/e² of its initial value after this interval.