Question

The half-life of the chemical reaction, A \(\rightarrow\) Product, for initial reactant concentrations of 0.1 and 0.4 mol L\(^{-1}\) are 200 and 50 s, respectively. The order of the reaction is

• A. 0
• B. 1
• C. 2
• D. 3

Hint:

For first-order reactions, the half-life is independent of the initial concentration. For zero- and second-order reactions, the half-life depends on the initial concentration.

Answer 1

The Correct Option is C

Step 1: Understand the relationship for half-life.
The half-life of a reaction depends on its order. For a reaction of order \(n\), the half-life \( t_{1/2} \) is given by: - For a zero-order reaction: \( t_{1/2} = \frac{[A_0]}{2k} \) - For a first-order reaction: \( t_{1/2} = \frac{0.693}{k} \) - For a second-order reaction: \( t_{1/2} = \frac{1}{k[A_0]} \) Step 2: Apply the data.
We have two different initial concentrations (0.1 and 0.4 mol L\(^{-1}\)) and corresponding half-lives (200 and 50 s). If the reaction is first-order, the half-life should be independent of the initial concentration. This matches the observed data, suggesting the reaction is first-order.
Step 3: Conclusion.
The order of the reaction is 1, corresponding to option (B).