Question

For a first-order reaction, the half-life is given by \( t_{1/2} = \dfrac{0.693}{k} \). Which conclusion is correct?

• A. Depends on initial concentration
• B. Is inversely proportional to \( k \)
• C. Is directly proportional to concentration
• D. Increases with time

Hint:

Only first-order reactions have half-life independent of initial concentration. This is one of their most important properties.

Answer 1

The Correct Option is B

Concept: For a first-order reaction, the half-life expression is: \[ t_{1/2} = \frac{0.693}{k} \] where \( k \) is the rate constant.

Step 1: Understanding the formula.
From the formula: \[ t_{1/2} \propto \frac{1}{k} \] This means the half-life decreases if the rate constant increases.

Step 2: Checking dependence on concentration.
The formula contains only the rate constant \( k \) and no concentration term. Therefore, half-life of a first-order reaction is independent of initial concentration.

Step 3: Final conclusion.
Since half-life varies inversely with \( k \), the correct statement is: \[ \boxed{\text{(B) Is inversely proportional to } k} \]