Question

For product formation from only one type of reactant (e.g. A \(\rightarrow\) product), the CORRECT match for the order of the reaction (given in Column I) with the half-life expression (given in Column II) is:
(\([A]_0 \) is the initial concentration and \( k_r \) is the rate constant)

• A. i–R, ii–P, iii–S
• B. i–Q, ii–P, iii–R
• C. i–S, ii–i, iii–Q
• D. i–Q, ii–P, iii–S

Hint:

For a reaction of order \( n \), the half-life expressions are different:
- Zero order: \( t_{1/2} = \frac{[A]_0}{2k_r} \),
- First order: \( t_{1/2} = \frac{\ln 2}{k_r} \),
- Second order: \( t_{1/2} = \frac{1}{k_r[A]_0} \).

Answer 1

The Correct Option is B

To determine the correct matching, let's consider the half-life expressions for each order of reaction: 
- i. Zero Order: For a zero-order reaction, the half-life is independent of the initial concentration and is given by the expression: \[ t_{1/2} = \frac{[A]_0}{2k_r}. \] Thus, the correct match for zero-order is \( i \)–Q. 
- ii. First Order: For a first-order reaction, the half-life depends on the rate constant and is given by: \[ t_{1/2} = \frac{\ln 2}{k_r}. \] Thus, the correct match for first-order is \( ii \)–P. 
- iii. Second Order: For a second-order reaction, the half-life is inversely proportional to the initial concentration and is given by: \[ t_{1/2} = \frac{1}{k_r[A]_0}. \] Thus, the correct match for second-order is \( iii \)–R. 
Therefore, the correct answer is option (B).