Question

For a first order reaction, which of the following statements are correct? A. The half life are independent of initial concentration. B. The rate of constant has unit of \(s^{-1}\). C. The plot of \(\ln[A]\) vs. time is linear. D. A rate is independent of reactant concentration.

• A. A, B and C only
• B. A, B, C and D
• C. A and B only
• D. B and C only

Hint:

For a first order reaction, remember: \(t_{1/2}=\frac{0.693}{k}\), unit of \(k\) is \(s^{-1}\), and \(\ln[A]\) vs time gives a straight line.

Answer 1

The Correct Option is A

Concept:
For a first order reaction, the rate of reaction depends directly on the concentration of one reactant. The general rate law is: \[ \text{Rate} = k[A] \] where \(k\) is the rate constant and \([A]\) is the concentration of reactant.

Step 1: Check statement A.
For a first order reaction, half-life is given by: \[ t_{1/2} = \frac{0.693}{k} \] This formula does not contain initial concentration. Therefore, the half-life of a first order reaction is independent of initial concentration. \[ A \text{ is correct} \]

Step 2: Check statement B.
For a first order reaction: \[ \text{Rate} = k[A] \] The unit of rate is: \[ \text{mol L}^{-1}\text{s}^{-1} \] The unit of concentration is: \[ \text{mol L}^{-1} \] So, \[ k = \frac{\text{Rate}}{[A]} \] \[ k = \frac{\text{mol L}^{-1}\text{s}^{-1}}{\text{mol L}^{-1}} \] \[ k = s^{-1} \] Therefore, the unit of rate constant for a first order reaction is \(s^{-1}\). \[ B \text{ is correct} \]

Step 3: Check statement C.
The integrated rate equation for a first order reaction is: \[ \ln[A] = \ln[A]_0 - kt \] This equation is similar to: \[ y = c + mx \] Hence, the plot of \(\ln[A]\) versus time is a straight line. \[ C \text{ is correct} \]

Step 4: Check statement D.
For a first order reaction: \[ \text{Rate} = k[A] \] This shows that the rate depends on reactant concentration. Therefore, the statement that rate is independent of reactant concentration is wrong. \[ D \text{ is incorrect} \] Thus, correct statements are: \[ A, B \text{ and } C \text{ only} \] \[ \therefore \text{Correct Answer is (A)} \]