Question

Which of the following correctly represents the integrated rate law equation for a first order reaction in the gas phase?

• A. \( k = \frac{2.303}{t} \times \log \frac{P_i}{P_i - P} \)
• B. \( k = \frac{2.303}{t} \times \log \frac{P_i}{2P_i - P} \)
• C. \( k = \frac{2.303}{t} \times \log \frac{2P_i}{P_i - P} \)
• D. \( k = \frac{2.303}{t} \times \log \frac{P_i - P}{2P_i} \)

Hint:

For first-order reactions, the integrated rate law involves a logarithmic relationship between the concentration and time.

Answer 1

The Correct Option is A

Step 1: Understand the integrated rate law for a first order reaction.
For a first-order reaction, the integrated rate law is given by: \[ \ln \frac{P_i}{P_i - P} = kt \] We can express this in log base 10 as: \[ \log \frac{P_i}{P_i - P} = \frac{kt}{2.303} \] Rearranging for \( k \): \[ k = \frac{2.303}{t} \times \log \frac{P_i}{P_i - P} \] Thus, the correct answer is (A).