Question

The time required to decompose SO\(_2\)Cl\(_2\) to half of its initial amount is 60 minutes. Calculate rate constant for this first order reaction?

• A. \( 1.551 \times 10^{-2} \, \text{min}^{-1} \)
• B. \( 4.158 \times 10^{-2} \, \text{min}^{-1} \)
• C. \( 1.155 \times 10^{-2} \, \text{min}^{-1} \)
• D. \( 2.651 \times 10^{-2} \, \text{min}^{-1} \)

Hint:

For first-order reactions, the rate constant can be calculated using the equation \( t_{1/2} = \frac{0.693}{k} \), where \( t_{1/2} \) is the half-life of the reaction.

Answer 1

The Correct Option is C

Step 1: Understanding the first order reaction.
For a first-order reaction, the half-life (\( t_{1/2} \)) is related to the rate constant \( k \) by the equation: \[ t_{1/2} = \frac{0.693}{k} \] Rearranging the formula, we can solve for the rate constant: \[ k = \frac{0.693}{t_{1/2}} \] Step 2: Substituting the known values.
Given that the half-life \( t_{1/2} = 60 \, \text{min} \), we can substitute this into the equation to find \( k \): \[ k = \frac{0.693}{60} = 1.155 \times 10^{-2} \, \text{min}^{-1} \] Step 3: Conclusion.
The correct answer is (C) \( 1.155 \times 10^{-2} \, \text{min}^{-1} \).