Question

For the first order thermal decomposition reaction, following data was obtained : Calculate rate constant.
[Given : log 3 = 0.48]

Hint:

In gas phase kinetics, always derive the expression for partial pressure of the reactant in terms of total pressure based on the stoichiometry of the reaction.

Answer 1

Step 1: Understanding the Concept:
For a gas phase reaction \( A \rightarrow B + C \), the pressure increases as the reaction proceeds. We relate the partial pressure of reactant A to the total pressure.
Step 2: Detailed Explanation:
Given: \( P_i = 0.30 \) atm, \( P_t = 0.50 \) atm, \( t = 30 \) s.
Denominator \( = 2(0.30) - 0.50 = 0.60 - 0.50 = 0.10 \) atm.
\[ k = \frac{2.303}{30} \log \left( \frac{0.30}{0.10} \right) \]
\[ k = \frac{2.303}{30} \log 3 \]
\[ k = \frac{2.303}{30} \times 0.48 \]
\[ k = \frac{1.10544}{30} = 0.036848 \]
Step 3: Final Answer:
The rate constant is \( 0.0368 s^{-1} \).