For the first order thermal decomposition reaction, following data was obtained : Calculate rate constant. [Given : log 3 = 0.48]
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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.
Step 1: Conceptual Overview:
For a gas-phase reaction of the form \( A \rightarrow B + C \), the pressure increases as the reaction progresses. We relate the partial pressure of reactant A to the total pressure in order to calculate the rate constant of the reaction. Step 2: Detailed Explanation:
Given:
- Initial pressure of A (\( P_i \)) = 0.30 atm
- Total pressure after 30 seconds (\( P_t \)) = 0.50 atm
- Time (\( t \)) = 30 s
We start by calculating the denominator of the rate constant expression. The change in pressure from reactant A is calculated as:
\[
\text{Denominator} = 2(0.30) - 0.50 = 0.60 - 0.50 = 0.10 \text{ atm}.
\]
The rate constant \( k \) can be calculated using the integrated rate law for a reaction where the pressure increases, as follows:
\[
k = \frac{2.303}{t} \log \left( \frac{P_i}{P_t - P_i} \right)
\]
Substituting the values:
\[
k = \frac{2.303}{30} \log \left( \frac{0.30}{0.10} \right)
\]
\[
k = \frac{2.303}{30} \log 3
\]
\[
k = \frac{2.303}{30} \times 0.4771
\]
\[
k = \frac{1.096}{30} = 0.0368 \, \text{s}^{-1}.
\]
Step 3: Final Conclusion:
The rate constant for the reaction is \( 0.0368 \, \text{s}^{-1} \).
