Consider the first-order gas-phase decomposition reaction given below.
A(g) → B(g) + C(g)
The initial pressure of the system before the decomposition of A was . After the lapse of time t, the total pressure of the system increased by X units and became . The rate constant k for the reaction is:
1. | 2. | ||
3. | 4. |
HINT: Use First order gas-phase reaction
Explanation:
Initially At time t
For the first order reaction
\(\begin{aligned} & \mathrm{P}_{\mathrm{t}}=\mathrm{P}_{\mathrm{i}}-\mathrm{x}+\mathrm{x}=\mathrm{}\mathrm{P}_{\mathrm{i}}+\mathrm{x} \\ & \mathrm{x}=\mathrm{P}_{\mathrm{t}}-\mathrm{P}_{\mathrm{i}} \\ & \mathrm{k}=\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{P}_i}{\mathrm{P}_i-\mathrm{x}} \\ & =\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{P}_i}{\mathrm{P}_i-\left(\mathrm{P}_{\mathrm{t}}-\mathrm{P}_i\right)} \\ & =\frac{2.303}{\mathrm{t}} \log \frac{\mathrm{P}_i}{2 \mathrm{P}_i-\mathrm{P}_{\mathrm{t}}} \end{aligned}\)
According to the problem, the initial pressure of the system is Pi, and after a certain time t, the total pressure of the system increased by X units and became Pt. As X is partial pressure and we write our final expression in initial pressure and final pressure so most suitable answer will be the 2nd one not 1st as it uses the term X as the it is a partial pressure .
Hence, option second is the correct answer.
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