JEE MAIN - Chemistry (2025 - 7th April Evening Shift - No. 16)
A(g) → B(g) + C(g) is a first order reaction.
| Time | t | ∞ |
|---|---|---|
| Psystem | Pt | P∞ |
The reaction was started with reactant A only. Which of the following expressions is correct for rate constant k?
$\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{p}_{\infty}}{\mathrm{p}_{\mathrm{t}}}$
$\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{p}_{\infty}}{2\left(\mathrm{p}_{\infty}-\mathrm{p}_{\mathrm{t}}\right)}$
$\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{2\left(\mathrm{p}_{\infty}-\mathrm{p}_{\mathrm{t}}\right)}{\mathrm{p}_{\mathrm{t}}}$
$\mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{p}_{\infty}}{\left(\mathrm{p}_{\infty}-\mathrm{p}_{\mathrm{t}}\right)}$
Explanation
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$$\begin{aligned} & \mathrm{P}_{\mathrm{t}}=\mathrm{P}^{\mathrm{o}}+\mathrm{x} \Rightarrow \mathrm{x}=\mathrm{P}_{\mathrm{t}}-\mathrm{P}^{\mathrm{o}}=\mathrm{P}_{\mathrm{t}}-\frac{\mathrm{P}_{\infty}}{2} \\ & \mathrm{P}_{\infty}=2 \mathrm{P}^{\mathrm{o}} \Rightarrow \mathrm{P}^{\mathrm{o}}=\frac{\mathrm{P}_{\infty}}{2} \\ & \mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}^{\mathrm{o}}}{\mathrm{P}^o-\mathrm{x}} \\ & \mathrm{k}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}_{\infty}}{2\left(\mathrm{P}_{\infty}-\mathrm{P}_{\mathrm{t}}\right)} \end{aligned}$$
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