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 ${\mathrm{P}}_{\mathrm{i}}$. After the lapse of time t, the total pressure of the system increased by X units and became ${\mathrm{P}}_{\mathrm{t}}$. The rate constant k for the reaction is:

1. $\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{P_{\mathrm{i}}}{P_{\mathrm{i}}-\mathrm{x}}$

2. $\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{P_{\mathrm{i}}}{2P_{\mathrm{i}}-P_{\mathrm{t}}}$

3. $\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{P_{\mathrm{i}}}{2P_{\mathrm{i}}+P_{\mathrm{t}}}$

4. $\mathrm{k}=\frac{2.303}{\mathrm{t}}\log \frac{P_{\mathrm{i}}}{P_{\mathrm{i}}+\mathrm{x}}$

A first-order reaction is 50 % completed in 1.26 x 10¹⁴ s. The time required for 100 % completion
of the reaction will be:

1. 1.26 × 10¹⁵ s

2. 2.52 × 10¹⁴ s

3. 2.52 × 10²⁸ s

4. Infinite

The value of the rate constant of a pseudo-first-order reaction-

The correct statements among the following regarding a balanced chemical equation of an elementary reaction are-

1. (a, b)
2. (b, c)
3. (c, d)
4. (a, d)

The correct graphical representation of first-order reaction is:

(a)		(b)
(c)		(d)