First order gas phase reaction
$$A \to B + C$$
$$p_i$$ = initial pressure of gas A, $$p_t$$ = total pressure of the reaction mixture at time $$t$$
Expression of rate constant (k) is

A

$$\frac{1}{t} \ln \frac{p_i}{2p_i - p_t}$$

B

$$\frac{1}{t} \ln \frac{2p_i}{p_i - p_t}$$

C

$$\frac{1}{t} \ln \frac{p_i}{3p_i - 2p_t}$$

D

$$\frac{1}{t} \ln \frac{3p_t}{4p_i - p_t}$$