Question

For a homogeneous gaseous reaction, $A⟶B+C+D$, the initial pressure was $P_0$ while pressure at time $t$ was $P$. Derive an expression for rate constant $K$ in terms of $P_0,P$ and $t$.

[Assume first-order reaction]

Answer 1

$A\to$ $B+C+D$

At $t=0$ $P^0$ 0 0 0

At $t=t$ $P^0-P_1$ $P_1$ $P_1$ $P_1$

P is the pressure $P_1$ is the supposed quantity

$P=P^0-P_1+P_1+P_1+P_1=2P_1+P_0$

$P_1=\frac{P-P_0}{2}$

$P^0=P^0-\frac{P}{2}+\frac{P^0}{2}$

$K=\frac{2.303}{t}log\frac{P^0}{{P^0-P}_1}$

$K=\frac{2.303}{t}log\frac{2P^0}{{3P}^0-P}$