Question

Consider a first order gas phase decomposition reaction given below : $A\left(g\right)\to B\left(g\right)+C\left(g\right)$ The initial pressure of the system before decomposition of A was pi. After lapse of time ‘t’, total pressure of the system increased by x units and became ‘pt’. The rate constant k for the reaction is given as _________.

• A. $k=\frac{2.303}{t}log\frac{pi}{pi-x}$
• B. $k=\frac{2.303}{t}log\frac{pi}{2pi+pt}$
• C. $k=\frac{2.303}{t}log\frac{pi}{pi+x}$
• D. $k=\frac{2.303}{t}log\frac{pi}{2pi-pt}$

Answer 1

The correct option is D $k=\frac{2.303}{t}log\frac{pi}{2pi-pt}$

First order gas phase decomposition reaction is given:

$A\left(g\right)\to B\left(g\right)+C\left(g\right)$

For this reaction, pressure of the system after time t can be shown as:
$A\left(g\right)\to B\left(g\right)+C\left(g\right)$

$t=0p_{i}00$

$t=t{p}_i-xxx$

Total pressure at time t

$p_i-x+x+x=p_t$

$p_i+x=p_t$

$x=p_t-p_i$

Rate constant (𝑘) for the first order reaction is given in terms of pressure of the reactant(A) is given as:

$k=\frac{2.303}{t}log\frac{p_i}{p_i-x}=\frac{2.303}{t}log\frac{p_i}{pi-(p_t-p_i)}$

$k=\frac{2.303}{t}log\frac{p_i}{2p_i-p_t}$

Hence, option (B) is correct.