1. Tardigrade
  2. Question
  3. Chemistry
  4. Consider a first order gas phase decomposition reaction given below: A(g)arrow B(g)+C(g) 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 .

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Q. Consider a first order gas phase decomposition reaction given below: $A_{\left(g\right)}\rightarrow B_{\left(g\right)}+C_{\left(g\right)}$
The initial pressure of the system before decomposition of $A$ was $p_{i}.$ After lapse of time ‘t’ total pressure of the system increased by $x$ units and became $‘p_{t}’.$ The rate constant $k$ for the reaction is given as _____________ .

Chemical Kinetics

Solution:

If $x$ atm be the decrease in pressure of $A$ at time $t$ and one mole each of $B$ and $C$ is being formed, the increase in pressure of $B$ and $C$ will also be $x$ atm each.
$\begin{matrix}A_{\left(g\right)}&\rightarrow&B_{\left(g\right)}&+&C_{\left(g\right)}\end{matrix}$
$\begin{matrix}At\,t=0&p_{i} atm&0\,atm&0\,atm\\ At\, time\,t&\left(p_{i}-x\right)atm&x atm&x atm\end{matrix}$
where, $p_{i}$ is the initial pressure at time $t = 0$
$p_{t}$ $=\left(p_{i}-x\right)+x+x=p_{i}+x$
$x=\left(p_{t}-p_{i}\right)$
where, $p_{A}=p_{i}-x=p_{i}-\left(p_{t}-p_{i}\right)=2p_{i}-p_{t}$
$k=\left(\frac{2.303}{t}\right)$ $\left(log\frac{p_{i}}{p_{A}}\right)$ $=\frac{2.303}{t}log\frac{p_{i}}{\left(2p_{i}-p_{t}\right)}$