Question

For the reaction, $A\left(g\right) + 2B\left(g\right) \to C\left(g\right) +D\left(g\right)$
$\frac{dx}{dt} = k\left[A\right]\left[B\right]^{2}$
Initial pressure of $A$ and $B$ are respectively $0.60$ atm and $0.80$ atm. At a time when pressure of $C$ is $0.20$ atm, ratio of initial rate and final rate is $y$. What is the value of $y$?

Answer 1

$\left(\frac{dx}{dt}\right)_{\text{initial}} =kp_{A}p^{2}_{B} =k\left(0.60\right)\left(0.80\right)^{2}$
$\begin{matrix}A\left(g\right) +&2B\left(g\right) \to&C\left(g\right) +&D \left(g\right)\\ 0.60&0.80&0&0\\ \left(0.60 -x\right)&\left(0.80 -2x\right)&x&x\end{matrix}$
$p_{c} =X = 0.20$ atm
$\therefore p_{A} = 0.60 - 0.20 = 0.40$ atm
$p_{B} = 0.80 -0.40 = 0.40$ atm
$\therefore \left(\frac{dx}{dt}\right)_{\text{final}} = kp_{A}p^{2}_{B} =k\left(0.40\right)\left(0.40\right)^{2}$
$\therefore \frac{\left(\frac{dx}{dt}\right)_{\text{initial}}}{\left(\frac{dx}{dt}\right)_{\text{final}}}=\frac{k\left(0.60\right)\left(0.80\right)^{2}}{k\left(0.40\right)\left(0.40\right)^{2}} =6$
Thus, $y=6$