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

Answer: 6

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