Question

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

• A. $\frac{1}{6}$
• B. $\frac{1}{48}$
• C. $\frac{1}{4}$
• D. $\frac{1}{24}$

Answer 1

The correct option is A $\frac{1}{6}$

$A+2B⟶C+D$

$0.6-x$ $0.8-2x$ $x$ $x$

Given : $x=0.2$

$\therefore P_A=0.6-0.2=0.4,P_B=0.8-(2\times 0.2)=0.4$

Rate at this time $=K\left[A\right][B{]}^2=K\times 0.4\times (0.4{)}^2$

Initial rate $=K\times 0.6\times (0.8{)}^2$

$\therefore$ Relative rate ratio $=\frac{K\times 0.4\times (0.4{)}^2}{K\times 0.6\times (0.8{)}^2}=\frac{1}{6}$

Therefore, the correct option is A.