Question

A reaction $2A+B\stackrel{K}{\to }C+D$ is first order w.r.t. and second order w.r.t. . Initial conc. (t=0) of is $C_0$ while is $2C_0$. If at as 300 minutes the conc. of C is $\frac{C_0}{4}$ then rate expression at t = 300 minutes is

• A. $R=7C_0^3\frac{k}{16}$
• B. $R=27C_0^3\frac{k}{32}$
• C. $R=247C_0^3\frac{k}{64}$
• D. $R=49C_0^3\frac{k}{32}$

Answer 1

The correct option is D $R=49C_0^3\frac{k}{32}$

$\begin{array}{ccccccc}2A& +& B& \stackrel{K}{\to }& C& +& D\\ C_0& & {}^2{C}_0-x& & 0& & 0\\ C_0-2x& & 2C_0-x& & x& & x\end{array}$
$X=\frac{C_0}{4}\left[A\right]=C_0-\frac{C_0}{2}=\frac{C_0}{2}\left[B\right]=2C_0-\frac{C_0}{4}=\frac{7C_0}{4}R=K.\left[A\right][B{]}^2=K.\frac{C_0}{2}.{\left(\frac{7C_0}{4}\right)}^2=\frac{49C_0^{3}K}{32}$