Question

A reaction $2A+B\stackrel{k}{\to }C+D$ is first order with respect to $A$ and 2nd order with respect to B. Initial conc. $(t=0)$ of $A$ is $C_0$ while $B$ is $2$ $C_0$. If at $t=30$ minutes the conc. of $C$ is $\frac{C_0}{4}$ then rate expression at the same time is:

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

Answer 1

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

The reaction is first order with respect to A and 2nd order with respect to B .
Rate $=k\left[A\right][B{]}^2$
The initial concentration $(t=0)$ of A is $C_0$ while that of B is $2C_0$.
At $t=30$ minutes the concentration of C is $\frac{C_0}{4}$
The concentration of B at $t=30$ minutes will be $2C_0-\frac{C_0}{4}=\frac{7C_0}{4}$
The concentration of A at $t=30$ minutes will be $C_0-\frac{C_0}{2}=\frac{C_0}{2}$
The rate expression at $t=30$ is
rate $=k\left[A\right][B{]}^2$
rate $=k\frac{C_0}{2}\times (\frac{7C_0}{4}{)}^2$
rate $=\frac{49C_0^{3}k}{32}$