Question

Rate equation for autocatalytic reaction
$A + R \stackrel{k}{\longrightarrow } R + R \text { is }-\frac{d C_{ A }}{d t}=k C_{ A } \cdot C_{ R }$
the rate of disappearance of $A$ is maximum when

• A. $C_{ A }=2 C_{ R }$
• B. $C_{ A }=C_{ R }$
• C. $2 C_{ A }=C_{ R }$
• D. $C_{ A }=\left(C_{ R }\right)^{1 / 2}$

Answer 1

Answer: (C)

$A+R \longrightarrow R+R$



Rate is max. when

$\frac{d^{2} x}{d t^{2}}=0 \doteq 2 k(a-2 x) \frac{d x}{d t}$

$[A]_{t}=\frac{[R]}{2}$

$[A]=C_{A},[R]=C_{R}, $

$\Rightarrow C_{A}=C_{R} / 2$

$ \Rightarrow 2 C_{A}=C_{R}$