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Question: Rate equation for autocatalytic reaction A+R \(\overset{\quad k\quad}{\rightarrow}\) R + R is \(–\f...

Rate equation for autocatalytic reaction

A+R →k\overset{\quad k\quad}{\rightarrow} R + R is –dCAdt–\frac{dC_{A}}{dt} = k CA× CR

The rate of disappearance of A is maximum when

A

CA = 2CR

B

CA = CR

C

2CA = CR

D

CA = (CR)1/2

Answer

2CA = CR

Explanation

Solution

A + R ¾® R + R

t = 0 a R R R

t = t a–x x x

i.e [A]t = a–x [R] = 2x

Rate is max. when

d2xdt2\frac{d^{2}x}{dt^{2}} = 0 = 2k(a – 2x) dxdt\frac{dx}{dt} [A]t = [R]2\frac{\lbrack R\rbrack}{2}