Question

Given two separate reactions
(I) $⟶$ Products
(II) $⟶$ Products,
Reaction (I) follows first order kinetics while reaction (II) follows second order kinetics. Both the reactions have same half lives. When the initial concentration of

Answer 1

Answer: 2

For (A), rate $=k_A[A]$
$\left(t_{1/2}\right)A=\frac{0.693}{k_A}$
For (B), rate $=k_B[B{]}^2$
${\left(t_{1/2}\right)}_B=\frac{1}{a\cdot k_B}$, where a is the conc. of $[B]$ at the start of reaction
Since half lives are same
$\frac{0.693}{k_A}=\frac{1}{a\cdot k_B}$
$\frac{k_A}{k_B}=0.693a$
Since initial concentration of (A) is $n$ times that of (B).
$[A]=na$
$\frac{r_A}{r_B}=\frac{k_A}{k_B}\times \frac{\text{ na }}{a_2},\text{ given }\frac{r_A}{r_B}=1.386$
$1.386=0.693a\times \frac{na}{a^2}$
$n=\frac{1.386}{0.693}=2$