Rate equation for autocatalytic reaction A + R stackrelk longrightarrow R + R text is -(d C A /d t)=k C A ⋅ C R the rate of disappearance of A is maximum when

Question

Rate equation for autocatalytic reaction A + R stackrelk longrightarrow R + R text is -(d C A /d t)=k C A ⋅ 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 =(C R )1 / 2

Tardigrade Admin · Accepted Answer

A+R longrightarrow R+R <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/chemistry/ae18d5092c9b44273632e79d60cb583b-.png" /> Rate is max. when (d2 x/d t2)=0 doteq 2 k(a-2 x) (d x/d t) [A]t=([R]/2) [A]=CA,[R]=CR, ⇒ CA=CR / 2 ⇒ 2 CA=CR

Q. Rate equation for autocatalytic reaction
$A + R ⟶ k R + R is - \frac{d C _{A}}{d t} = k C_{A} \cdot C_{R}$
the rate of disappearance of $A$ is maximum when

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

$C_{A} = C_{R}$

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

$C_{A} = (C_{R})^{1/2}$

$A + R ⟶ R + R$

Rate is max. when

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

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

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

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

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

Q. Rate equation for autocatalytic reaction A+R⟶k​R+R is −dtdCA​​=kCA​⋅CR​ the rate of disappearance of A is maximum when

CA​=2CR​

CA​=CR​

2CA​=CR​

CA​=(CR​)1/2