Question

If d x d t = k [ H + ] n dxdt=k[H+]n and rate becomes 100 times when pH changes from 2 to 1. Find the order of reaction

Answer 1

$\bold{\text{Given,}}$
$\frac{dx}{dt}=k[H^+]^n$

Now, question says : rate becomes 100 times when pH change 2 to 1 .
we know, $pH=-log[H^+]$
Then, when pH = 2 ,
2 = - log[H⁺] ⇒[H⁺] = 10⁻² M

similarly , when pH = 1
1 = -log[H⁺] ⇒ [H⁺] = 10⁻¹ M

Now, Let rate = r₁ , when pH = 2
then, r₁ = (10⁻²)ⁿ --------------------(1)

when pH changes then, rate will be 100 times of r₁
so, 100r₁ = (10⁻¹)ⁿ ------------(2)

dividing equations (2) and (1) ,
1/100 = (10⁻²)ⁿ/(10⁻¹)ⁿ
1/100 = (1/10)ⁿ
1/10² = (1/10)ⁿ ⇒n = 2

Hence, order of reaction is 2

Answer 2

Answer:

pH values is defined as

pH = -log[H^+]