Question

Doubling the concentration of the reactant $A$ increases the rate by $4$ times and tripling the concentration of $A$ increases the rate by $9$ times, the rate of the reaction is proportional to:

• A. concentration of $A$
• B. square of concentration of $A$
• C. under root of concentration of $A$
• D. cube of concentration of $A$

Answer 1

Answer: (B)

square of concentration of $A$

The expression for the rate of the reaction is $r=k[A{]}^n$......(1)

When the concentration of A is doubled, the rate increases 4 times.

$r^{\prime }=4r=[2A{]}^n$......(2)

Dividing (2) by (1), we get

$\frac{4r}{r}=\frac{[2A{]}^n}{k[A{]}^n}$

$n=2$.

When the concentration of A is tripled, the rate increases 9 times.

$r^{\prime }=9r=k\left(\right[3A{]}^n)$......(1)

Dividing (3) by (1), we get

$\frac{9r}{r}=\frac{k[3A{]}^n}{k[A{]}^n}$

$n=2$