In a reaction, A + B arrow Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as :

Question

In a reaction, A + B arrow Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as : (A) Rate = k[A]2[B]2 (B) Rate = k[A] [B] (C) Rate = k[A]2 [B] (D) Rate = k[A] [B2]

Tardigrade Admin · Accepted Answer

Let the orders of reaction with respect to A and B be x and y respectively. Hence the rate law will be
R =

k [A]^{x} [B]^{y}

.....(i)
When the concentration of B only is doubled, the rate is also doubled.
Hence

R_{1} = k [A]^{x} [B]^{y}

.....(ii)
When concentration of both the reactants is doubled, the rate is 8 times
Hence

R_{2} = k [2 A]^{x} [2 B]^{y} = 8 R

.....(iii)
or

8 R = k \times 2^{x} \times 2^{y} [A]^{x} [B]^{y}

.....(iv)
From eq.

(i)

and eq.

(ii)

we get

\frac{2 R}{R} = \frac{[ A ] ^{x} [ 2 B ] ^{y}}{[ A ] ^{x} [ B ] ^{y}}

∴

2 = 2 y

or

y = 1

From eq.

(i)

and

(i v)

, we get

\frac{8 R}{R} = \frac{2 ^{x} . 2 ^{y} [ A ] ^{x} [ 2 B ] ^{y}}{[ A ] ^{x} [ B ] ^{y}}

or

8 = 2^{x} .2 y

Substituting the value of y
8 =

2^{x} . 2^{1}

or 4 =

2^{x}

or

(2)^{2} = (2)^{x}

∴

x = 2

Substituting the values of x and y in eqn.

(i)

or R =

k [A]^{2} [B]

Q. In a reaction, $A + B \to$ Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as :

Rate = $k [A]^{2} [B]^{2}$

Rate = k[A] [B]

Rate = $k [A]^{2} [B]$

Rate = $k [A] [B^{2}]$

Q. In a reaction, A+B→ Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as :

Rate = k[A]2[B]2

Rate = k[A] [B]

Rate = k[A]2[B]

Rate = k[A][B2]

Q. In a reaction, $A + B \to$ Product, rate is doubled when the concentration of B is doubled, and rate increases by a factor of 8 when the concentrations of both the reactants (A and B) are doubled, rate law for the reaction can be written as :

Rate = $k [A]^{2} [B]^{2}$

Rate = $k [A]^{2} [B]$

Rate = $k [A] [B^{2}]$