Question

consider a reaction aG+bH = product. when Concentration of both the reactants G and H is doubled, the rate increases by eight times. however, when concentration of G is doubled keeping the concentration of H fixed, the rate is doubled. find order of reaction.

Answer 1

Answer: Order of the reaction is 3.

Explanation:

According to rate law, the rate of the reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.

$aG+bH\rightarrow product$.

$Rate=k[G]^a[H]^b$

On doubling the concentration of G and H,

$8\times Rate=k[2G]^a[2H]^b$....(1)

On doubling the concentration of G and keeping H constant

$2\times Rate=k[2G]^a[H]^b$....(2)

Dividing 1 by 2

$4=[2]^b$

$2^2=[2]^b$   Therefore, b=2

Putting the value of b=2 in (1)

$8\times Rate=k[2G]^a[2H]^b$....(1)

$8\times Rate=k[2]^a[G]^a[2]^b[H]^b$

$8\times Rate=[2]^a[2]^b\times Rate$

$8=[2]^a[4]$

$2=[2]^a$, therefore a=1

Total order(n) = a+b = 1+2 = 3.

Answer 2

Answer: The order of the reaction is 3.

Explanation:

Order of the reaction is the sum of the concentration of terms on which the rate of the reaction actually depends. It is equal to the sum of the exponents of the molar concentration in the rate law expression.

Rate law is defined as the expression which expresses the rate of the reaction in terms of molar concentration of the reactants with each term raised to the power their stoichiometric coefficient of that reactant in the balanced chemical equation.

For the given chemical reaction:

$aG+bH\rightarrow \text{product}$

The rate law expression for the above reaction is:

$\text{Rate}_1=k[G]^a[H]^b$          .......(1)

Total order of the reaction = a + b

When concentration of G and H are doubled, rate becomes:

$8\times \text{Rate}_1=k[2G]^a[2H]^b$          .......(2)

When concentration of only G is doubled, rate becomes:

$2\times \text{Rate}_1=k[2G]^a[H]^b$           ......(3)

Dividing equation 3 by 2, we get:

$\frac{8\times \text{Rate}_1}{2\times \text{Rate}_1}=\frac{k[2G]^a[2H]^b}{k[2G]^a[H]^b}\\\\4=2^b\\\\2^2=2^b\\b=2$

Now, putting value of 'b' in equation 2, we get:

$8\times \text{Rate}_1=k[2G]^a[2H]^2\\\\8\times \text{Rate}_1=k(2)^a[G]^a(2)^2[H]^b\\\\8\times \text{Rate}_1=(2)^a(2)^2\times k[G]^a[H]^b\\\\8\times \text{Rate}_1=(2)^a(2)^2\times \text{Rate}_1\\\\\frac{8}{4}=(2)^a\\\\2=2^a\\a=1$

Total order of the reaction = 1 + 2 = 3

Hence, the order of the reaction is 3.