The rate of decomposition of a gas is 10 mM s^-1 when 10% is reacted and it is 5 mM s^-1 when 40% is reacted. The order of the reaction is:

Concept:

• Rate of a reaction is defined as the change in concentration of reactant or product with the course of time.
• Rate expression/ Rate law is proportional to the concentration of reacting species raised to some exponent.

                  \(Rate = k[A]^p[B]^q...\)

Here, [A], [B].. are concentration of reacting species

p, q.. are experimentally determined values.

 k is the rate constant

Explanation:

• Since its a decomposition reaction, we can represent the chemical reaction as:

\(A(g) \rightarrow B(g) + C(g) +D(g)+...\)

• Lets consider order of reaction with respect to decomposing gas (A) to be n.

\(Rate =k[A]^n\)       -------(1)

Given,

• Case 1); Rate = 10mMs^-1 when 10% of gas is reacted, that is,  R₁ = 10mMs^-1 and [A]₁ = 0.9 mM. Putting values in equation (1) will give

\( 10mMs^{-1} = k\times(0.9 mM)^n\)      .........(2)

• Case 2); Rate = 5mMs-1 when 10% of gas is reacted, that is, R₂ = 10mMs-1 and [A]₂ = 0.6 mM. Putting values in equation (1) will give

\( 5mMs^{-1} = k\times(0.6mM)^n\)      ............(3)

Dividing equation (2) and (3) gives:

\(\frac{10}{5} = (\frac{0.9}{0.6})^n\)

\(2=(1.5)^n\)

\(n=1.71\)

Conclusion:

Therefore, the order of the decomposition of gas is 1.71.