Question

Which of the following is an example of a fractional-order reaction?
(A) $N{{H}_{4}}N{{O}_{3}}\to {{N}_{2}}+2{{H}_{2}}O$
(B) $NO+{{O}_{3}}\to N{{O}_{2}}+{{O}_{2}}$
(C) $2NO+B{{r}_{2}}\to 2NOBr$
(D) $C{{H}_{3}}CHO\to C{{H}_{4}}+CO$

Answer 1

The order of a reaction is the relationship between the rate of a chemical reaction and the concentrations of chemical species involved in this reaction. To understand the chemical composition in the mixture of all species in the reaction from the rate equation of the same reaction.

Complete step by step solution:
The order of reaction is defined as the power dependence of the rate on the concentration of all reactants. Some important characteristics of the reaction order for a chemical reaction are:
The order reaction represents the number of species in which concentration directly impacts the rate of reaction.
Reaction order can be obtained by adding all the exponents of the concentration terms in the rate expression.
The value of the order of reaction may be integer or fraction or zero.
The order of reaction depends on the concentration of reactants only, not depends on the concentration of products.
$aA+bB\to cC+dD$
The rate of reaction, $r=k{{[A]}^{a}}{{[B]}^{b}}$
In the above reaction, r = rate of reaction
K = rate constant, [A], [B] are the concentrations of reactants. The exponent of the reactant concentrations ‘a’ and ‘b’ are partial orders of the reaction, where the sum of all the partial orders of the reaction represents the overall order of the reaction.
Chemical reactions are classified based on the dependence of rate reactions as follows:
(1) Zero-order reactions
(2) First order reactions
(3) Second-order reactions
(4) Fractional-order of reactions
(A) $N{{H}_{4}}N{{O}_{3}}\to {{N}_{2}}+2{{H}_{2}}O$
The rate of the above reaction= k $[N{{H}_{4}}N{{O}_{3}}]$
Hence this is the first order reaction because the exponent of the concentration of reactant is 1.
(B) $NO+{{O}_{3}}\to N{{O}_{2}}+{{O}_{2}}$
The rate of the above reaction = $k[N{{O}_{2}}][{{O}_{3}}]$
The above reaction is second order because the sum of exponents of the concentration of reactants is 2.
(C) $2NO+B{{r}_{2}}\to 2NOBr$
The rate of the above reaction = $k{{[NO]}^{2}}[B{{r}_{2}}]$
The above reaction is third order because the sum of exponents of the concentrations of reactants is 3.
(D) $C{{H}_{3}}CHO\to C{{H}_{4}}+CO$
In the steady-state, the rates of formation and destruction of methyl radicals are equal, which is pyrolysis of acetaldehyde into methane and carbon dioxide. The order of reaction depends on the concentration of acetaldehyde and methyl radical.
The rate of reaction = $k[C{{H}_{3}}CHO]{{[\bullet C{{H}_{3}}]}^{1/2}}$
The order of the reaction is 1.5 is a fractional-order reaction.

Hence, the correct answer is option D.

Note: Another type of order of the reaction is pseudo-first-order, in which the concentration of one reactant remains constant and included in the rate expression. Sometimes the concentration of reactants may be catalyst or constant because it is present in excess compared to the concentrations of reactants.