Question

For the reaction, $2N{H_3} \to {N_2} + 3{H_2}$
$- \dfrac{{\Delta \left[ {N{H_3}} \right]}}{{\Delta t}} = {K_1}\left[ {N{H_3}} \right];\dfrac{{\Delta \left[ {{N_2}} \right]}}{{\Delta t}} = {K_2}\left[ {N{H_3}} \right];\dfrac{{\Delta \left[ {{H_2}} \right]}}{{\Delta t}} = {K_3}\left[ {N{H_3}} \right]$
Then relation between ${k_1},{k_2},{k_3}$is:
A. $1.5{k_1} = 3{k_2} = {k_3}$
B. $2{k_1} = {k_2} = 3{k_3}$
C. ${k_1} = {k_2} = {k_3}$
D. ${k_1} = 3{k_2} = 2{k_3}$

Answer 1

To answer this question, you must recall the formula for rate of reaction. The rate of change of concentration of reactant is a negative quantity since the concentration is decreasing with time, while the rate of change of concentration of product is positive.
Formula used:
For the reaction: ${\text{aA + bB}} \to {\text{cC}}$
${\text{rate = - }}\dfrac{{\text{1}}}{{\text{a}}}\dfrac{{{{\Delta }}\left[ {\text{A}} \right]}}{{{{\Delta t}}}}{\text{ = - }}\dfrac{{\text{1}}}{{\text{b}}}\dfrac{{{{\Delta }}\left[ {\text{B}} \right]}}{{{{\Delta t}}}}{\text{ = }}\dfrac{{\text{1}}}{{\text{c}}}\dfrac{{{{\Delta }}\left[ {\text{C}} \right]}}{{{{\Delta t}}}}$
Where a, b and c are the stoichiometric coefficients, A, B and C are the concentration of the reactants and products in molarity.

Complete step by step answer:
For the given reaction, $2N{H_3} \to {N_2} + 3{H_2}$,
We can write the rate of the reaction as, ${\text{Rate}} = - \dfrac{1}{2}\dfrac{{\Delta \left[ {N{H_3}} \right]}}{{\Delta t}} = \dfrac{{\Delta \left[ {{N_2}} \right]}}{{\Delta t}} = \dfrac{1}{3}\dfrac{{\Delta \left[ {{H_2}} \right]}}{{\Delta t}}$
Substituting the values given in the question, we can write,
$\dfrac{1}{2}{k_1} = {k_2} = \dfrac{1}{3}{k_3}$
$\Rightarrow 1.5{k_1} = 3{k_2} = {k_3}$

Thus, the correct option is A.

Additional information:
While studying a chemical reaction, it is important for us to consider not only the chemical properties of the reactants, but also the conditions under which the reaction is taking place, the mechanism by which it is proceeding, the rate at which it is occurring, and the equilibrium toward which it is moving.
The law of mass action states that, at a constant temperature the rate of a chemical reaction at a constant temperature depends only on the concentrations of the substances influencing the rate. The substances influencing the rate of reaction are usually one or more of the reactants, but occasionally include products. Catalysts, which do not appear in the balanced overall chemical equation, also influence reaction rate.

Note:
The rate law is an experimentally determined quantity and can be used to predict the relationship between the concentrations of reactants and the rate of the reaction. For elementary reactions, the rate equation can be simply derived from first principles using the collision theory. The rate equation of a reaction with a multi-step mechanism cannot be calculated from the stoichiometric coefficients of the overall reaction.