Question

${N_2} + {O_2} \rightleftharpoons 2NO;{K_1} \\\ (\frac{1}{2}){N_2} + (\frac{1}{2}){O_2} \rightleftharpoons NO;{K_2} \\\ 2NO \rightleftharpoons {N_2} + {O_2};{K_3} \\\ NO \rightleftharpoons (\frac{1}{2}){N_2} + (\frac{1}{2}){O_2};{K_4} \\\$

Correct relation(s) between K1, K2, K3 and K4 is/ are:
A.${K_1} \times {K_2} = 1$
B.$\sqrt {{K_1} \times } {K_4} = 1$
C.$\sqrt {{K_3}} \times {K_2} = 1$
D.None

Answer 1

The branch of chemistry which deals with the rate of change of the chemical reaction with the decrease in the concentration of the reactant or increase in the concentration of the product with the time is known as chemical kinetics.

Complete step by step answer:
The above reaction is the series of reactions and is complex in nature since the rate constants for every step of the reaction is given which in turn alters the rate of the reaction. The speed of every reaction is different and the slowest step of the reaction determines the rate of the reaction.
As per the complex reaction given the steps involved in the reaction be equation 1, 2, 3 and 4:
As is evident from the above equations, reaction 3 is the reverse of reaction 1.

${N_2} + {O_2} \rightleftharpoons 2NO;{K_1}...................(1) \\\ 2NO \rightleftharpoons {N_2} + {O_2};{K_3}.............(3) \\\$
Hence K1 x K3=1
Similarly on dividing equation 1 by 2 and on reversing that obtained result we will get the reaction 1 again.
Thus $\sqrt {{K_1} \times } {K_3} = 1$
Again on dividing equation 3 by 2 and on reversing that obtained result we will get the reaction 3 back thus:
$\sqrt {{K_3}} \times {K_2} = 1$
In this way each and every step is linked in the complex reaction where the steps of the reaction drastically vary in the speed of the reaction only. A correlation exists between each reaction constant as all the steps are interlinked in a series of reactions.
The rate of the reaction depends on the concentration of the reactants, products, temperature, nature of the surface on which the reaction occurs, and on the presence of the catalyst as well.

Therefore, option (C) is correct.

Note: The thermodynamics of the reaction is opposite of the kinetics of the reaction; it only gives information about the direction in which the reaction mechanism proceeds but gives no information about the change in the rate of the reaction.