Question

Equilibrium constant for the reactions:
$2NO+O_{2}\leftrightarrows2NO_{2} is \ K_{c_{1}}$
$NO+SO_{2}\leftrightarrows2SO_{3}+NO is \ K_{c_{2}}$
$2SO_{3}\leftrightarrows2SO_{2}+O_{2} is \ K_{c_{3}}$
Then correct relation is:
A. $K_{c_{3}}=K_{c_{1}}\times K_{c_{2}}$
B. $K_{c_{3}}\times K_{c_{1}}\times K^{2}_{c_{2}}=1$
C. $K_{c_{3}}\times K_{c_{1}}\times K_{c_{2}}=1$
D. $K_{c_{3}}\times K^{2}_{c_{1}}\times K_{c_{2}}=1$

Answer 1

Hint The equilibrium constant of a chemical reaction provides a better understanding of the relationship between reactants and the products when a reaction is at equilibrium.

Complete step by step answer:
- Equilibrium constant is basically the ratio of the products to the concentration of the reactions, where each reactant, as well as product, is raised to their respective stoichiometric coefficients.
- Equilibrium constant is used to determine chemical behaviour.
- For the given question, we will first write down the equilibrium constant for each of the given equations.

$$\begin{aligned} K_{c_{1}}=\dfrac{[NO_{2}]^{2}}{[NO]^{2}[O_{2}]} \end{aligned}$$ $$\begin{aligned} K_{c_{2}}=\dfrac{ [NO][SO_{3}]}{[NO]^{2}[SO_{2}]} \end{aligned}$$ $$\begin{aligned} K_{c_{3}}=\dfrac{[O_{2}][SO_{2}]^{2}}{[SO_{3}]^{2}} \end{aligned}$$

Now, on multiplying equilibrium constants of equation 1 and 3, we get

$$\begin{aligned} K_{c_{1}}\times K_{c_{3}}=\dfrac{[NO_{2}]^{2}}{[NO]^{2}[O_{2}]}\times\dfrac{[O_{2}][SO_{2}]^{2}}{[SO_{3}]^{2}} \end{aligned}$$

Since

$$\begin{aligned} K_{c_{1}}=\dfrac{[NO_{2}]^{2}}{[NO]^{2}[O_{2}]} \end{aligned}$$

The equation will become

$$\begin{aligned} K_{c_{1}}\times K_{c_{3}}=\dfrac{[NO_{2}]^{2}[SO_{2}]^{2}}{[NO]^{2}[SO_{3}]^{2}} \end{aligned}$$

So,

$$\begin{aligned} K_{c_{1}}\times K_{c_{3}}\times K^{2}_{c_{2}}=1 \end{aligned}$$

Therefore, the answer to the question is an option (B).

Additional information:
As we know that K is the ratio of certain amounts of products to their reactants at equilibrium, Q is the ratio at any particular point of time of the reaction. The spontaneity of the process is related to free energy change which is denoted by \Delta G.

Note: It is important for us to remember that there are several different types of equilibrium constants that provide us with the relationships between products and their reactants of a certain reaction.