Question

The equilibrium constant for a reaction is K and the reaction quotient is Q. For a reaction mixture, the ratio ${\displaystyle \frac{K}{Q}}$ is 0.33. This means that-
[A] The reaction mixture will equilibrate to form more reactant species
[B] The reaction mixture will equilibrate to form more reactant species
[C] The equilibrium ratio of reactant to product concentration will be 3
[D] The equilibrium ratio of reactant to product concentration will be 0.33

Answer 1

Hint:. To solve this, know that equilibrium constant is given by the product of the concentration of the product divided by the product of the concentration of the reactant. The equilibrium constants are related and the direction of reaction depends upon the value of their ratio.

Complete step by step answer:
Before answering this question, let us discuss the meaning of reaction quotient and equilibrium constant.
Let us take a system at equilibrium like-
     $$aA+bB\rightleftharpoons cC+dD$$
The equilibrium constant for the above reaction will be $K_{eq}={\displaystyle \frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}}$

The equilibrium constant depends upon the concentration of the reactants and the products.
We know that the reaction quotient will give us the direction of the reaction. We denote the reaction quotient as ‘Q’
Now, we know that the reaction quotient is given to us by the concentration of the products divided by that of the reactants.
The value of reaction quotient and the equilibrium quotient are interrelated. With their ratio or values, we can determine the fate of the reaction,
- If the reaction quotient is higher than the equilibrium constant, the reaction will proceed in the backward direction.
- If the reaction quotient is lower than the equilibrium constant, the reaction proceeds in the forward direction.
- If the reaction quotient is equal to the equilibrium constant, then the system attains equilibrium and the reaction will not proceed in any direction.
Now, let us see the question given to us.
Here, the ratio of equilibrium constant and reaction quotient is given to us as 0.33.
I.e. ${\displaystyle \frac{K}{Q}}$ = 0.33
Or, we can write that ${\displaystyle \frac{K}{Q}}$ < 1.
It means that the reaction quotient is greater than the equilibrium constant and we have already discussed above that if this is the case, the reaction proceeds backward i.e. reactant species are formed.
So, the correct answer is “Option A”.

Note: For gases we use equilibrium constant at constant pressure or concentration using the ideal gas equation as $K_{p}and{K}_c$ .
It is important to remember that the value of $K_{p}and{K}_c$ is different for different reactions. The general relation between $K_{p}and{K}_c$ can be written as $$K_p=K_c{\left(RT\right)}^{\mathrm{\Delta }n}$$ where the terms have their usual meanings and $\mathrm{\Delta }n$ is the difference between the total number of moles of reactants and total number of moles in the product.