Write a relation between ∆G and Q and define the meaning of each term and answer the following :
(a) Why a reaction proceeds forward when Q < K and no net reaction occurs when Q = K.
(b) Explain the effect of increase in pressure in terms of reaction quotient Q. for the reaction: CO(g) + 3H2(g) + 3H2 (g) ⇋ CH4 (g) + H2 O (g)
Relation between ΔG and Q can be given as
ΔG = ΔG° + RT lnQ ...(1)
Where, ΔG° = standard Gibb’s energy
ΔG = Gibb’s energy change
R = gas constant
T = absolute temperature
Q = reaction quotient
This relationship can be further simplified as follows-
We know that at Equilibrium, ΔG° = -RT lnK ...(2)
Where K = Equilibrium constant
Putting (2) in (1),
ΔG = -RT lnK + RT lnQ
ΔG = RT ln(Q/K) ...(3)
As we know, Kc (Equilibrium constant) is the ratio of concentration of products to that of reactants each raise to their stoichiometric coefficients at Equilibrium.
Whereas, Qc (reaction quotient) is the ratio of concentration of products to that of reactants each raise to their stoichiometric coefficients at any time during the reaction.
(a) If Q< K, it means concentration of products is to be increased so as to reach Equilibrium concentration thus the net reaction proceeds in the forward direction.
When Q= K, that means Equilibrium is achieved and thus no net reaction occurs.
(b) CO(g) + 3H2(g) ⇋ CH4 (g) + H2 O (g)
According to Le Chatiliers principle, on increasing the pressure, the Equilibrium will shift in a direction where the number of gas molecules are less.
In the given reaction,
Number of moles of reactants = 1 + 3 = 4
Number of moles of product = 1 + 1 = 2
And thus the Equilibrium will shift in forward direction as number of moles of product is less.
We know that when Q < K, the Equilibrium shifts in forward direction. Thus, for the following reaction Q < K.