`=>` The value of `color{red}(K_c)` for a reaction does not depend on the rate of the reaction. However, as you have studied in Unit 6, it is directly related to the thermodynamics of the reaction and in particular, to the change in Gibbs energy, `color{red}(DeltaG)`. If,

• `color{red}(DeltaG)` is negative, then the reaction is spontaneous and proceeds in the forward direction.

• `color{red}(DeltaG)` is positive, then reaction is considered non-spontaneous. Instead, as reverse reaction would have a negative `color{red}(DeltaG)`, the products of the forward reaction shall be converted to the reactants.

• `color{red}(DeltaG)` is `0`, reaction has achieved equilibrium; at this point, there is no longer any free energy left to drive the reaction.

A mathematical expression of this thermodynamic view of equilibrium can be described by the following equation:

`color{red}(DeltaG = DeltaG^(⊖) + RT ln Q)` ...........(7.21)

where, `color{red}(G^(⊖))` is standard Gibbs energy. At equilibrium, when `color{red}(DeltaG = 0)` and `color{red}(Q = K_c)`, the equation (7.21) becomes,
`color{red}(DeltaG = DeltaG^(⊖) + RT ln K = 0)`
`color{red}(DeltaG^(⊖) = – RT lnK)` ......................... (7.22)
`lcolor{red}(nK = – DeltaG^(⊖) // RT)`
Taking antilog of both sides, we get,

`color{red}(K = e^(-DeltaG^(⊖) // RT))` .............(7.23)

Hence, using the equation (7.23), the reaction spontaneity can be interpreted in terms of the value of `color{red}(DeltaG^(⊖))`.

• If `color{red}(DeltaG^(⊖) < 0),` then `color{red}(–DeltaG^(⊖)//RT)` is positive, and `color{red}(e^(-DeltaG^(⊖)//R T) > 1)`, making `color{red}(K > 1)`, which implies a spontaneous reaction or the reaction which proceeds in the forward direction to such an extent that the products are present predominantly

• If `color{red}(DeltaG^(⊖) > 0),` then `color{red}(–DeltaG^(⊖)//RT)` is negative, and `color{red}(e^(-DeltaG^(⊖) //RT < 1)`, that is , `color{red}(K < 1)`, which implies a non-spontaneous reaction or a reaction which proceeds in the forward direction to such a small degree that only a very minute quantity of product is formed.

`=>` One of the principal goals of chemical synthesis is to maximise the conversion of the reactants to products while minimizing the expenditure of energy. This implies maximum yield of products at mild temperature and pressure conditions. If it does not happen, then the experimental conditions need to be adjusted.

`=>` For example, in the Haber process for the synthesis of ammonia from `color{red}(N_2)` and `color{red}(H_2)`, the choice of experimental conditions is of real economic importance. Annual world production of ammonia is about hundred million tones, primarily for use as fertilizers.

=>` `Equilibrium constant, `color{red}(K_c)` is independent of initial concentrations. But if a system at equilibrium is subjected to a change in the concentration of one or more of the reacting substances, then the system is no longer at equilibrium; and net reaction takes place in some direction until the system returns to equilibrium once again.

`=>` Similarly, a change in temperature or pressure of the system may also alter the equilibrium.

`=>` In order to decide what course the reaction adopts and make a qualitative prediction about the effect of a change in conditions on equilibrium we use Le Chatelier’s principle.

`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
Le Chatelier’s principle: It states that a change in any of the factors that determine the equilibrium conditions of a system will cause the system to change in such a manner so as to reduce or to counteract the effect of the change. This is applicable to all physical and chemical equilibria.

We shall now be discussing factors which can influence the equilibrium.

`=>` In general, when equilibrium is disturbed by the addition/removal of any reactant/ products, Le Chatelier’s principle predicts that:

• The concentration stress of an added reactant/product is relieved by net reaction in the direction that consumes the added substance.

• The concentration stress of a removed reactant/product is relieved by net reaction in the direction that replenishes the removed substance. or in other words,

`=>` When the concentration of any of the reactants or products in a reaction at equilibrium is changed, the composition of the equilibrium mixture changes so as to minimize the effect of concentration changes”.

`=>` Let us take the reaction,
`color{red}(H_2(g) + I_2(g) ⇌2HI(g))`

If `color{red}(H_2)` is added to the reaction mixture at equilibrium, then the equilibrium of the reaction is disturbed. In order to restore it, the reaction proceeds in a direction wherein `color{red}(H_2)` is consumed, i.e., more of `color{red}(H_2)` and `color{red}(I_2)` react to form `color{red}(HI)` and finally the equilibrium shifts in right (forward) direction (Fig.7.8). This is in accordance with the Le Chatelier’s principle which implies that in case of addition of a reactant/product, a new equilibrium will be set up in which the concentration of the reactant/product should be less than what it was after the addition but more than what it was in the original mixture.


`=>` The same point can be explained in terms of the reaction quotient, `color{red}(Q_c)`

`color{red}(Q_c = [HI]^2 // [H_2] [I_2])`


`=>` Addition of hydrogen at equilibrium results in value of `color{red}(Q_c)` being less than `color{red}(K_c)` . Thus, in order to attain equilibrium again reaction moves in the forward direction.

`=>` Similarly, we can say that removal of a product also boosts the forward reaction and increases the concentration of the products and this has great commercial application in cases of reactions, where the product is a gas or a volatile substance.

`=>` In case of manufacture of ammonia, ammonia is liquified and removed from the reaction mixture so that reaction keeps moving in forward direction. Similarly, in the large scale production of `color{red}(CaO)` (used as important building material) from `color{red}(CaCO_3)`, constant removal of `color{red}(CO_2)` from the kiln drives the reaction to completion. It should be remembered that continuous removal of a product maintains `color{red}(Q_c)` at a value less than `color{red}(K_c)` and reaction continues to move in the forward direction.

`=>` A pressure change obtained by changing the volume can affect the yield of products in case of a gaseous reaction where the total number of moles of gaseous reactants and total number of moles of gaseous products are different.

`=>` In applying Le Chatelier’s principle to a heterogeneous equilibrium the effect of pressure changes on solids and liquids can be ignored because the volume (and concentration) of a solution/liquid is nearly independent of pressure.

Consider the reaction,

`color{red}(CO(g) + 3H_2(g) ⇌ CH_4(g) + H_2O(g))`

•Here, 4 mol of gaseous reactants `color{red}((CO + 3H_2))` become 2 mol of gaseous products `color{red}((CH_4 + H_2O))`.

•Suppose equilibrium mixture (for above reaction) kept in a cylinder fitted with a piston at constant temperature is compressed to one half of its original volume.

•Then, total pressure will be doubled (according to `color{red}(pV =)` constant).

•The partial pressure and therefore, concentration of reactants and products have changed and the mixture is no longer at equilibrium.

•The direction in which the reaction goes to re-establish equilibrium can be predicted by applying the Le Chatelier’s principle. Since pressure has doubled, the equilibrium now shifts in the forward direction, a direction in which the number of moles of the gas or pressure decreases (we know pressure is proportional to moles of the gas).

•This can also be understood by using reaction quotient, `color{red}(Q_c)`. Let `color{red}([CO] [H_2][CH_4])` and `color{red}([H_2O])` be the molar concentrations at equilibrium for methanation reaction. When volume of the reaction mixture is halved, the partial pressure and the concentration are doubled. We obtain the reaction quotient by replacing each equilibrium concentration by double its value.

`color{red}(Q_c = ( [CH_4 (g) ] [ H_2O (g)])/([CO(g)] [H_2(g)]^3))`

As `color{red}(Q_c < K_c)` , the reaction proceeds in the forward direction. In reaction `color{red}(C(s) + CO_2(g) ⇌ 2CO(g)),` when
pressure is increased, the reaction goes in the reverse direction because the number of moles of gas increases in the forward direction.

`=>` If the volume is kept constant and an inert gas such as argon is added which does not take part in the reaction, the equilibrium remains undisturbed.

`=>` It is because the addition of an inert gas at constant volume does not change the partial pressures or the molar concentrations of the substance involved in the reaction.

`=>` The reaction quotient changes only if the added gas is a reactant or product involved in the reaction.

`=>` Whenever an equilibrium is disturbed by a change in the concentration, pressure or volume, the composition of the equilibrium mixture changes because the reaction quotient, `color{red}(Q_c)` no longer equals the equilibrium constant, `color{red}(K_c)`. However, when a change in temperature occurs, the value of equilibrium constant, `color{red}(K_c)` is changed.

In general, the temperature dependence of the equilibrium constant depends on the sign of` color{red}(DeltaH)` for the reaction.

• The equilibrium constant for an exothermic reaction (negative `color{red}(DeltaH)`) decreases as the temperature increases.

• The equilibrium constant for an endothermic reaction (positive `color{red}(DeltaH)`) increases as the temperature increases. Temperature changes affect the equilibrium constant and rates of reactions.

Production of ammonia according to the reaction,

`color{red}(N_2(g) +3H_2 (g) ⇌ 2NH_3(g))`

`color{red}(DeltaH = -92.38 kJ mol^(-1))`

is an exothermic process.

`=>` According to Le Chatelier’s principle, raising the temperature shifts the equilibrium to left and decreases the equilibrium concentration of ammonia.

`=>` In other words, low temperature is favourable for high yield of ammonia, but practically very low temperatures slow down the reaction and thus a catalyst is used.

`=>` A catalyst increases the rate of the chemical reaction by making available a new low energy pathway for the conversion of reactants to products.

`=>` It increases the rate of forward and reverse reactions that pass through the same transition state and does not affect equilibrium.

`=>` Catalyst lowers the activation energy for the forward and reverse reactions by exactly the same amount. Catalyst does not affect the equilibrium composition of a reaction mixture. It does not appear in the balanced chemical equation or in the equilibrium constant expression .

`=>` Let us consider the formation of `color{red}(NH_3)` from dinitrogen and dihydrogen which is highly exothermic reaction and proceeds with decrease in total number of moles formed as compared to the reactants.

`=>` Equilibrium constant decreases with increase in temperature. At low temperature rate decreases and it takes long time to reach at equilibrium, whereas high temperatures give satisfactory rates but poor yields.

`=>` German chemist, Fritz Haber discovered that a catalyst consisting of iron catalyse the reaction to occur at a satisfactory rate at temperatures, where the equilibrium concentration of `color{red}(NH_3)` is reasonably favourable. Since the number of moles formed in the reaction is less than those of reactants, the yield of `color{red}(NH_3)` can be improved by increasing the pressure.

`=>` Optimum conditions of temperature and pressure for the synthesis of `color{red}(NH_3)` using catalyst are around `500°C` and 200 atm.

`=>` Similarly, in manufacture of sulphuric acid by contact process,

`color{red}(2SO_2 (g) +O_2 (g) ⇌ 2SO_3 (g) ; K_c = 1.7 xx 10^(26))`

though the value of `color{red}(K)` is suggestive of reaction going to completion, but practically the oxidation of `color{red}(SO_2)` to `color{red}(SO_3)` is very slow. Thus, platinum or divanadium penta-oxide `color{red}((V_2O_5))` is used as catalyst to increase the rate of the reaction.

`color{red}("Note")`: If a reaction has an exceedingly small `color{red}(K),` a catalyst would be of little help.