Chemistry Factors affecting equilibria

### Topic to be covered

star Relationship between equilibrium constant K , Reaction quotient Q and Gibbs energy G.
star Factors Affecting Equilibria.
star Effect of Concentration Change.
star Effect of Concentration – An experiment.
star Effect of Pressure Change.
star Effect of Inert Gas Addition.
star Effect of Temperature Change.
star Effect of Temperature – An experiment .
star Effect of a Catalyst.

### RELATIONSHIP BETWEEN EQUILIBRIUM CONSTANT K, REACTION QUOTIENT Q AND GIBBS ENERGY G

=> 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.
Q 3069791615

The value of DeltaG^(⊖) for the phosphorylation of glucose in glycolysis is 13.8 kJ//mol. Find the value of K_c at 298 K.

Solution:

DeltaG^(⊖) = 13.8 kJ//mol = 13.8 × 10^3J//mol
Also, DeltaG^(⊖) = – RT lnK_c
Hence, ln K_c = –13.8 × 10^3J//mol
(8.314 J mol^(–1)K^(–1) × 298 K)
ln K_c = – 5.569K_c = e^(–5.569)
K_c = 3.81 × 10^(–3)
Q 3029891711

Hydrolysis of sucrose gives,

text(Sucrose) + H_2O ⇌ text(Glucose) + text(Fructose)

Equilibrium constant K_c for the reaction is 2 ×10^(13) at 300K. Calculate DeltaG^(⊖) at 300K.

Solution:

DeltaG^(⊖) = -RT ln K_c

DeltaG^(⊖) = - 8.314 J mol^(-1) K^(-1) xx 300K xx ln (2 xx 10^(13))

DeltaG^(⊖) = -7.64 xx 10^4 J mol^(-1)

### FACTORS AFFECTING EQUILIBRIA

=> 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.

### Effect of Concentration Change

=> 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.

### Effect of Concentration – An experiment

=> This can be demonstrated by the following reaction:

color{red}(undersettext(yellow)(Fe^(3+) (aq)) +undersettext(colourless)(SCN^(-) (aq)) ⇌ undersettext(deep red)([Fe(SCN)]^(2+) (aq))) ...............(7.25)

color{red}(K_c = ([ Fe(SCN)^(2+) (aq) ])/([Fe^(3+) (aq) ][SCN^(-) (aq)])) ..............(7.25)

•A reddish colour appears on adding two drops of 0.002 M potassium thiocynate solution to 1 mL of 0.2 M iron(III) nitrate solution due to the formation of color{red}([Fe(SCN)]^(2+)). The intensity of the red colour becomes constant on attaining equilibrium.

• This equilibrium can be shifted in either forward or reverse directions depending on our choice of adding a reactant or a product. The equilibrium can be shifted in the opposite direction by adding reagents that remove color{red}(Fe^(3+)) or color{red}(SCN^–) ions.

• For example, oxalic acid color{red}((H_2C_2O_4)), reacts with color{red}(Fe^(3+)) ions to form the stable complex ion color{red}([Fe(C_2O_4)_3]^(3 –)), thus decreasing the concentration of free color{red}(Fe^(3+)(aq)). In accordance with the Le Chatelier’s principle, the concentration stress of removed Fe^(3+) is relieved by dissociation of color{red}([Fe(SCN)]^(2+)) to replenish the color{red}(Fe^(3+)) ions. Because the concentration of color{red}([Fe(SCN)]^(2+)) decreases, the intensity of red colour decreases.

•Addition of aq. color{red}(HgCl_2) also decreases red colour because color{red}(Hg^(2+)) reacts with color{red}(SCN^–) ions to form stable complex ion color{red}([Hg(SCN)_4]^(2–)). Removal of free color{red}(SCN^– (aq)) shifts the equilibrium in equation (7.24) from right to left to replenish color{red}(SCN^–) ions. Addition of potassium thiocyanate on the other hand increases the colour intensity of the solution as it shift the equilibrium to right

### Effect of Pressure Change

=> 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.

### Effect of Inert Gas Addition

=> 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.

### Effect of Temperature Change

=> 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.

### Effect of Temperature – An experiment

=> Effect of temperature on equilibrium can be demonstrated by taking color{red}(NO_2) gas (brown in colour) which dimerises into color{red}(N_2O_4) gas (colourless).

color{red}(2NO_2(g) ⇌ N_2O_4(g); DeltaH = –57.2 kJ mol^(–1))

color{red}(NO_2) gas prepared by addition of color{red}(Cu) turnings to conc. color{red}(HNO_3) is collected in two 5 mL test tubes (ensuring same intensity of colour of gas in each tube) and stopper sealed with araldite. Three 250 mL beakers 1, 2 and 3 containing freezing mixture, water at room temperature and hot water (363K ), respectively, are taken (Fig. 7.9). Both the test tubes are placed in beaker 2 for 8-10 minutes. After this one is placed in beaker 1 and the other in beaker 3. The effect of temperature on direction of reaction is depicted very well in this experiment. At low temperatures in beaker 1, the forward reaction of formation of color{red}(N_2O_4) is preferred, as reaction is exothermic, and thus, intensity of brown colour due to color{red}(NO_2) decreases. While in beaker 3, high temperature favours the reverse reaction of formation of color{red}(NO_2) and thus, the brown colour intensifies.

=> Effect of temperature can also be seen in an endothermic reaction,

color{red}(undersettext(pink)([Co(H_2O_6)_6]^(3+)(aq)) + undersettext(colourless)(4Cl^- (aq)) ⇌ undersettext(blue)([CoCl_4]^(2-) (aq))+6H_2O(l))

At room temperature, the equilibrium mixture is blue due to color{red}([CoCl_4]^(2–)). When cooled in a freezing mixture, the colour of the mixture turns pink due to color{red}([Co(H_2O)_6]^(3+)) .

### Effect of a Catalyst

=> 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.