Characteristics of Equilibrium Constant:

• It has a definite value for every chemical reaction at a particular temperature.
• It is independent of the initial concentrations of the reacting species.
• It changes with the change in the temperature.
• It depends on the nature of the reaction.
• It is independent of the change of pressure, volume and concentrations of the reactants and products.
• It is not affected by the introduction of the catalyst.
• The expression for it may contain the concentrations of gases or molecules and ions in solution but not of pure solids or pure liquids.
• The expression for it and its magnitude depends on the stoichiometric form of the balanced chemical equation.
• When the equation for equilibrium is multiplied by a factor, then the equilibrium constant must be raised to the power equal to the factor.

If K_c is equilibrium constant for reaction aA + bB ⇌  cC + dD

Then its value for reaction naA + nbB ⇌  ncC + ndD is given by

K’_c = (K_c)ⁿ

• When the addition of two equilibria leads to another equilibrium then the product of their equilibrium constants gives the value of K_C of the resultant equilibrium.

K_(resultant) = K_{(Reaction 1)}  x K_{(Reaction 2)}

• If K₁, k₂, K₃, …. are equilibrium constant for recation₁, reaction₂, reaction₃, ……. Then the value of K_C for reaction, a x recation₁+ b x reaction₂, c x reaction₃, ……. is given by

K_C = (K₁)^a(K₂)^b(K₃)^c……..

• For a reversible reaction, the value of K_C for the backward reaction is inverse of the equilibrium constant for the forward reaction

K_(backward) = 1 / K_(forward)

• If it is expressed in terms of concentration, it has different units for different reactions.

K_C is Dimensionless Unitless Quantity:

Depending upon the stoichiometric coefficients of a chemical reaction, the equilibrium constant should have a unit. Its unit should be

(mol dm^-3)^{(∑n products – ∑n reactants)}

Note that 1 dm³ = 1 L. Hence concentration can be expressed as (mol L^-1)

These days we specify equilibrium constant in terms of dimensionless quantities by specifying the standard state of reactants and products. The standard state pressure for pure gas is 1 bar and the partial pressures of the gases are measured with respect to this standard state.

If a gas has a partial pressure of 1.5 bar, then in terms of standard state its pressure would be equal to 1.5 bar/1bar = 1.5, a dimensionless number. Similarly, for concentrations, the standard state is 1 M ( 1mol dm^-3). If the concentration of the substance is 2.0 M. Then in terms of standard state it will be expressed as 2.0 M/1 M = 2. Thus using partial pressures and concentrations K_P and K_C obtained are dimensionless. Hence equilibrium constant is considered as dimensionless, unitless quantity.

K_C of a General Reaction and its Multiple:

Consider a hypothetical reversible reaction

aA + bB ⇌  cC + dD

The equilibrium constant of the reaction given by

Consider a multiple of above reaction

naA + nbB ⇌  ncC + ndD

The equilibrium constant of the reaction given by

Thus when the equation for an equilibrium is multiplied by a factor, then the equilibrium constant must be raised to the power equal to the factor.

K_C for the addition of Two Chemical Equilibria:

Consider following equilibria

1) N_2(g) +   O_2(g)  ⇌     2NO_(g)

The equilibrium constant for the reaction is

2)   2NO_(g) +   O_2(g)  ⇌     2NO_2(g) 

The equilibrium constant for the reaction is

3)  N_2(g) +  2O_2(g)   ⇌   2NO_2(g)

The equilibrium constant for the reaction is

Multiplying equation (1) by (2) we get

Thus When the addition of two equilibria leads to another equilibrium then the product of their equilibrium constants gives the equilibrium constant of the resultant equilibrium.

Temperature Dependence of Equilibrium Constant:

At chemical equilibrium, the rate of the forward reaction is equal to the rate of backward reaction. When the temperature is increased, in general, the rate of both the forward reaction and the backward reaction increases. As the energy of activation of the forward reaction and the backward reaction are different, the extent of the increase of the forward reaction and the backward reaction is different. Thus the value of K_f (rate constant for the forward reaction) and K_b (rate constant for the backward reaction) changes to a different extent. Thus the ratio K_f / K_b changes. i.e. the value of equilibrium constant changes with the change in temperature.

The value of the equilibrium constant for endothermic reaction increases with an increase in temperature, while the value of the equilibrium constant for exothermic reaction decreases with an increase in temperature. The temperature dependence of equilibrium constant can be written mathematically as

Uses of K_C:

It helps in the prediction of the extent of reaction:

The magnitude of the K_C tells us about the extent in which the reactants are converted into the products before the equilibrium is attained. Larger values of K indicates that the extent of reactants converting into products is greater. The generalization is

• If K_C > 10³ Products predominates the reactants. i.e. the concentration of products is very high compared to that of reactants t equilibrium and the reaction proceeds nearly to completion
• If K_C < 10^-3 Reactants predominates the products. i.e. the concentration of products is very less compared to that of reactants t equilibrium and the reaction hardly proceeds.
• 10^-3 < K_C < 10^-3 , appreciable concentrations of both the reactants and products are present at equilibrium

It gives us an idea of relative stabilities of reactants and products:

If the K_C is large products are more stable than the reactants. Whereas, If the value of the equilibrium constant is small reactants are more stable than the products.  The generalisation is

If K_C > 10³ Products are stable than reactants.

If K_C < 10^-3 Reactants are stable than products.

It helps in the prediction of the direction of a net reaction.

The value of K_C helps in the prediction of the direction in which the net reaction is proceeding at given concentrations or partial pressures of reactants and products. If Q_c is the concentration quotient and K_c be the equilibrium constant of a chemical reaction.

For reaction aA + bB ⇌  cC + dD

When computing Q_C the concentration at that instant are used

When computing K_C the concentration at equilibrium are used. The generalization is

• If Q_C > K_C , the reaction is taking place in a backward direction i.e. in the direction of reactants
• If Q_C <  K_C , the reaction is taking place in a forward direction i.e. in the direction of products.
• If Q_C =  K_C The reaction is in the equilibrium state and hence no net reaction is taking place.

It helps in the calculation of equilibrium constants and equilibrium pressures. 

If the equilibrium concentrations of various reactants and products are known for a reaction, the equilibrium constant can be calculated. On the other hand, if the equilibrium constant is known, the equilibrium concentrations can be calculated.

Steps Involved in the Calculation of K_C and Equilibrium Pressures:

1. Write the chemical equation for the equilibrium
2. Write expression for K_C or K_P for the reaction.
3. Express all unknown concentrations or partial pressures in terms of a single variable x.
4. Substitute equilibrium concentrations or partial pressures in terms of x in the expression for K_C or K_P.
5. Solve the equation for x
6. Substitute the value obtained for x in the expression in step 3 to calculate equilibrium concentrations or equilibrium partial pressures

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In this article, we shall stuudy to write expression for equilibrium constant.

Steps Involved in Writing Expression for Equilibrium Constant of a Reaction:

• Write the balanced chemical equation for the reaction.
• Write the products of equilibrium concentrations of the products in the numerator. Omit pure solids, pure liquids and the solvents in dilute solutions.
• Write the products of equilibrium concentrations of the reactants in the denominator. Omit pure solids, pure liquids and the solvents in dilute solutions.
• Raise each concentration term to the power equal to stoichiometric coefficients of the species in the equation.

Homogeneous Equilibrium:

The equilibrium in which all the substances involved exist in a single homogeneous phase is called homogeneous equilibrium.

Examples:

N_2(g) +  3 H_2(g)  ⇌     2NH_3(g)

H_2(g) +  I_2(g) ⇌     2HI_(g)

2SO_2(g) +  O_2(g)  ⇌   2SO_3(g)

NH_3(aq) + H₂O_(l) ⇌     2NH₄+_(aq) +  OH-_(aq)

2N₂O_(g) ⇌ 2N_2(g)  +   O_2(g)

CH₃COOC₂H_5(aq) + H2O_(l) ⇌ CH₃COOH_(aq) +   C2H5OH_(aq)

Heterogeneous Equilibrium:

The equilibrium in which the substance involved are present in different phases is called heterogeneous equilibrium.

Examples:

CaCO_3(s) ⇌  CaO_(s) + . CO_2(g)

CaCO_3(s)+H₂O(l)+CO₂(g) ⇌ Ca²⁺_(aq)+ 2HCO₃^–_(aq)

(NH₄)₂CO_3(s) ⇌ 2NH_3(g) + CO_2(g)+  H₂O_(g)

2Mg_(s) + O2_(g)  ⇌    2MgO_(s)

Note: Pure liquids and solids are ignored while writing the equilibrium constant expression.

Now, for pure solids and pure liquids, the molar mass M and density ρ are constant. Hence the concentration remains constant.

• When pure solids are involved in equilibrium, its concentration remains constant no matter how much of it is present. Therefore by convention, the concentrations of all solids involved in equilibrium are taken as unity.
• When pure liquids are involved in equilibrium, its concentration remains constant no matter how much of it is present. Therefore by convention, the concentrations of all liquids involved in equilibrium are taken as unity.
• For equilibria in the aqueous medium, the concentration of solvent (water) will not change appreciably because it is present in large excess. Hence by convention, the concentration of solvent (water) is taken as unity.
• Hence in general, pure liquids, pure solids, and solvents can be ignored while writing the equilibrium constant expression.

Writing the Expression for K_c and K_p:

BaCO_3(s)  ⇌  BaO_(s) + CO_2(g)

4NH_3(g) + 5O_2(g) ⇌   4NO_(g)+ 6H₂O_(g)

NH_3(g) + HCl_(g)  ⇌  NH₄Cl_(s)

3Cl_2(g) + 2NO_2(g)  ⇌  2NO₂Cl_3(g)

Fe³⁺_(aq) + SCN^–_(aq) ⇌ FeNCS²⁺_(aq)

CH_4(g) + 2H₂S_(g)  ⇌  CS_2(g)+ 4H_2(g)

MgCO_3(s)  ⇌  MgO_(s)  + CO_2(g)

AgBr_(s) ⇌ Ag⁺_(aq)+ Br^–_(aq)

K_c = [Ag⁺][Br ^–]

CH₃COCH_3(l) ⇌CH₃COCH_3(g)

K_c = [CH₃COCH_3(g)]

CH_4(g) + 2O_2(g) ⇌ CO_2(g)+ 2H₂O_(g)

Al_(s) + 3H⁺_(aq) ⇌ Al³⁺_(aq)+ 3/2H_2(g)

HPO₄^2-_(aq) + H₂O_(l) ⇌ H₃O⁺_(aq)+ PO₄^3-_(aq)

Ag₂O_(s) + 2HNO_3(aq) ⇌  2AgNO_3(aq)+ H₂O_(l)

Ni_(s) + 4CO_(g) ⇌  Ni(CO)_4(g)

CuO_(s) + H_2(g) ⇌  Cu_(s)+ H₂O_(g)

N_2(g) + 3H_2(g) ⇌  2NH_3(g)

Fe³⁺_(aq) + 3OH^–_(aq) ⇌  Fe(OH)_3(s)

2N₂O_(g) ⇌ 2N_2(g) + O_2(g)

C_(s)+  CO_2(g) ⇌  2CO_(g)

Consider a hypothetical reversible reaction involving homogeneous gaseous phase

aA(g) + bB(g) ⇌  cC(g) + dD(g)

The equilibrium constant in terms of the partial pressure is given by

This is the relation between K_c and K_p.

Where Δn = (Sum of the exponents in the numerator of concentration quotient) – (Sum of the exponents in the denominator of concentration quotient)

Steps Involved in Finding Relation Between K_c and K_p :

• Write the balanced chemical equation for the reaction.
• Find the change in the number of moles of gaseous species by the following formula.

• Now, use the relation

Examples to Find Relation between Between K_c and K_p :

Example – 01:

Example – 02:

Example – 03:

Example – 04: 

For the reaction N_2(g) + 3H_2(g) ⇌  2NH_3(g), the value of the equilibrium constant K_p is 3.6 x 10^-2 at 500 K. Calculate the value of K_c for the reaction at the same temperature. Take R = 0.0831 bar lit mol^-1 K^-1.

Example – 05:

For the reaction 2SO_2(g)) + O_2(g) ⇌ 2SO_3(g), the value of the equilibrium constant K_p is 2.0 X 10¹⁰ bar^-1 at 450 K. Calculate the value of K_c for the reaction at the same temperature. Take R = 0.0831 bar lit mol^-1 K^-1.

Example – 06:

For the reaction 2NOCl_(g) ⇌ 2NO_(g)+ Cl_2(g), the value of the equilibrium constant K_p is1.8 X 10^-2 at 500 K. Calculate the value of K_c for the reaction at the same temperature. Take R = 0.0831 bar lit mol^-1 K^-1.

Example – 07:

For the reaction CaCO_3(s)  ⇌ CaO_(s)+ CO_2(g), the value of equilibrium constant K_p is 167 at 1073 K. Calculate the value of K_c for the reaction at the same temperature. Take R = 0.0831 bar lit mol^-1 K^-1.

Example – 08:

Find the ratio of K_p/K_c for the reaction, CO(g) + 1/2O_2(g)  ⇌  2CO_2(g), at 500 K. Take R = 0.0831 bar lit mol^-1 K^-1.

Example – 09:

Find the ratio of K_p/K_c  for the reaction, N_2(g) + O_2(g) ⇌   2NO_(g)

Example – 10:

The equilibrium constant K_p for the reaction H_2(g)  + I_2(g)  ⇌  2HI_(g) is 130 at 510 K. Calculate K_c for following reactions a) 2HI_(g)  ⇌ H_2(g)  + I_2(g),  b) HI_(g)  ⇌ 1/2H_2(g)  + 1/2I_2(g), c) 1/2H_2(g)  + 1/2I_2(g)  ⇌  HI_(g).

∴  K_c = 130

For the reaction 2HI_(g)  ⇌ H_2(g)  + I_2(g),

For the reaction, HI_(g)  ⇌ 1/2H_2(g)  + 1/2I_2(g)

For reaction, 1/2H_2(g)  + 1/2I_2(g)  ⇌  HI_(g).

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In this article, we shall study more examples of physical equilibrim and the dynamic nature of equilibrium.

Dissolution of solids in liquids:

It is not possible to dissolve just any amount of a solute in a given amount of solvent. A stage will be reached when no more salt can be dissolved. A solution in which no more solute can be dissolved is called a saturated solution.

The amount of solute required to prepare a saturated solution in a given quantity of a solvent at given temperature is known as the solubility of the solute at that temperature. The saturated solution corresponds to the state of physical equilibrium.

When a solid (say sugar) is dissolved in a liquid (say water) then due to molecular vibrations the molecules on the surface of the crystal leaves, the crystal and start moving in the solvent freely. At the same time the molecule which already left the crystal return back to the crystal. Initially, the rate of leaving of the molecule from the crystal is much greater than their rate of returning to the crystal.

As the number of molecules in the solution increases the rate leaving of molecules from crystal decreases while the rate of returning of molecules to the crystal increases. A stage is reached when the rate of leaving of the molecules from the crystal surface (the rate of dissolution) is equal to the rate of returning of the molecules to the crystal surface (the rate of precipitation). Thus equilibrium state is attained.

Thus at equilibrium, Sugar_{(in solution)} ⇌ Sugar_(solid)

Dynamic Nature of Equilibrium of Dissolution of Solid in Liquid:

The dynamic nature of equilibrium of dissolution of a solid in the liquid can be experimentally demonstrated by dissolving radioactive sugar (containing radioactive carbon) into a saturated solution of non-radioactive sugar. After some time it is observed that the solution becomes radioactive, while the quantity of non-dissolved sugar remains the same.

It clearly indicates that in saturated solution radioactive sugar is getting dissolved into the solution at the same time non-radioactive sugar is getting precipitated out. Thus even if the process of dissolution seems to be stopped, actually both dissolution and precipitations are going on such that their rates are equal. This experiment demonstrates the dynamic nature of equilibrium of the dissolution of the solid in a liquid.

Effect of Increase in Temperature on Solubility of Solid in Liquid:

Solid molecules are at fixed positions in their crystal lattice. When solid is dissolved in liquid, the molecules of the solid acquire randomness. Thus the kinetic energy of the molecules of the solid after dissolving in liquid increases. This increase in kinetic energy is due to absorption of heat from the system. Thus dissolution of a solid in a liquid is an endothermic process.

By Le-Chatelier’s principle, if we increase the temperature, then the reaction proceeds in a direction to decrease the temperature. Hence the forward reaction is favoured. Hence the increase in the temperature of the endothermic reaction increases the rate of reaction. Hence the solubility of a solid in liquid increases with increase in temperature

Dissolution of Gases in Liquids:

The best example of this type of equilibrium is in soda water. When the bottle is opened the carbon dioxide gas dissolved in it fizzles out rapidly.

By Henry’s law “The mass of a gas dissolved in a given mass of a solvent, at a given temperature, is directly proportional to the pressure of the gas above the solvent”. In sealed soda water bottle the carbon dioxide gas is filled with high pressure. Due to the high-pressure appreciable amount of the gas is dissolved in water. When the cap is opened the gas pressure above the solution decreases and the gas dissolved under pressure fizzes out of the solution to attain new equilibrium state. In the case of gas in liquid solution, the solubility of the gas in liquid decreases with increase in the temperature.

The pressure exerted by the vapors in equilibrium with liquid at a particular temperature is called a vapor pressure of the liquid at that temperature.

Henry’s Law:

This law explains the effect of pressure on the solubility of a gas in a liquid. It states that “The mass of a gas dissolved in a given mass of a solvent, at a given temperature, is directly proportional to the pressure of the gas above the solvent”.

Explanation: If ‘m’ is the mass of the gas dissolved in the solvent and ‘p’ is the pressure of the gas above the solvent then

m α p i.e. m = kP

Effect of Increase in Temperature on Solubility of Gas (Carbon dioxide) in Liquid (Water):

Gas molecules are always in the state of random motion. When gas is dissolved in water, the randomness of molecules decreases. Thus the kinetic energy of the molecules of the gas after dissolving in liquid decreases. This decrease in kinetic energy results in the evolution of heat. Thus dissolution of a gas in a liquid is an exothermic process.

By Le-Chatelier’s principle, if we increase the temperature, then the reaction proceeds in a direction to decrease the temperature. Hence the backward reaction is favoured. Hence the increase in the temperature of exothermic reaction decreases the rate of reaction. Hence the solubility of a gas in water decreases with increase in temperature

Characteristics of Physical Equilibrium:

• In the case of Liquid Gas equilibrium, the vapour pressure of the liquid is constant at equilibrium at a particular temperature.
• For Solid Liquid equilibrium, there is only one temperature at which the two phases can co-exist at a particular pressure. This temperature is known as the melting point of the solid or freezing point of the liquid.
• For dissolution of solids in liquids, the solubility is constant at a given temperature.
• For dissolution of gases in liquids, the concentration of a gas in a liquid, at a given temperature is directly proportional to the pressure of the gas over the liquid.
• At physical equilibrium, the measurable properties of the system become constant.
• At physical equilibrium, there is a dynamic balance between the two opposite processes.
• The equilibrium is attained only in a system which cannot gain matter from the surroundings or lose matter to the surroundings. i.e. the system should be a closed system.
• When the equilibrium is attained, there exists an expression involving the concentration of substances involved in equilibrium which reaches a constant value at a given temperature. For the dissolution of carbon dioxide in water, the following expression has a constant value.

• The magnitude of the constant value of the concentration-related expression indicates the extent to which the process proceeds before reaching equilibrium. In above expression if the value of the ratio is higher then the numerator should be greater, hence more carbon dioxide gas is dissolved in water.

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In this article, we shall study the law of mass action and its application to chemical equlibrium.

Rate of Chemical Reaction:

The change in the concentration of the reactants (or products) per unit time is called the rate of reaction Mathematically it can be expressed as, The rate of Reaction = Change in Concentration of Products or Reactants/time in which change is taking place Hence the rate of chemical reaction is the change in concentration of the reactants in unit time. It’s S.I. unit is mol dm^-3 s^-1.

Active Mass:

Active mass is the molar concentration per unit volume of that substance. It is denoted by enclosing the symbol or formula of that substance in the square bracket. For solutions, it is expressed in “ moles dm^-3”. For gases, it is expressed in “ mol dm^-3” or pressure in the atmosphere (atm) or bar or pascal (Pa).

Factors Affecting the Rate of Chemical Reaction:

Concentration:

If the concentration of reactants increases then the rate of reaction increases.

Pressure:

Change in pressure plays an important role in gaseous reactions. There can be three types of gaseous reactions:

Reaction with the increase  in volume:

The reduction in pressure for a gaseous reaction accompanied by an increase in volume increases the rate of reaction.

e.g.  PCI_5(g)    ⇌    PCl_3(g)   +     Cl_2(g)

Reaction with the decrease in volume:

The increase in pressure for a gaseous reaction accompanied by a decrease in volume increases the rate of reaction.

e.g. N_2(g) +  3 H_2(g)   ⇌    2NH_3(g)

Reaction with no change in volume:

The gaseous reaction of equilibrium, involving no change in volume is independent of pressure.

e.g.  H_2(g) + Cl_2(g)  ⇌  2HCl_(g)

Temperature:

In general rate of reaction increases with increase in temperature.

Catalyst:

In a chemical reaction, catalyst increases the rate of reaction.

Light:

The reactions which take place in the presence of light are called photochemical reactions. Such reactions are influenced by light.

Size of particles:

If solid reactants are used in powdered form instead of granular form, the rate of reaction increases due to an increase in the surface area available for reaction

Law of Mass Action:

In 1864, Norwegian chemists Cato Guldberg and Peter Wage put forward the law of mass action

Law of mass action states that  “The rate of a chemical reaction is directly proportional to the product of active masses of reactants, at given temperature at that instant”.

Where active mass is molar concentration per unit volume of that substance.  It is denoted by enclosing the symbol or the formula of that substance in the square bracket and expressed in mol dm^-3.

Explanation of Law of Mass Action:

Consider a hypothetical reaction

A + B →  Products.

According to the law of mass action the rate of reaction

R ∝ [A] [B].

For any general reaction

aA + bB → Products.

According to the law of mass action the rate  of reaction

R ∝ [A]^a [B]^b

Equilibrium mixture:

The mixture of reactants and products formed at the chemical equilibrium state is called equilibrium mixture.

Equilibrium Concentrations:

The concentrations of the reactants and products in a chemical equilibrium state for a reversible reaction are called equilibrium concentrations.

The Expression for Equilibrium Constant in Terms of Concentrations:

Consider a hypothetical reversible reaction

A + B  ⇌  C + D

According to the law of mass action the rate of the forward reaction

R_f ∝ [A] [B]

∴  R_f  =  K_f [A] [B]

Where K_f  = rate constant for the forward reaction

According to the law of mass action the rate of the backward reaction

R_b ∝ [C] [D]

∴  R_b =  K_b [C] [D]

Where K_b = rate constant for the backward reaction

Now, for a chemical equilibrium,

R_f = R_b

K_f [A] [B] = K_b [C] [D]

Where K_C is known as equilibrium constant and the equation is called “mass law equation”.

Consider a general reversible reaction

aA + bB + cC + …   ⇌  lL  + mM  + nN + ….,    Then,

The equilibrium constant ‘ K_C‘ is defined as the ratio of the product of the equilibrium concentrations of the products to that of the reactants with each concentration term raised to the power equal to the stoichiometric coefficients of the substance in the balanced chemical equation.

Concentration is expressed in terms of mol dm^-3 or mol L^-1 or M. The equilibrium constant is denoted by Kc.

More is the numerical value of ‘K’ then more is the concentration of products in comparison with reactants & vis-a-vis.

Concentration Quotient of a Chemical Reaction:

At a given temperature, the ratio of the product of the equilibrium concentrations of the products to that of the reactants with each concentration term raised to the power equal to the stoichiometric coefficients of the substance in the balanced chemical equation is called concentration ratio or concentration quotient. It is denoted by Q_C.

At equilibrium, the concentration ratio is equal to the equilibrium constant Kc.

Its significance is that it helps in the prediction of the direction in which the net reaction is proceeding at given concentrations or partial pressures of reactants and products.

The generalization is

• If Q_C > K_C: The reaction is taking place in a backward direction i.e. in the direction of reactants.
• If Q_C < K_C: The reaction is taking place in a forward direction i.e. in the direction of products.
• If Q_C = K_C: The reaction is in an equilibrium state and hence no net reaction is taking place.

Law of Chemical Equilibrium:

At a given temperature, the ratio of the product of the equilibrium concentrations of the products to that of the reactants with each concentration term raised to the power equal to the stoichiometric coefficients of the substance in the balanced chemical equation has a constant value.

The Expression for Equilibrium Constant in Terms of Partial Pressure:

Partial Pressure:

It is the pressure exerted by a gas in a mixture of gases if it alone occupies the entire volume of the mixture of gases. The partial pressure of a gaseous component is proportional to the mole fraction. The partial pressure of a gas is calculated using the following formula

Where, n = Number of moles of gaseous component

N = Total moles of a gaseous system

P = Total pressure of the gaseous system

The Expression for Equilibrium Constant:

In the gaseous system, the concentrations in concentration quotients are replaced by partial pressure, because for given temperature the partial pressure of the gas is directly proportional to its concentration.

Consider a hypothetical reversible reaction

aA_(g) + bB_(g) ⇌  cC(g) + dD_(g)

Then the equilibrium constant in terms of partial pressures is given by

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Gibb’s Energy or Free Energy:

Gibb’s energy or free energy is a thermodynamic function which helps us in the development of a criterion of spontaneity or feasibility of a process. It refers to the capacity of the system to do useful work.

Gibb’s energy is defined as the amount of energy available from a system at a given set of conditions that can be put into useful work. It is also called free energy.

Mathematically,   G = U + PV – TS

Where      G = Gibb’s energy

U = Internal energy of the system

P = Pressure of the system

V = Volume of the system

T = Absolute temperature of the system

S = Entropy of the system

The absolute value of Gibb’s energy cannot be calculated. But the change in it can be calculated as

ΔG = ΔU + Δ(PV) – Δ(TS)

For constant pressure and constant temperature process

ΔG = ΔU + PΔV – TΔS

But ΔU + PΔV = ΔH

∴ ΔG = ΔH – TΔS

This relation is known as Gibb’s Helmholtz equation.

Where,      ΔG = Change in Gibb’s energy

ΔH = Change in enthalpy of the system

T = Absolute temperature of the system

ΔS = Change in entropy of the system

The spontaneity of a Reaction w.r.t. Gibb’s Energy and Total Entropy:

Let ΔS_Total be the total enthalpy of the system and ΔG_T,P is Gibb’s energy at constant temperature and pressure.

• If ΔS_Total > 0 (positive) or ΔG_T,P < 0 (negative), the process will be spontaneous and proceeds in a backward direction. It nears to completion. (K > 1)
• If ΔS_Total < 0 (negative) or ΔG_T,P > 0 (positive), the process will be non-spontaneous. and favoured in backward direction. (K < 1)
• If ΔS_Total = 0 or ΔG_T,P = 0, the process will be in equilibrium state. (K = 1)

Relation Between Gibb’s Energy and Chemical Equilibrium:

For spontaneous process Gibb’s energy is negative. For a reversible reaction, there is a decrease in Gibb’s energy during the course of reaction whether we start from reactants or products. Let us consider a hypothetical reaction

A ⇌ B

A graph is drawn by taking Gibb’s energy on the y-axis and the change in the composition of the reacting mixture with time on the x-axis. The graph is as follows.

The minima in the curve correspond to the composition of the reaction mixture at the equilibrium state at which Gibb’s energy is minimum.

From graph following points should be noted.

• In reaching the equilibrium state whether from A or from B, the ΔG is negative.
• At equilibrium state, there is no change in Gibb’s energy. i.e. ΔG at equilibrium = 0.
• If minima of the curve lie very close to the products, then it means that the equilibrium composition strongly favours the products and hence K >> 1. i.e. reaction will proceed to completion.
• If minima of the curve lie very close to the reactants, then it means that the equilibrium composition strongly favours the reactants and hence K < 1. i.e. the reaction hardly proceeds.

Relation Between Standard Gibb’s Energy change and Equilibrium Constant:

Let us consider a hypothetical reaction

A + B  ⇌  C + D

The relation between Gibb’s energy change (ΔG)and standard Gibb’s energy change ΔG^o is given by

ΔG = ΔG^o  + RT ln Q

Where      R = Universal gas constant

T = Absolute temperature of the system

Q = Concentration coefficient

At equilibrium ΔG = 0 and Q = K_c

∴   0 = ΔG^o  + RT ln K_c

∴    ΔG^o  = – RT ln K_c

∴    ΔG^o  = – 2.303 RT log ₁₀ K_c

This is the relation between the standard Gibb’s energy change and equilibrium constant. In exponential form, the expression can be written as

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Rate of a Chemical Reaction:

Rate of reaction is the quantities of the reactants converted into the products in unit time. Or Number of moles of the reactants used up or the number of moles of the products formed per unit time.

                        Mathematically it can be expressed as,

Rate of Reaction = No. of moles of reactants consumed / Time

Thus, the rate of chemical reaction is the change in concentration of the reactants in unit time.

Active Mass:

Active mass is molar concentration per unit volume of that substance.  It is denoted by enclosing the symbol or formula of that substance in square bracket and expressed in ” moles/ litres”.

Active Mass = No. of moles of substance/Volume in litres

Demonstration of Chemical Equilibrium:

Hydrogen and iodine are heated in a closed vessel. The reacting mixture is deep violet in colour due to the presence of iodine vapours. At 717 K the reaction between the reactants takes place. Gradually the deep violet colour of the mixture becomes faint indicating that iodine is being consumed. After some time it is observed that the intensity of violet colour becomes constant, indicating that the reaction is stopped although both hydrogen and iodine are present. This happens because equilibrium is reached. Thus the reaction is reversible and can be represented by

H_2(g) +  I_2(g)  ⇌    2HI_(g)

Chemical Equilibrium:

Chemical equilibrium is a state of a system of reacting substances at which the rate of the forward reaction is equal to the rate of backward reaction.

Explanation:

Consider general reversible reaction

A + B  ⇌  C + D

At the start of the reaction, only reactants are present. Hence concentrations of A and B are maximum and that of C and D are minimum (zero). Hence the rate of the forward reaction is maximum and that of the backward reaction is zero. As the reaction proceeds reactants A and B react to produce products C and D. Thus the concentrations of reactants A and B decrease and that of products increases. Thus the rate of the forward reaction decreases and that of the backward reaction increases.

A point will be reached when the rate of the forward reaction is equal to the rate of the backward reaction. This state of the reaction is called the chemical equilibrium. At chemical equilibrium concentration of reactants and product remains unchanged throughout.  It means that at equilibrium neither forward nor backward reaction stops, but are continued at equal rates in opposite directions.  Hence we can say that the equilibrium is dynamic and not static. It is to be noted that the reversible reactions involving gaseous substances are carried out in a closed vessel.

Graphical Representation:

Chemical Equilibrium a Dynamic Equilibrium:

• Chemical equilibrium is a state of a system of reacting substances at which the rate of the forward reaction is equal to the rate of the backward reaction
• At chemical equilibrium concentration of reactants and products remains unchanged throughout.  It means that at equilibrium neither forward nor backward reaction stops, but are continued at equal rates in opposite directions.
• The concentrations of reactants and products at chemical equilibrium are constant. At the same time, all the observable properties of the system become constant. Hence we can say that the equilibrium is dynamic and not static.

Characteristics of Chemical Equilibrium:

• Chemical equilibrium exists in reversible reactions only.
• At equilibrium, the rate of the forward reaction is equal to the rate of the backward reaction.
• At equilibrium, the concentrations of reactants and products remain constant. These concentrations are called equilibrium concentrations.
• At equilibrium, both the forward reaction and the backward reaction do not stop. Actually, all the reactants and products are present at the equilibrium
• At equilibrium, neither the forward reaction nor the backward reaction has ceased. Both reactions proceed in opposite directions with an equal rate. Thus chemical equilibrium is dynamic in nature.
• At the chemical equilibrium, the observable properties of the system like pressure, colour, concentrations, etc. become constant and remain unchanged thereafter.
• The equilibrium can be approached from either direction.
• Equilibrium can only be attained only if the system is closed.
• State of chemical equilibrium is unaffected by catalyst because the presence of catalyst equally increases the speed of both the forward and the backward reaction.
• State of chemical equilibrium changes with the change in factors like concentration, temperature and pressure.

Factors Affecting Chemical Equilibrium:

Effect of the Change of Concentration:

If the concentration of reactants increases then there will be a rise in the concentration of the products and thus equilibrium is shifted from left to right.

Explanation: By the law of mass action, the rate of a chemical reaction is directly proportional to the product of active masses of reactants, at given temperature at that instant. As the concentration of reactants is increased, the product of concentrations of reactants increases thus to keep the value of equilibrium constant the same the product of concentrations of products is increased. Thus more products are formed. Hence equilibrium is shifted from left to right.

Effect of the Change of Pressure:

Change in pressure plays an important role in gaseous reactions.  There can be three types of gaseous reactions:

• Chemical reactions accompanied by the increase in volume
• Chemical reactions accompanied by the decrease in volume
• Chemical reactions accompanied by no change in volume

Chemical reactions accompanied by the increase in volume:

Consider reaction.

PCI_5(g)    ⇌    PCl_3(g)   +     Cl_2(g)

1 Vol             1 Vol              1 Vol

1 Vol                     2 Vol

In this reaction, 1 volume of reactants gives 2 volumes of products.  Thus in this reaction volume is increased.

The chemical reactions involving gases and accompanied by the increase in volume are favoured by a reduction in pressure. Thus by decreasing the pressure at equilibrium, equilibrium is shifted towards the right.

Chemical reactions accompanied by the decrease in volume:

Consider the reaction.

N_2(g) +  3 H_2(g)   ⇌    2NH_3(g)

1 Vol       3 Vol              2 Vol

4 Vol                        2 Vol

In this reaction, 4 volumes of reactants give 2 volumes of products.  Thus in this reaction volume is decreased.

Chemical reactions involving gases and accompanied by a decrease in the volume are favoured by an increase in pressure. Thus by increasing the pressure at equilibrium, equilibrium is shifted towards the right.

Chemical reactions accompanied by no change in volume:

Consider following reaction.

H_2(g) + Cl_2(g)  ⇌  2HCl_(g)

1 Vol        1 Vol             2 Vol

2 Vol                     2 Vol

In this reaction, 2 volumes of reactants give 2 volumes of products.  Thus in this reaction volume is not changed.

Chemical reactions involving gases and accompanied by no change in volume are not affected by the change in pressure.

Effect of the Change of Temperature:

If the temperature of the exothermic chemical reaction is increased, then the concentration of products reduces and thus the equilibrium is shifted towards left. Hence the reduction in temperature favours exothermic reaction at equilibrium and increase in temperature favours endothermic reaction.

It is to be noted that in a reversible reaction if one reaction is exothermic then another reaction is endothermic. Thus the effect of change of temperature on the two reactions is different.

Effect of Presence of a Catalyst:

A catalyst is a substance which increases or decreases the rate of a reaction without taking part in the chemical reaction.

In a reversible reaction at equilibrium, catalyst affects the rate of both the forward reaction and the backward reaction to the same extent. Hence catalyst at equilibrium does not affect chemical equilibrium.

Addition of Inert Gas at Constant Volume:

If the inert gas is added to the reaction at constant volume It will result in the increase of the total pressure of the system. At the start, the partial pressures of the reactants and pressure will get changed. But in short time they will attain their equilibrium values before addition of the inert gas. Thus partial pressures of reactants and products are not getting affected. Hence there is no effect of the addition of inert gas on equilibrium at constant volume.

Addition of Inert Gas at Constant Pressure:

If the inert gas is added to the reaction at constant pressure It will result in an increase in the volume of the system. Thus the concentration of the reactants and products will decrease. To counterbalance this stress (change) the equilibrium will shift to the side where the number of moles is increased.

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