Chemistry

Key unit competence

To write expressions and calculate the values of equilibrium constant, interpret the

values of Kc in relation to the yield of the products in reversible reactions.

Learning objectives

At the end of this unit , students will be able to:

• Explain how the temperature affects the magnitude of equilibrium constant

Kc;

• Derive the relationship between Kc and Kp;

• Write expression for Kc and Kp;

• Interpret the Kc values in relation to the yield of the reversible reactions;

• Compare the Kc value with Qc value and predict if a reaction is at equilibrium

or not.

• Compare and interpret the values of Kc and Kp of different reactions;

• Perform calculations involving equilibrium constants in terms of concentration(Kc), and partial prsessure (Kp).

In most of the chemical reactions, the reactants are not completely converted into products. The reaction proceeds to a certain extent and reaches a state at which the concentrations of both reactants and products remain constant with time.

Chemical equilibrium is the state in which both reactants and products of a chemical reaction are present in concentrations that do not change with time. Chemical equilibrium deals with the reversible reactions, which reach equilibrium state; where the forward reaction proceeds at the same rate as the reverse reaction. The scope of chemical equilibrium includes the study of characteristics and factors affecting the chemical equilibrium.

8.1. Definition and characteristics of equilibrium constant Kc

8.1.1. Definition

 The equilibrium constant expresses ratio between the concentrations of the products and the concentrations of the reactants under the given conditions. The equilibrium constant is symbolized by Kc , and the ratio Q expresses the value of the reaction quotient when the forward and reverse reactions occur at the same rate. When the reaction reaches the equilibrium, no change is observed between the chemical composition of the mixture with time and the enthalpy of the products is equal to that of the reagents while the Gibbs free energy change for the reaction is equal to zero. By definition: The equilibrium constant, Kc, is the ratio of the equilibrium concentrations of products over the equilibrium concentrations of reactants each raised to the power of their stoichiometric coefficients at given temperature.

8.1.2. Characteristics of equilibrium

Consider the following reversible reaction involving homogeneous system;

Note: All the concentrations used to calculate Kc are measured at homogeneous

equilibrium.

Where, A, B, C, and D are chemical species, and a, b, c, and d are their respective

stoichiometric coefficients.

• If Kc value >> 1, the direct reaction is favored and the reaction mixture contains

mostly products.

• If Kc value <<1, the reverse reaction is favored and the reaction mixture

contains mostly reactants.

• If the Kc value is close to 1 (0.10 < Kc < 10), the mixture contains appreciable

amounts of both reactants and products

Examples: Write the equilibrium constant expression, Kc, for the following reactions:

Note:

i. The equilibrium can be approached from either direction (forward or

backward direction).

ii. The equilibrium constant Kc does not depend on the initial concentrations

of reactants and products but it depends on temperature.

The equilibrium is described as homogeneous if all species are in the same phase

and heterogeneous if they are in different phases.

Worked examples:

Write the equilibrium constant expression, Kc, for the reactions

Evaluating K_c  for a reaction:

In order to determine the value of an equilibrium constant, when amounts of

reactants are known at equilibrium. The amount of one of the substances in the

equilibrium mixture is found by experiment. The amounts of the others can then

be worked out from the stoichiometric equation as shown in the following worked example.

Examples

1. 2.0 mol of ethanoic acid and 2.0 mol of ethanol are mixed and allowed to come

to equilibrium with the ethyl ethanoate and water they have produced. At

equilibrium, the amount of ethanoic acid present is 0.67 mol. Calculate K_c.

Solution

therefore the concentration units cancel out, and K is a unitless number.

Characteristics of the equilibrium constant Kc

The equilibrium constant, K_c is governed by temperature, which is the only factor

that can change the internal potential energy of the reactants or products.

i. If the forward reaction is exothermic, K_c decreases with the increase in

temperature.

ii. If the forward reaction is endothermic, K_c increases with the increase in

temperature.

iii. The application of a catalyst to a reaction has no effect on a K_c value.

8.2. Deriving equilibrium constant Kc

8.2.1. Deriving equilibrium constant Kc from thermodynamic approach

The equilibrium constant gives the rate of transformation and expresses the ratio

of the concentrations between the products and the reagents under the given

conditions.

A relation can be derived between the change of standard free enthalpy and the

equilibrium constant. Enthalpies and entropies are important thermodynamic

functions used for a wide variety of applications. Enthalpy and entropy express the

energy and the randomness of a reaction respectively. In chemistry, the temperature

is an important factor that often can influence the rate of the reaction.

The application of thermodynamic data is expanded due to the introduction of the

Gibb’s energy, because of its link to the equilibrium constant, Kc.

 A relationship between the equilibrium constant, Kc, and Gibb’s energy, G, entropy

S at temperature T have been introduced.

8.3. Mass action law and equilibrium constant expression

Activity 8.3

1. Explain briefly the mass action law.

2. By giving an example, deduce the unit of concentration.

8.3.1. Mass action law

In chemistry, all the species involved in the chemical reaction must be equal in both

sides of reaction (reactants and products). This is the basic explanation of the mass

action law which can be defined as follows: Law of Mass Action or Equilibrium law

states that “The ratio of an equilibrium concentrations of products and reactants

each raised to the power of their coefficients in the balanced stoichemetric

equations is a constant, Kc, at a constant temperature".

The molar concentration i.e. number of moles per litre is also called Active Mass. It is

expressed by enclosing the symbols of formulae of the substance in brackets.

For example, molar concentration of A is expressed as [A].

According to law of mass action: the total mass of A and B involved in the collision

must be equal to the total mass of new formed compounds

8.4. Definition of equilibrium constant in terms of partial pressures “Kp”

Activity 8.4

1. Write down the ideal gas equation and explain all terms involved in.

2. Explain the term “partial pressure’’

For gaseous equilibria, the concentration of reactants and products can be expressed

in terms of pressures of the different components. If the reaction mixture behaves as

an ideal gas, the ideal gas equation is PV = nRT. The molar concentration [X], which is

n/V, is then equal to P/RT. This shows that, at a given temperature when T is constant,

the pressure of a component is proportional to its molar concentration.

The equilibrium constant with the concentrations of reactants and products

expressed in terms of molarity is expressed by Kc. 

   Determination of the partial pressure

8.5. Relationship between Kc and Kp

Activity 8.5

Explain the terms Kc and Kp

The pressure and molarity are related by the Ideal Gas Law, PV = nRT where

P = nRT/V

Consider the general reaction:

Δn = moles of gaseous products - moles of gaseous reactants

K_p= equilibrium constant in gaseous phase expressed in partial pressures

K_c = equilibrium constant in molar concentrations

Note: Kc = Kp when the number of gas molecules are the same in both sides

 (Δn = 0).

Characteristics of equilibrium constant

• The value of the equilibrium constant is independent of the original

concentration of reactants.

• The equilibrium constant has a definite value for every reaction at a particular

temperature. However, it varies with change in temperature.

• For a reversible reaction, the equilibrium constant for the forward reaction is

inverse of the equilibrium constant for the backward reaction.

• In general, K_forward reaction = 1/K’_backward reaction and vice-versa

• The value of an equilibrium constant tells the extent to which a reaction proceeds in the forward or reverse direction.

• The equilibrium constant is independent of the presence of catalyst.

8.6. Calculations on Kc and Kp

8.7. Comparison between reaction quotient Qc and equilibrium constant Kc

Activity 8.7

1. What do you understand by the term reaction quotient

2. By giving an example differentiate the reaction quotient and reaction

constant Kc.

The reaction quotient, Q, is the resulting value when we substitute reactant and the

product concentrations into the equilibrium expression. A reaction quotient (Qr or

Q) is a function of the activities or concentrations of the chemical species involved

in a chemical reaction.

The difference is that Q can be calculated at any conditions (not only on equilibrium

conditions) while the equilibrium constant is determined when there is a reversible

reaction.

Example:

Consider for the following general equation:

• If Q = Kc, the reaction is at equilibrium and the concentrations will not change

since the rates of forward and backward reactions are equal.

• If Q < Kc, the ratio of products over the reactants is too small and the reaction

is not at equilibrium; the reaction will move toward the equilibrium by forming

more products.

• If Q > Kc, the ratio of products over the reactants is too large and the reaction

is not at equilibrium; the reaction will move toward the equilibrium by forming

more reactants.