# Equilibrium Constant

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#### Characteristics of Equilibrium Constant:

• It has a definite value for every chemical reaction at a particular temperature.
• It is independent of 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 an equilibrium is multiplied by a factor, then the equilibrium constant must be raised to the power equal to the factor.

If Kc is equilibrium constant for reaction aA + bB   cC + dD

Then equilibrium constant for reaction naA + nbB   ncC + ndD is given by

K’c = (Kc)n

• 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.

K(resultant) = K(Reaction 1)  x K(Reaction 2)

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

K = (K1)a(K2)b(K3)c……..

• For a reversible reaction, the equilibrium-constant 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.

#### Equilibrium Constant 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 KP and KC obtained are dimensionless. Hence equilibrium constant is considered as dimensionless, unitless quantity.

#### Equilibrium Constant 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.

#### Equilibrium Constant for the addition of Two Chemical Equilibria:

Consider following equilibria

1) N2(g) +   O2(g)  ⇌     2NO(g)

The equilibrium constant for the reaction is 2)   2NO(g) +   O2(g)  ⇌     2NO2(g)

The equilibrium constant for the reaction is 3)  N2(g) +  2O2(g)   ⇌   2NO2(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 Kf (rate constant for the forward reaction) and Kb (rate constant for the backward reaction) changes to a different extent. Thus the ratio Kf / Kb changes. i.e. the value of equilibrium constant changes with the change in temperature.
• Value of equilibrium constant for endothermic reaction increases with increase in temperature, while the value of equilibrium constant for exothermic reaction decreases with increase in temperature,
• The temperature dependence of equilibrium constant can be written mathematically as • #### It helps in the prediction of the extent of reaction:

• The magnitude of the KC 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 KC > 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 KC < 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 < KC < 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 KC 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 KC > 103 Products are stable than reactants.
• If KC < 10-3 Reactants are stable than products.
• #### It helps in the prediction of the direction of a net reaction.

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

For reaction aA + bB   cC + dD When computing QC the concentration at that instant are used When computing KC the concentration at equilibrium are used

• The generalization is
• If QC > KC , the reaction is taking place in a backward direction i.e. in the direction of reactants
• If QC <  KC , the reaction is taking place in a forward direction i.e. in the direction of products.
• If QC =  KC 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 KC and Equilibrium Pressures:

1. Write the chemical equation for the equilibrium
2. Write equilibrium constant expression 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 equilibrium constant.
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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