# THE CONCEPT OF CHEMICAL EQUILIBRIUM

## Chemical Equilibrium

In a chemical reaction, chemical equilibrium is the state in which both reactants and products are present in concentrations which have no further tendency to change with time.

The chemical equilibrium is achieved when the rate of forward reaction is same as the reverse reaction. Since the rates are equal, there are no net changes in the concentrations of the reactant(s) and product(s). This state is known as dynamic equilibrium.

The entire process can be graphically represented by this diagram.

## Law of Chemical Equilibrium & Equilibrium Constant Kc

• Chemical Equilibrium can easily be understood by understanding Chemical Kinetics. It is the study of the rate of the reactions under various conditions.
• Another concept that forms the basis is the Law of mass action.
• Law of mass action states that the Rate of a chemical reaction is directly proportional to the product of the concentrations of the reactants raised to their respective stoichiometric coefficients.
• So, Given a reaction:
aA(g) + bB(g) ⇌ cC(g) + dD(g)
Using the Law of mass action,
Forward reaction rate
= k[A]a[B]b
Backward reaction rate
= k– [C]c[D]d

where, [A], [B], [C] and [D] being the active masses and k+ and k are rate constants.

• At equilibrium forward and backward rates are equal and the ratio of the rate constants is a constant and is known as an equilibrium constant.
• In a reaction mixture at equilibrium, the concentrations of the reactants and products are related by an equilibrium constant. For the reaction
aA(g) + bB(g) ⇌ cC(g) + dD(g)

Forward reaction rate
= Backward reaction rate
k[A]a[B]= k– [C]c[D]d
We have,
Kc = k/ k
Kc = [ C ]c·[ D ]d / [ A ]a·[ B ]b

• Equilibrium Constant & Gibbs Free energy:
• Temperature Dependency: Equilibrium constant Kdepends on thetemperature of the reaction and the relation is given by Van’t Hoff equation. • In the above equation,
• K1 is the equilibrium constant at absolute temperature T1,
• K2 is the equilibrium constant at absolute temperature T2,
• R is the ideal gas constant,
• ΔH reaction enthalpy assumed to be constant over the temperature range.
• This equation can be used to estimate a new equilibrium constant at a new absolute temperature assuming a constant standard enthalpy change over the temperature range.
• Now, Let’s understand the change in the equilibrium constant for two different kinds of reactions: Endothermic & Exothermic. Using the definition of Gibbs free energy & Gibbs free energy Isotherm equation, we have: • In the above equation,
• Keq is the equilibrium constant at temperature T.
• ΔH and ΔS are constants and are enthalpy and entropy of the system respectively.
• This graph of this equation is called the Van ‘t Hoff plot. The plot is used to estimate the enthalpy and entropy of a chemical reaction.
• From the plot between “ln Keq” & “1/T“, we have  −ΔH/R as the slope, and ΔS/R as the intercept of the linear fit.
• Exothermic reactions
• Endothermic reactions
• For an endothermic reaction, heat is absorbed, making the net enthalpy change positive.
• ΔH > 0, so slope (−ΔH/R) is negative.
•  Van ‘t Hoff plot has a negative slope.

## Types of Chemical Equilibria

There are two types of chemical equilibria:

• Homogeneous equilibria
• Heterogeneous equilibria

Homogeneous Equilibria

• The equilibrium reactions in which all the reactants and the products are in the same phase are known as homogeneous equilibrium reactions. These are divided into two categories:
• The number of product molecules is equal to the number of reactant molecules. For example:
• N2 (g) + O2 (g) ⇌ 2NO (g)
• H2 (g) I2 ⇌ 2HI (g)
• The number of product molecules is not equal to the number of reactant molecules.
• COCl2 (g) ⇌ CO (g) + Cl2 (g)
• 2SO2 (g) + O2 (g) ⇌ 2SO3 (g)
• In gaseous phase, • In solution phase, • The equilibrium constant for the homogeneous reaction in gaseous systems:
• Ideal gas equation is given by, pV = nRT If concentration C is in mol L−1 or mol dm−3 and p is in bar, then we can write p = c RTOr, p = [gas] RT …..(i)Where R = 0.0831 bar L mol−1 K−1For a general reaction, • In the above equation,
• Δn = (number of moles of gaseous products)− (number of moles of gaseous reactants) in the balanced chemical equation
• While calculating Kp, pressure should be expressed in bar.
• 1 bar = 105 Pa = 105 Nm−2

Heterogeneous Equilibria • The concentrations of pure solids & pure liquids assumed to be constant and these do not appear in equilibrium concentration expression. By convention [solid] = 1 and [liquid] = 1

## Relation between K, Q, and G (Gibbs Energy)

• There is a very important relationship between Standard Gibbs free energy (Go) and the equilibrium constant (Keq).
• We know that the reaction quotient (Q) measures the relative amounts of products and reactants present during a reaction at a particular point in time.
• The free energy change at any point in of the chemical reaction is given by:

## • At equilibrium,  ΔG = 0 (zero) and Q = Keq. This condition gives the relation, •  The equilibrium constant (K) is another way we can tell if a reaction is spontaneous.
• Here,  ΔGo is equal to negative R, the gas constant, multiplied by the temperature in Kelvin, multiplied by the natural log of the equilibrium constant.
• This relationship allows us to directly relate the standard free energy change to the equilibrium constant. It also tells us about the extent of the reaction.
• If, ΔGo < 0, ln Keq = positive, Hence Keq > 1 implying that it is a spontaneous reaction.
• If, ΔGo < 0, ln Keq = negative, Hence Keq < 1 implying that it is a non-spontaneous reaction.

## Factors Affecting Chemical Equilibrium

• The factors that can influence chemical equilibrium are:
• Change in concentration
• Change in pressure (or volume)
• Change in temperature.
• The effect of the change in one of these factors on the extent of reaction can be qualitatively explained by using Le Chatelier’s principle.
• Le Chatelier’s principle
According to this principle, if a system is in equilibrium and it is subjected to any change in any of the factors that determine the equilibrium conditions of the system, then it will shift the equilibrium in such a way to reduce or to counteract the effect of the change.

To help you understand the effects of various changes better, here is the summary:

 Changes Effects Concentration Change Concentration stress of an added reactant/ product is relieved by the net reaction in the direction that consumes the added substance Concentration stress of a removed reactant/product is relieved by the net reaction in the direction that replenishes the removed substance Pressure Change In case of solids and liquids, the effect of pressure change is neglected (because the volume of solid or liquid is independent of pressure). If the pressure is increased, then the equilibrium shifts in the direction in which the number of moles of gas or pressure decreases. Addition of Inert Gas If an inert gas is added at constant volume, then the equilibrium remains undisturbed (because Partial pressures or molar concentrations of the substance do not change with the addition of inert gas at constant volume). Change in Temperature Change in the equilibrium constant with temperature depends upon the sign of ΔH for the reaction. For exothermic reaction (negative ΔH), the equilibrium constant decreases (Backward Shift) with the increase in temperature. For endothermic reaction (positive ΔH), the equilibrium constant increases (Forward Shift) with the increase in temperature. Catalyst A catalyst does not affect the equilibrium

Chemical equilibrium is a dynamic process that consists of a forward reaction, in which reactants are converted to products, and a reverse reaction, in which products are converted to reactants. At equilibrium, the forward and reverse reactions proceed at equal rates. Consider, for example, a simple system that contains only one reactant and one product, the reversible dissociation of dinitrogen tetroxide (N2O4) to nitrogen dioxide (NO2). You may recall from Chapter 14 “Chemical Kinetics” that NO2 is responsible for the brown color we associate with smog. When a sealed tube containing solid N2O4 (mp = −9.3°C; bp = 21.2°C) is heated from −78.4°C to 25°C, the red-brown color of NO2appears (Figure 15.1 “The “). The reaction can be followed visually because the product (NO2) is colored, whereas the reactant (N2O4) is colorless:

Equation 15.

The double arrow indicates that both the forward and reverse reactions are occurring simultaneously; it is read “is in equilibrium with.”

System at Different Temperatures

(left) At dry ice temperature (−78.4°C), the system contains essentially pure solid N2O4, which is colorless. (center) As the system is warmed above the melting point of N2O4 (−9.3°C), the N2O4 melts and then evaporates, and some of the vapor dissociates to red-brown NO2. (right) Eventually the sample reaches room temperature, and a mixture of gaseous N2O4 and NO2 is present. The composition of the mixture and hence the color do not change further with time: the system has reached equilibrium at the new temperature.

Figure 15.2 “The Composition of N” shows how the composition of this system would vary as a function of time at a constant temperature. If the initial concentration of NO2 were zero, then it increases as the concentration of N2O4 decreases. Eventually the composition of the system stops changing with time, and chemical equilibrium is achieved. Conversely, if we start with a sample that contains no N2O4 but an initial NO2 concentration twice the initial concentration of N2O4 in part (a) in Figure 15.2 “The Composition of N”, in accordance with the stoichiometry of the reaction, we reach exactly the same equilibrium composition, as shown in part (b) in Figure 15.2 “The Composition of N”. Thus equilibrium can be approached from either direction in a chemical reaction.

(a) Initially, this idealized system contains 0.0500 M gaseous N2O4 and no gaseous NO2. The concentration of N2O4 decreases with time as the concentration of NO2 increases. (b) Initially, this system contains 0.1000 M NO2 and no N2O4. The concentration of NO2 decreases with time as the concentration of N2O4 increases. In both cases, the final concentrations of the substances are the same: [N2O4] = 0.0422 M and [NO2] = 0.0156 M at equilibrium.

Figure 15.3 “The Forward and Reverse Reaction Rates as a Function of Time for the ” shows the forward and reverse reaction rates for a sample that initially contains pure NO2. Because the initial concentration of N2O4 is zero, the forward reaction rate (dissociation of N2O4) is initially zero as well. In contrast, the reverse reaction rate (dimerization of NO2) is initially very high (2.0 × 106 M/s), but it decreases rapidly as the concentration of NO2 decreases. (Recall from Chapter 14 “Chemical Kinetics” that the reaction rate of the dimerization reaction is expected to decrease rapidly because the reaction is second order in NO2: rate = kr[NO2]2, where kr is the rate constant for the reverse reaction shown in Equation 15.1.) As the concentration of N2O4 increases, the rate of dissociation of N2O4 increases—but more slowly than the dimerization of NO2—because the reaction is only first order in N2O4 (rate = kf[N2O4], where kf is the rate constant for the forward reaction in Equation 15.1). Eventually, the forward and reverse reaction rates become identical, kF = kr, and the system has reached chemical equilibrium. If the forward and reverse reactions occur at different rates, then the system is not at equilibrium.

The rate of dimerization of NO2 (reverse reaction) decreases rapidly with time, as expected for a second-order reaction. Because the initial concentration of N2O4 is zero, the rate of the dissociation reaction (forward reaction) at t = 0 is also zero. As the dimerization reaction proceeds, the N2O4 concentration increases, and its rate of dissociation also increases. Eventually the rates of the two reactions are equal: chemical equilibrium has been reached, and the concentrations of N2O4 and NO2 no longer change.

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