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# Chemical Equilibrium

On a microscopic scale most reaction can occur in both the forward and reverse directions.

When we say that a reaction is going forward what we mean is that the rate of the forward reaction is larger than the rate of the reverse reaction.

In other words at any given moment more reactant mass converts into products than there is product mass converting back into reactant.

Remember, the chemical reactions simply convert a given amount of mass between states.

Once the chemical system achieves equilibrium the concentration of reactants and products no longer changes.
The resulting combination of concentration is called an equilibrium mixture and can be used to characterize the reaction.

Chemical equilibrium is the state in which forward and reverse chemical reactions occur simultaneously at the same rate.

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## Forward Reaction

Chemical equilibrium is a condition which means that the rate of the forward reaction is equal to the rate of the backward reaction. Equilibrium reaction is one in which there is no change in the concentration of the reactant or product.

Though concentration of the reactant and the product remains the same, the forward reaction and the backward reaction take place simultaneously. Thus chemical equilibrium is a Dynamic one, that is, both the forward reaction and the back ward reaction take place simultaneously.

Consider the reaction,
A $\rightleftharpoons$ B + C ---(1)

The forward reaction in this equilibrium process is
A B + C
The forward reaction is one in which the reactant reacts to form products. So, A reacts to give B and C the forward reaction.

## Backward Reaction

For the reaction 1, the backward reaction which is also called as the reverse reaction is
B + C A
The product reacting back to form the reactant is the backward reaction. Some time the backward reaction rate is so fast that it seems as if the reaction has not occur at all because whatever product is formed, it immediately reacts to give back the reactant. So the product is not seen in the reaction itself.

## Overall Reaction

The overall reaction is the full equilibrium, that is, the forward reaction and the backward reaction taking place. And equilibrium condition is said to be reached when the rate of the forward reaction is equal to the rate of the backward reaction.

When the Equilibrium is reached, there is no change in the concentration of the reactant and the product. Although the concentration of the reactant and the product does not change under equilibrium condition, the concentration of the reactant and the product is not same. They would be different.

## Conditions of Equilibrium

The first condition for the equilibrium is that the forward and the backward reaction rates should be equal. The pressure, temperature and the concentration of the reactant and the product do not change. There should not be any change during the equilibrium. Equilibrium is reached only in the closed vessel.

In the open vessel some of the reactant or product may get evaporated, so closed vessel is an important condition for the equilibrium to occur.

## Reversibility and Equilibrium

It has been established that when a chemical reaction proceeds, energy will be conserved during the chemical changes and all across the reaction when products are formed. But we have not found a way of predicting in which direction the reaction will go. In other words, we have not found a suitable definition of the position of equilibrium. We have discovered that for molecular systems the energy unlike the potential energy in mechanical systems does not provide a sufficient criterion for equilibrium.

A new factor must be introduced which will enable us to understand why heat always flows from hot to clod bodies and why a perfect gas will expand to fill its container even though no loss of energy accompanies these processes.
We have observed that in our considerations of mechanical systems, if a change occurs in such a way that a system is always in equilibrium then the change will proceed infinitely slowly and will be capable of doing maximum amount of work. Such a change is called reversible. The conditions which must be satisfied for a reversible change are the same conditions that must be satisfied if the system is to be in the state of equilibrium.

For a reversible change the work done by the system is a maximum. Thus, for a reversible change dw is more negative than for the equivalent irreversible spontaneous change. dU must be the same for a given change whatever way it is carried out. Therefore, for a reversible change since dwrev < dwirr we have dqrev > dqirr.

During a reversible change a system absorbs the maximum heat from its surroundings and does the maximum work on its surroundings. Observable spontaneous processes absorb less heat and do less work than the corresponding reversible process.

The equilibrium reaction is when the forward and reverse reaction should take place simultaneously. Reversibility is the important condition for the equilibrium, when the reaction is not reversible then the reaction is said to be spontaneous reaction. So reversibility is the important criteria for equilibrium.

## Acid Base Equilibria

Acid-base equilibria are important chemical processes both in thermal and in photochemical reactions, since many molecules have an 'acid' form AH and a 'base' form A which is connected by the transfer of a proton.

For example

AH+ A + H+

The equilibrium constant for this reversible proton transfer reaction is
K = [A] [H+] / [AH+]

This is usually given by the pK of the reaction, which is the pH of the solution in which the concentrations of the acid and base forms are equal.

These acid-base equilibria are important since the acid and base forms of many molecules have quite different physical and chemical properties.

### Redox Behavior

Redox process is conceptually helpful and serves as a thread throughout by three major differences.
1. H+ in some hydrated form, exists as a species in water but e- does not.
2. Acid-base reactions in solution are typically fast, whereas redox reactions are typically slow and mediated by organisms. Total equilibrium for redox processes in natural water results in meaningless and lifeless models.
3. Unlike those for acid-base reactions, equilibrium constants for redox reactions are often extremely large or small. The free energies involved are much larger in redox than in acid-base processes and at equilibrium redox reactions proceed to completion in one direction or the other.

### Thermal Properties

The specific heat capacity (commonly called specific heat) of a material is defined as the quantity of thermal energy required to raise the temperature of unit on the material by 1oC, its units are J / Kg / K.

The specific heat of fluid milk products is temperature dependent, so amount of heat energy to be added or removed to affect a given temperature change is given by the equation.

q = ∫ c(θ) d (θ)

where q is quantity of heat energy per kg. θ is temperature (oC), θ2 - θ1 is temperature change brought about by adding or removing q and c(θ) is specific heat expressed as some function of temperature.

### Chemical Properties

Acid and base are collective terms defined by chemist in such a way as to indicate all compounds having similar chemical properties. Several times in the history of chemistry, chemists have noted additional groups of compounds that show many properties of reactions analogous to those of recognized acids and bases.

This type of Equilibrium, that is, the acid base equilibrium comes under ionic equilibrium. An acid is a substance which can donate a proton to the solution and the base is substance which can accept the proton from the acid.

Consider the following equilibrium

CH3COOH $\rightleftharpoons$ CH3COO- + H+

The acetic acid is a weak acid, which means that it does not dissociate fully. The product that is the acetate ion reacts with proton to give acetic acid and acetic acid dissociates to give acetate ion. So equilibrium is established between the proton, acetate ion and acetic acid.

## Chemical Equilibrium in Solutions

The key to understand reaction in aqueous solution is to recognize that reactions are often reversible and they tend towards equilibrium state.

### Equilibria in aqueous solution are of two fundamental types

1. Dissociation between a dissolved, undissolved species and its component parts.
2. Solubility between a pure phase and its characteristic species in solution.
In addition, the simultaneous establishment of two or more equilibria in the same solution are also worth considering.

Pure water is slightly dissociated as
H2O $\to$ H+ + OH-

Therefore, in pure water and in all aqueous solution we must satisfy the condition

K = $\frac{[H+] [OH-]}{[H2O]}$

In dilute solutions, the concentration of H2O is a constant (large amount) which can be combined with K as follows.

K[H2O] = Kw = [H+] [OH-]

Kw is usually called ionic product of water and it equals to 1.0 x 10-14 at 25oC but it increases with slight increase in temperature. Chemical equilibrium can also take place in solution for example consider the

CH3COOH(aq) + H2O(l) $\rightleftharpoons$ CH3COO- (aq) + H3O+(aq)

Here water is in the liquid phase and all others are in the solution. This type of equilibrium is homogenous equilibrium.

## Equilibrium Between Gaseous Reactants

Consider the equilibrium

A (g) B(g)

This is the simplest type of chemical equilibrium and corresponds to the equilibrium between two isomers such as n-butane and isobutane.
If dnA moles of A are converted into dnB moles of B at constant T and P we have

dG = (+ μA dnA + μB dnB)

where dnA is negative and dnB is positive. We can define an extent of reaction which is 0 when the reaction position is entirely to the left of the equation and is 1 when one mole of reactant has gone over entirely to products. In our simple example we may write

dξ = dnB = -dnA
and dG = ( μB - μA ) dξ at constant T and P

The reaction will proceed until G reaches a minimum value and

(∂G / ∂ξ) T,P = 0
(∂G / ∂ξ) T,P = μB - μA

This is the position where μA = μB
If the components follow perfect gas law then

μi = μio + RT ln (Pi / atm)

Therefore,

(∂G / ∂ξ) T,P = μB - μA = μBo - μAo+ RT ln (PB / PA)

μBo - μAo = ΔGo

(∂G / ∂ξ) T,P = ΔGo+ RT ln (PB / PA)

At equilibrium
ΔG' = 0

and as

ΔG' = ΔGo+ RT ln (PB / PA)

ΔGo = - RT ln (PB / PA)

We call the value of (PB / PA) at equilibrium is the equilibrium constant of the reaction Kp.
ΔGo = - RT ln Kp

This important equation tells how the position of chemical equilibrium can be defined in terms of the free energies of the reactants and products at 1 atm pressure.

O2(g) + 2H2(g) $\rightleftharpoons$ 2H2O(g)

Here in this equilibrium all the reactant and the products are in gaseous state. This type of equilibrium is more affected by the pressure. When the pressure of the equilibrium is increased or decreased then the equilibrium condition would change. In this reaction when the pressure is increased the forward reaction is favored.

## Equilibrium Redox Behavior

Redox reaction is the one in which there is a transfer of electron between the reactants. One of the reactant is oxidized and the other is reduced. So the equilibrium:

Here, in the forward reaction the oxygen is reduced and hydrogen is oxidized, but in the reverse reaction, the oxygen is oxidized and hydrogen is reduced. This type of reaction involving the transfer of electron is called as redox reaction.

## Equilibrium by Protolysis

Acid base equilibrium can be viewed as the equilibrium due to protolysis. Again consider the acetic acid and water equilibrium

CH3COOH(aq) + H2O(l) $\rightleftharpoons$ CH3COO- (aq) + H3O+(aq)

Here water acts as an base, it gets the proton from the acetic acid and forms hydronium ion. In the backward reaction the hydronium ion acts as an acid and gives the proton to the acetate ion. At equilibrium concentration of the acetic acid, acetate ion and the hydronium ion do not change.