Chemical Equilibrium

Equilibrium Constant

When forward and reverse reactions occur at the same rate, the system reaches dynamic equilibrium. Chemical equilibrium occurs when dynamic equilibrium realizes for ALL steps of the reaction, i.e. the equilibrium between reagents and the products is achieved.

At a given temperature, the equilibrium composition is related to the equilibrium constant, K_c. For the general reaction aA + bB --> cC + dDK_c is the ratio of the product concentrations divided by the reactant concentrations, with each concentration raised to the power of its coefficient in the balanced chemical reaction.

K_c =	[C]^c[D]^d

	[A]^a[B]^b

Regardless of the initial concentrations, the final equilibrium concentrations must satisfy the equation specified by K_c. Usually K_cis written without units.

If an equilibrium involves reactants and products in a single phase that is called a homogeneous equilibrium, opposite to a heterogeneous equilibrium which involves reactants and products in more than one phase. For the latter case when phases are separated (for example solid presipitation) the phases with defined and thus not variable concentartions are excluded from the equilibrium constant expression. Example:

3Fe(s) + 4H₂O(g) --> Fe₃O₄(s) + 4H₂(g)

For the reaction of iron with steam, you would write

K_c =	[H₂]⁴

	[H₂O]⁴

Concentrations of Fe and Fe₃O₄ are omitted, because whereas the concentration of a gas can have various values, the concentration of a pure solid or a pure liquid is a constant at a given temperature. For the same reason, concentration of liquid solvent is usually omitted as well.

Qualitatively Interpreting the Equilibrium Constant

If K_c for a reaction, aA + bB -->cC + dD

is large, the equilibrium mixture is mostly products. If K_c is small, the equilibrium mixture is mostly reactants. When K_c is approximately 1, the equilibrium mixture contains appreciable amounts of both reactants and products.

Predicting the Direction of Reaction

The reaction quotient, Q_c, is an expression that has the same form as the equilibrium constant expression but whose concentration values are not necessarily those at equilibrium. For the general reaction

aA + bB -->cC + dD.

the reaction quotient, Q_c, is defined as

Q_c =	[C]_i^c[D]_i^d

	[A]_i^a[B]_i^b

where the subscript i on the concentrations means that the instantaneous concentration (not necessarily the equilibrium concentration) is to be used. To predict the direction of a reaction, substitute the concentrations of reactants and products at a particular time into the reaction quotient expression, and compare Q_c with the equilibrium constant K_c:

If Q_c > K_c, the reaction will go to the left.
If Q_c < K_c, the reaction will go to the right.
If Q_c= K_c, the reaction mixture is at equilibrium.

Calculating Equilibrium Concentrations

The equilibrium constant allows us to calculate final equilibrium composition of reactants and products for given initial concentrations. This can be accomplished in three steps:

Set up a table of concentrations (starting, change, and equilibrium expressions) using x for unknown quantities;
Substitute the values for equilibrium concentrations into the equilibrium-constant expression;
Solve the equilibrium-constant equation for the values of the equilibrium concentrations.

Multiple Equilibria

When equilibrium constant for a reaction needs to be calculated from equilibrium constants of individual steps one should take approach analogous to the use of Hess's law. As the enthalpy change for the overall equation equals the sum of the enthalpy changes for the individual steps, so the equilibrium constant for the overall equation equals the product of induvidual equilibrium constants in the power representing the coefficient for each reaction in the overall reaction, i.e. if for reaction

aA + bB <==>cC + dD the equlibrium constant is K_c, for the reaction

n * (aA + bB <==>cC + dD) the equlibrium constant will be K_cⁿ.

Example

Enthalpy

Equilibrium Constant

coefficient

Modified K_c

aA + bB <==>cC + dD

DH₁

K_c1 =	[C]^c[D]^d

	[A]^a[B]^b

same

C <==> eE + f D

DH₂

K_c2 =	[E]^e[D]^f

	[C]

K'_c2=	[E]^ce[D]^cf

	[C]^c

aA + bB <==>(ce)E + (cd+f)D

DH₁ = DH₁ + cDH₂

K_c =	[E]^ce[D]^(cd+f)

	[A]^a[B]^b

Le Chatelier's Principle

Changing the reaction conditions can affect the outcome of a reaction. Le Chatelier's principle is useful in predicting the results of these changes. It states that when a system in chemical equilibrium is disturbed by a change of temperature, pressure, or concentration, the system shifts its equilibrium composition in a way that tends to counteract the disturbance.

There are four changes to reaction conditions that we can consider:
     Adding or removing reactants or products - more products added - the equilibrium responds by increasing the amount of reagents and vice versa
     Changing the pressure or volume of the system - usually for gas phase reactions, depends on net change in moles in a course of a reaction, aA + bB -->cC + dD : if c+d > a+b, then pressure increase makes less products and vice versa
     Changing the temperature of the system - if reaction is exothermic, aA + bB -->cC + dD; DH < 0, (heat is produced, not consumed), increase of T causes decrease in the products and vice versa. Nav't Hoff's equation: K_c = A exp(-DH/RT)
     Adding a catalyst to the system - does not make any difference