# Chemical Equilibrium | General Chemistry 3

Chemical equilibria are studied in this chapter: equilibrium-constant expression, properties of equilibrium constants, Le Chatelier’s principle, reaction quotient and the approach to equilibrium

## Chemical Equilibrium

State in which both reactants and products are present in concentrations that no longer change over time
⇒ [reactant]eq = constant; [product]eq = constant

Chemical equilibrium is a dynamic equilibrium: the forward and reverse reactions still occur but reactants and products are formed at such rate that their concentration does not change
⇒ rate of the forward reaction = rate of the reverse reaction

A chemical equilibrium can be attained from any direction:
- starting only with all reactants
- starting with a mixture
⇒ at the equilibrium,  $\frac{\mathrm{products}}{\mathrm{reactants}}$ = constant for a given temperature, regardless of starting concentrations

## Equilibrium-Constant Expressions

Equilibrium constant K: ratio of product concentrations to reactant concentrations at the equilibrium
KC: equilibrium-constant expressed in terms of concentrations
KP: equilibrium-constant expressed in terms of pressures

Important points:
- K = constant at a given temperature
- equilibrium concentration is raised to a power equal to the stoichiometric coefficient
- pure solids/pure liquids reactants and products do not appear in the equilibrium-constant expression (= 1 by convention)

2 H(g) + CO (g) $⇌$ CH3OH (g)
KC =

PCl(l) + Cl(g) $⇌$ PCl(s)
KC = $\frac{1}{\left[{\mathrm{Cl}}_{2}\right]}$
(by convention [PCl3] = 1 and [PCl5] = 1; pure liquid and pure solid)

Ideal-gas law: PV = nRT ⇒ P = $\frac{\mathrm{n}}{\mathrm{V}}$RT = [gas]RT
⇒ equilibrium constants can be expressed in terms of partial pressures ⇒ KP

Relationship between KP and KC: KP = K(RT)Δνgas
with Δνgas = stoichiometric coefficients of products – stoichiometric coefficients of reactants

C (s) + CO(g) $⇌$ 2 CO (g)

KC = $\frac{{\left[\mathrm{CO}\right]}^{2}}{\left[{\mathrm{CO}}_{2}\right]}$

KP = $\frac{{{\mathrm{P}}_{\mathrm{CO}}}^{2}}{{\mathrm{P}}_{{\mathrm{CO}}_{2}}}$ = $\frac{{\left[\mathrm{CO}\right]}^{2}}{\left[{\mathrm{CO}}_{2}\right]}$ RT = KRT

## Properties of Equilibrium Constants

Kr = $\frac{1}{{\mathrm{K}}_{\mathrm{f}}}$

Kr = equilibrium constant of the reverse reaction
Kf = equilibrium constant of the forward reaction

K(1+2) = K1 x K2

K(1+2) = equilibrium constant of the overall reaction (1 + 2)
K1 = equilibrium constant of reaction 1
K2 = equilibrium constant of reaction 2

## Le Châtelier’s Principle

If a dynamic equilibrium is disturbed by changing the conditions, the equilibrium position moves to counteract the change. Quantities whose change may affect an equilibrium:

- concentration of a reactant or product
- reaction volume
- applied pressure
- temperature

Let the equilibrium A (g) + B (g) $⇌$ C (g). According to Le Chatelier’ principle, the position of equilibrium will move in such a way as to counteract the change:

It moves to the right (side with fewest moles of gas) if:

[reactant] increases
OR volume decreases
OR pressure increases
OR temperature increases (for endothermic reactions)
OR temperature decreases (for exothermic reactions)

It moves to the left (side with most moles of gas) if:

[reactant] decreases
OR volume increases
OR pressure decreases
OR temperature decreases (for endothermic reactions)
OR temperature increases (for exothermic reactions)

Adding a catalyst does not shift the position of an equilibrium system

## Approach to Equilibrium

Reaction quotient QC: ratio of product concentrations to reactant concentrations at a given time

CO(g) + H(g) $⇌$ CO (g) + H2O (g)

At time = t, QC =

If QC < K, the reaction will move to the right ⇒ net formation of product
If QC > K, the reaction will move to the left ⇒ net formation of reactants
If QC = K ⇒ equilibrium