# Chemical Equilibrium | General Chemistry 3

## 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 only with all products
- 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

K_{C}: equilibrium-constant expressed in terms of concentrations

K_{P}: 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

_{2 }(g) + CO (g) $\rightleftharpoons $ CH_{3}OH (g)

K_{C}= $\frac{\left[{\mathrm{CH}}_{3}\mathrm{OH}\right]}{{\left[{\mathrm{H}}_{2}\right]}^{2}\left[\mathrm{CO}\right]}$

PCl_{3 }(l) + Cl_{2 }(g) $\rightleftharpoons $ PCl_{5 }(s)

K_{C}= $\frac{1}{\left[{\mathrm{Cl}}_{2}\right]}$

(by convention [PCl_{3}] = 1 and [PCl_{5}] = 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 ⇒ K_{P}

Relationship between K_{P} and K_{C}: K_{P} = K_{C }(RT)^{Δνgas}

with Δν_{gas} = stoichiometric coefficients of products – stoichiometric coefficients of reactants

C (s) + CO

_{2 }(g) $\rightleftharpoons $ 2 CO (g)K

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

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

## Properties of Equilibrium Constants

K_{r} = $\frac{1}{{\mathrm{K}}_{\mathrm{f}}}$

K_{r} = equilibrium constant of the reverse reaction

K_{f} = equilibrium constant of the forward reaction

K_{(1+2)} = K_{1} x K_{2}

K_{(1+2)} = equilibrium constant of the overall reaction (1 + 2)

K_{1} = equilibrium constant of reaction 1

K_{2} = 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) $\rightleftharpoons $ 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 Q_{C}: ratio of product concentrations to reactant concentrations at a given time

CO

_{2 }(g) + H_{2 }(g) $\rightleftharpoons $ CO (g) + H_{2}O (g)At time = t, Q

_{C }= $\frac{{\left[\mathrm{CO}\right]}_{\mathrm{t}}{\left[{\mathrm{H}}_{2}\mathrm{O}\right]}_{\mathrm{t}}}{{\left[{\mathrm{CO}}_{2}\right]}_{\mathrm{t}}{\left[{\mathrm{H}}_{2}\right]}_{\mathrm{t}}}$

If Q_{C} < K, the reaction will move to the right ⇒ net formation of product

If Q_{C} > K, the reaction will move to the left ⇒ net formation of reactants

If Q_{C} = K ⇒ equilibrium