Chemical Equilibrium notes

MDCAT Chemistry

Chemical equilibrium deals with reversible reactions that reach a state where the forward and reverse reaction rates become equal. This chapter explains equilibrium constants, Le Chatelier's principle, solubility product, common ion effect, buffer solutions and the industrial Haber process.

Reversible Reactions and Dynamic Equilibrium

A reversible reaction can proceed in both forward and backward directions under suitable conditions. It is represented by a double arrow, such as A + B ⇌ C + D. In a closed system, the reaction may reach equilibrium when the concentrations of reactants and products become constant.

Equilibrium is dynamic, not static. The forward and reverse reactions continue at equal rates, so there is no further visible change in concentration. Equilibrium can be reached from either the reactant side or the product side.

The law of mass action states that, at constant temperature, the rate of a reaction is proportional to the product of the active masses, or concentrations, of the reacting substances.

A reversible reaction occurs in both forward and backward directions.
Dynamic equilibrium is established in a closed system, not an open system.
At equilibrium, rate of forward reaction = rate of reverse reaction.
At equilibrium, concentrations of reactants and products remain constant, but they are not necessarily equal.
Equilibrium can be achieved starting with reactants or starting with products.
Equilibrium is dynamic because both reactions continue at the molecular level.
The law of mass action relates reaction rate to the product of the active masses of reactants.
A catalyst speeds up both forward and reverse reactions equally, so it does not change the equilibrium position.

Equilibrium Constant and Its Meaning

For a general reaction aA + bB ⇌ cC + dD, the equilibrium constant in terms of concentration is written as Kc = [C]^c[D]^d / [A]^a[B]^b. Square brackets indicate molar concentration in mol dm-3.

Pure solids and pure liquids are omitted from the equilibrium expression because their concentrations remain effectively constant. The numerical value of K depends on temperature, but not on the initial concentrations or the presence of a catalyst.

A large value of K means that products are favoured at equilibrium. A very small value of K means that reactants are favoured. For example, K = 6 x 10^-7 indicates that X and Y are favoured over Z in X + Y ⇌ Z.

For aA + bB ⇌ cC + dD, Kc = [C]^c[D]^d / [A]^a[B]^b.
The powers in the expression are the stoichiometric coefficients in the balanced equation.
Pure solids and pure liquids are not included in Kc expressions.
K has a fixed value only at a particular temperature.
K changes when temperature changes.
A large K value indicates a product-favoured equilibrium.
A small K value indicates a reactant-favoured equilibrium.
For 4NH3 + 5O2 ⇌ 4NO + 6H2O, Kc = [NO]^4[H2O]^6 / [NH3]^4[O2]^5.
For ester formation, Kc = [ethyl acetate][water] / [acetic acid][ethyl alcohol]. Using 40, 40, 18 and 22 mmol dm-3 gives Kc = 4.04.
For forward and reverse rate constants, Kc = kf / kb. If kf = 1 x 10^-2 and kb = 2 x 10^-3, Kc = 5.

Units of Equilibrium Constants and Kp

The units of Kc depend on the difference between the total powers of concentration terms in products and reactants. If the total concentration powers are equal, Kc has no unit. If they are not equal, a concentration unit remains.

For gaseous equilibria, equilibrium may be expressed using partial pressures. This constant is called Kp. Kp is related to Kc by Kp = Kc(RT)^Δn, where Δn is moles of gaseous products minus moles of gaseous reactants.

When the number of gaseous moles is the same on both sides, Δn = 0. Therefore, Kp = Kc.

Kp is used for gaseous equilibria and is expressed using partial pressures.
Δn = total gaseous moles of products minus total gaseous moles of reactants.
Kp = Kc(RT)^Δn.
If Δn = 0, Kp and Kc have the same numerical value.
For a reaction with one more mole of gaseous product, the Kc unit may be concentration^+1.
Kc for 4NH3 + 5O2 ⇌ 4NO + 6H2O has concentration^1 because the total product power is 10 and reactant power is 9.
The units of Kc are absent when the total powers of concentration are equal on both sides.
The equilibrium constant is not a measure of reaction rate.

Le Chatelier's Principle

Le Chatelier's principle states that when a system at equilibrium is disturbed by changing concentration, pressure or temperature, the system shifts in the direction that reduces the effect of the disturbance.

Adding a reactant shifts equilibrium towards products. Removing a product also shifts equilibrium towards products. Adding a product shifts equilibrium towards reactants. A catalyst does not shift equilibrium because it affects both directions equally.

For gaseous reactions, increasing pressure favours the side with fewer gaseous moles. Decreasing pressure favours the side with more gaseous moles. Pressure has no effect when gaseous moles are equal on both sides.

Addition of a reactant favours the forward reaction.
Removal of a product favours the forward reaction.
Addition of a product favours the reverse reaction.
Removal of a reactant favours the reverse reaction.
Increasing pressure favours the side with fewer gaseous molecules.
Decreasing pressure favours the side with more gaseous molecules.
Pressure does not affect an equilibrium if gaseous moles are equal on both sides.
For A(g) ⇌ 2B(g), decreasing pressure favours the forward reaction because the product side has more gas molecules.
For an exothermic reaction, increasing temperature favours the reverse, endothermic direction.
For an endothermic reaction, increasing temperature favours the forward direction.
Only temperature changes the value of the equilibrium constant.

Temperature Effects and Industrial Applications

In an exothermic reaction, heat behaves like a product. Therefore, lowering temperature favours the forward exothermic reaction. In an endothermic reaction, heat behaves like a reactant, so increasing temperature favours the forward reaction.

The oxidation of sulphur dioxide is exothermic: 2SO2(g) + O2(g) ⇌ 2SO3(g) + heat. The forward reaction is favoured by low temperature and high pressure. However, an industrial process uses a suitable compromise temperature because a very low temperature makes the reaction too slow.

The Haber process is used to manufacture ammonia. Nitrogen and hydrogen react reversibly and exothermically. High pressure and low temperature favour ammonia formation, while an iron catalyst increases the rate without changing the equilibrium yield.

2SO2(g) + O2(g) ⇌ 2SO3(g) is exothermic.
The forward oxidation of SO2 is favoured by reduced temperature.
The forward oxidation of SO2 is favoured by increased pressure because 3 gaseous moles form 2 gaseous moles.
Haber process: N2(g) + 3H2(g) ⇌ 2NH3(g) + heat.
High pressure favours ammonia because 4 gaseous moles form 2 gaseous moles.
Low temperature favours ammonia because the reaction is exothermic.
The industrial Haber process uses a compromise temperature of about 450°C.
Iron is used as the catalyst in the Haber process.
Ammonia is removed by cooling and liquefaction, which shifts the equilibrium towards more ammonia.
For an exothermic reaction, temperature increase favours the endothermic reverse reaction.

Solubility Product and Precipitation

The solubility product, Ksp, is the equilibrium constant for the dissolving of a sparingly soluble ionic compound. It is calculated from the concentrations of ions in a saturated solution. The concentrations are raised to powers equal to their coefficients in the dissociation equation.

For a salt MX, MX(s) ⇌ M+(aq) + X-(aq), Ksp = [M+][X-]. Ksp can be used to calculate solubility and to predict whether precipitation will occur.

The ionic product, Qsp, is calculated using the ion concentrations at any time. If Qsp is greater than Ksp, precipitation occurs. If Qsp is less than Ksp, the solution is unsaturated. If Qsp equals Ksp, the solution is just saturated.

Ksp applies to sparingly soluble ionic compounds.
For AgCl ⇌ Ag+ + Cl-, Ksp = [Ag+][Cl-].
For Ca(OH)2 ⇌ Ca2+ + 2OH-, Ksp = [Ca2+][OH-]^2.
For Ca3(PO4)2 ⇌ 3Ca2+ + 2PO4 3-, Ksp = [Ca2+]^3[PO4 3-]^2.
Qsp > Ksp means precipitation takes place.
Qsp < Ksp means no precipitation takes place and more salt can dissolve.
Qsp = Ksp means the solution is saturated and at equilibrium.
For AgCl, Ksp = 2.0 x 10^-10. In pure water, [Ag+] = [Cl-] = s, so s = square root of Ksp = 1.41 x 10^-5 mol dm-3.
For Ca(OH)2, Ksp = 4s^3. If Ksp = 5.02 x 10^-5, solubility s is approximately 0.023 mol dm-3.

Solubility, Temperature and Common Ion Effect

Solubility is the maximum amount of a solute that dissolves in a specified amount of solvent at a given temperature. Solubility products can be compared only after considering the dissociation equations and stoichiometric coefficients.

The common ion effect is the decrease in solubility of a sparingly soluble salt when a soluble electrolyte containing one of its ions is added. It is explained by Le Chatelier's principle. Addition of a common ion shifts the dissolution equilibrium towards the solid.

Temperature affects solubility according to the heat change of dissolution. Endothermic dissolution is generally favoured by heating, whereas exothermic dissolution may be reduced by heating.

A common ion is an ion already present in the equilibrium mixture.
Adding Cl- to AgCl solution decreases the solubility of AgCl.
Adding Ag+ to AgCl solution decreases the solubility of AgCl.
The common ion effect is used in selective precipitation and qualitative analysis.
For AgBrO3, Ksp = s^2, so s = square root of 5.5 x 10^-5, approximately 7.4 x 10^-3 mol dm-3.
For Ag2SO4, Ksp = 4s^3, so s = cube root of 5.0 x 10^-6, approximately 1.7 x 10^-2 mol dm-3.
Therefore, with the given Ksp values, solubility of AgBrO3 is less than solubility of Ag2SO4.
The solubility of Ce2(SO4)3 decreases with increase in temperature, indicating that its dissolution is favoured at lower temperature.
Solubility comparisons must not be made by comparing Ksp values alone when the ion ratios are different.

Buffer Solutions and pH

A buffer solution resists a change in pH when a small amount of acid or base is added. An acidic buffer contains a weak acid and its salt with a strong base, such as CH3COOH and CH3COONa. A basic buffer contains a weak base and its salt with a strong acid, such as NH4OH and NH4Cl.

The pH scale measures acidity and basicity. At 25°C, a neutral solution has pH 7. A solution with pH less than 7 is acidic, while a solution with pH greater than 7 is basic.

In the NH4OH and NH4Cl buffer, NH4OH provides the weak base and NH4Cl provides NH4+. When H+ is added, it reacts with OH- or NH4OH according to the buffer system. The equilibrium shifts forward to replace the consumed basic species, so the pH changes only slightly.

A buffer resists sudden changes in pH.
An acidic buffer consists of a weak acid and its salt with a strong base.
Example of an acidic buffer: CH3COOH and CH3COONa.
A basic buffer consists of a weak base and its salt with a strong acid.
Example of a basic buffer: NH4OH and NH4Cl.
pH = 7 is neutral at 25°C.
pH less than 7 indicates an acidic solution.
pH greater than 7 indicates a basic solution.
In an NH4OH and NH4Cl buffer, added H+ is consumed and the equilibrium moves forward.
In an acidic buffer, added H+ is consumed mainly by the conjugate base, while added OH- is consumed by the weak acid.
The Henderson equation for an acidic buffer is pH = pKa + log([salt]/[acid]).

Key terms

Reversible reaction: A reaction that can proceed in both forward and backward directions under suitable conditions.
Dynamic equilibrium: A state in which forward and reverse reactions occur at equal rates and concentrations remain constant.
Law of mass action: The rate of a reaction is proportional to the product of the active masses of its reacting substances.
Equilibrium constant: A constant value showing the ratio of product concentrations to reactant concentrations at equilibrium at a fixed temperature.
Kc: The equilibrium constant expressed using molar concentrations.
Kp: The equilibrium constant expressed using partial pressures of gaseous substances.
Le Chatelier's principle: A system at equilibrium shifts in the direction that opposes an applied change.
Ksp: The equilibrium constant for the dissolution of a sparingly soluble ionic compound.
Ionic product, Qsp: The product of ion concentrations at any moment, used to predict precipitation.
Precipitation: Formation of an insoluble solid when the ionic product exceeds the solubility product.
Solubility: The maximum amount of a substance that dissolves in a specified amount of solvent at a given temperature.
Common ion effect: Decrease in the solubility of a sparingly soluble salt caused by adding a soluble compound containing a common ion.
Buffer solution: A solution that resists significant change in pH when small amounts of acid or base are added.
Acidic buffer: A buffer made from a weak acid and its salt with a strong base.
Basic buffer: A buffer made from a weak base and its salt with a strong acid.
Haber process: The industrial process for producing ammonia from nitrogen and hydrogen.

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Chemistry shortcuts

Finding the limiting reactant and percentage composition

Convert every given mass or volume into moles first. The reactant that produces the least amount of the required product is the limiting reactant.

Write the balanced equation and calculate moles using n = mass/Mr.
Use the mole ratio to calculate the product. For percentage composition, use percentage = mass of element in one mole of compound divided by molar mass, multiplied by 100.
Example: Percentage of nitrogen in KNO3 = 14/101 × 100 = 13.86%.
Answer: 13.86% nitrogen.

Use gas volume at molar volume only when the gas conditions are stated or are standard conditions.

Using gas volume, pressure and temperature relations

At the same temperature and pressure, gas volume is directly proportional to the number of molecules. For changing conditions, use P1V1/T1 = P2V2/T2.

At constant temperature and pressure, divide or multiply the volume in the same ratio as the number of molecules.
Example: 10 mL H2 contains 2 × 10^3 molecules. Oxygen in 200 mL contains 20 × 2 × 10^3 = 4 × 10^4 molecules.
Answer: 4 × 10^4 molecules.
For a rigid container, increasing temperature increases molecular speed and mean free path if the gas remains in the same phase.

The direct volume to molecule ratio does not apply when temperature or pressure changes.

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