Equilibria (A Level only)

Chemistry (9701) A Level Study Notes: Equilibria

Welcome to the world of Equilibria! In chemistry, most reactions do not simply run to completion—they find a balance point. Understanding this balance is vital for everything from designing industrial chemical plants (such as making fertilizers) to understanding how your body controls the pH of your blood.

We will start with the fundamentals of reversible reactions and then explore the quantitative aspects of equilibrium, acids, bases, buffers, solubility products, and partition coefficients.

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Section 7.1: Chemical Equilibria: Reversible Reactions and Dynamic Equilibrium (AS Level Content)

The Basics: Reversible Reactions and Closed Systems

Most reactions studied in introductory chemistry are irreversible (they proceed to completion). However, many chemical reactions are reversible.

Reversible Reactions

A reversible reaction is one where the products can react together to reform the original reactants. We use the symbol \(\rightleftharpoons\) to represent this.

Example: The Haber Process for ammonia synthesis:
\( \text{N}_{2}(\text{g}) + 3\text{H}_{2}(\text{g}) \rightleftharpoons 2\text{NH}_{3}(\text{g}) \)

Dynamic Equilibrium

Equilibrium is not static; it is dynamic.

Definition of Dynamic Equilibrium: Dynamic equilibrium is reached when:
1. The rate of the forward reaction equals the rate of the reverse reaction.
2. The concentrations of reactants and products remain constant (though not necessarily equal).

Crucial Requirement: Dynamic equilibrium can only be established in a closed system. This means no substances (reactants or products) can enter or leave the reaction vessel.

Analogy: Imagine two treadmills running side-by-side. On treadmill A, people run forward (Reactants \(\rightarrow\) Products). On treadmill B, people run backward (Products \(\rightarrow\) Reactants). If the same number of people step onto A as step onto B every second, the total number of people in each group remains constant, even though everyone continues moving.

Le Chatelier’s Principle

When a system at equilibrium is disturbed, the system responds to counteract the disturbance.

Definition: Le Chatelier's principle states that if a change is made to a system at dynamic equilibrium, the position of equilibrium moves to minimise this change.

Effect of Stressors on Equilibrium Position

The "position of equilibrium" refers to the relative amounts of reactants and products present. If the position shifts to the right, product yield increases.

1. Concentration Change

• If you increase the concentration of a reactant, the equilibrium shifts to the right to consume the added reactant.
• If you decrease the concentration of a product, the equilibrium shifts to the right to replace the removed product.

2. Pressure Change (Gaseous Systems Only)

Pressure changes affect only systems containing gases where there is a difference in the total number of gaseous moles on either side of the balanced equation.

• If you increase the pressure (by decreasing volume), the equilibrium shifts to the side with fewer moles of gas.
• If you decrease the pressure (by increasing volume), the equilibrium shifts to the side with more moles of gas.

3. Temperature Change

To predict the shift, determine whether the forward reaction is exothermic (\(\Delta H\) is negative) or endothermic (\(\Delta H\) is positive).

• If you increase the temperature, the equilibrium shifts in the endothermic direction to absorb heat.
• If you decrease the temperature, the equilibrium shifts in the exothermic direction to release heat.

4. Addition of a Catalyst

• A catalyst increases the rate of both forward and reverse reactions equally.
• It allows equilibrium to be reached faster, but it does not change the position of equilibrium or the equilibrium yield.

The Equilibrium Constants, \(K_c\) and \(K_p\)

While the position of equilibrium shifts with changes in concentration, pressure, and temperature, only temperature changes the numerical value of an equilibrium constant (\(K\)).

Defining \(K_c\) (Concentration)

For a general reversible reaction: \(\na\text{A} + b\text{B} \rightleftharpoons c\text{C} + d\text{D} \) The expression for \(K_c\) is: \(\nK_c = \frac{[\text{C}]^c [\text{D}]^d}{[\text{A}]^a [\text{B}]^b} \) where \([\dots]\) represents the equilibrium concentration in \(\text{mol}\ \text{dm}^{-3}\).

Key Point: Pure solids and pure liquids acting as solvents are omitted from the \(K_c\) expression because their concentrations remain constant.

Defining \(K_p\) (Partial Pressure)

For gaseous equilibria, equilibrium constants are expressed in terms of partial pressures (\(K_p\)).

The partial pressure of a gas in a mixture is the pressure it would exert if it occupied the entire container alone.

Mole Fraction (\(x_{\text{A}}\)): \(\nx_{\text{A}} = \frac{n_{\text{A}}}{n_{\text{total}}} \)
Partial Pressure (\(P_{\text{A}}\)): \(\nP_{\text{A}} = x_{\text{A}} \times P_{\text{total}} \)

For a gaseous reaction, the \(K_p\) expression is: \(\nK_p = \frac{(P_{\text{C}})^c (P_{\text{D}})^d}{(P_{\text{A}})^a (P_{\text{B}})^b} \)

Effect of Conditions on \(K\)

Only temperature changes the value of \(K_c\) or \(K_p\).

• Concentration, Pressure, and Catalysts: Do not change the value of \(K\). The system shifts its equilibrium position to restore the ratio equal to \(K\).
• Temperature:
  • If the forward reaction is exothermic, increasing \(T\) decreases \(K\).
  • If the forward reaction is endothermic, increasing \(T\) increases \(K\).

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Section 7.2 & 25.1: Acids and Bases: pH, \(K_a\), and Buffers (AS & A Level Content)

Brønsted–Lowry Theory

The Brønsted–Lowry theory defines acids and bases through proton (\(\text{H}^+\)) transfer:

• An Acid is a proton (\(\text{H}^+\)) donor.
• A Base is a proton (\(\text{H}^+\)) acceptor.

Conjugate Acid–Base Pairs

When an acid loses a proton, it forms its conjugate base. When a base accepts a proton, it forms its conjugate acid.

\( \text{CH}_{3}\text{COOH}(\text{aq}) + \text{H}_{2}\text{O}(\text{l}) \rightleftharpoons \text{CH}_{3}\text{COO}^{-}(\text{aq}) + \text{H}_{3}\text{O}^{+}(\text{aq}) \)

• \(\text{CH}_{3}\text{COOH}\) (Acid 1) and \(\text{CH}_{3}\text{COO}^{-}\) (Conjugate Base 1) form a conjugate pair.
• \(\text{H}_{2}\text{O}\) (Base 2) and \(\text{H}_{3}\text{O}^{+}\) (Conjugate Acid 2) form a conjugate pair.

Strong vs. Weak Acids and Bases

• Strong Acids/Bases: Fully dissociate in aqueous solution (e.g., \(\text{HCl}\), \(\text{NaOH}\)).
• Weak Acids/Bases: Only partially dissociate in aqueous solution (e.g., \(\text{CH}_{3}\text{COOH}\), \(\text{NH}_{3}\)).

The pH Scale and Water Ionisation

pH Definition: \( \text{pH} = -\log_{10}[\text{H}^{+}(\text{aq})] \)

The Ionic Product of Water (\(K_w\))

Water undergoes self-ionisation: \( \text{H}_{2}\text{O}(\text{l}) \rightleftharpoons \text{H}^{+}(\text{aq}) + \text{OH}^{-}(\text{aq}) \) \(\nK_w = [\text{H}^{+}(\text{aq})][\text{OH}^{-}(\text{aq})] \) At 298 K, \(K_w = 1.00 \times 10^{-14}\ \text{mol}^{2}\ \text{dm}^{-6}\).

• In pure water at 298 K, \([\text{H}^{+}] = [\text{OH}^{-}] = \sqrt{K_w} = 1.00 \times 10^{-7}\ \text{mol}\ \text{dm}^{-3}\), so \(\text{pH} = 7.00\).
• In acidic solutions, \([\text{H}^{+}] > [\text{OH}^{-}]\), so \(\text{pH} < 7\).
• In alkaline solutions, \([\text{OH}^{-}] > [\text{H}^{+}]\), so \(\text{pH} > 7\).

Acid Dissociation Constant (\(K_a\)) and \(\text{p}K_a\)

For a weak acid \(\text{HA}\): \( \text{HA}(\text{aq}) \rightleftharpoons \text{H}^{+}(\text{aq}) + \text{A}^{-}(\text{aq}) \) \(\nK_a = \frac{[\text{H}^{+}(\text{aq})][\text{A}^{-}(\text{aq})]}{[\text{HA}(\text{aq})]} \) \( \text{p}K_a = -\log_{10}(K_a) \)

A smaller \(K_a\) (or higher \(\text{p}K_a\)) indicates a weaker acid.

Calculating pH of a Weak Monoprotic Acid

Assuming \([\text{H}^{+}] \approx [\text{A}^{-}]\) and that dissociation is small enough that \([\text{HA}]_{\text{eq}} \approx [\text{HA}]_{\text{initial}}\): \( [\text{H}^{+}(\text{aq})] = \sqrt{K_a \times [\text{HA}]} \) \( \text{pH} = -\log_{10}[\text{H}^{+}] \)

Buffer Solutions

A buffer solution resists changes in pH when small amounts of acid or alkali are added.

Composition of Buffers

1. Acidic buffer: A weak acid and its conjugate base / salt (e.g., \(\text{CH}_{3}\text{COOH}\) and \(\text{CH}_{3}\text{COONa}\)).
2. Basic buffer: A weak base and its conjugate acid / salt (e.g., \(\text{NH}_{3}\) and \(\text{NH}_{4}\text{Cl}\)).

Mechanism of an Acidic Buffer (\(\text{HA} / \text{A}^-\))

Adding \(\text{H}^+\): The conjugate base reacts with added hydrogen ions: \( \text{A}^{-}(\text{aq}) + \text{H}^{+}(\text{aq}) \rightarrow \text{HA}(\text{aq}) \)

Adding \(\text{OH}^-\): The weak acid neutralizes added hydroxide ions: \( \text{HA}(\text{aq}) + \text{OH}^{-}(\text{aq}) \rightarrow \text{A}^{-}(\text{aq}) + \text{H}_{2}\text{O}(\text{l}) \)

Uses of Buffers

• Blood buffer system: The \(\text{HCO}_{3}^{-} / \text{H}_{2}\text{CO}_{3}\) hydrogencarbonate buffer system maintains blood pH in the range 7.35 to 7.45.

Buffer Calculations

\( [\text{H}^{+}(\text{aq})] = K_a \times \frac{[\text{acid}]}{[\text{salt}]} \) \( \text{pH} = -\log_{10}[\text{H}^{+}] \)

pH Titration Curves and Indicator Selection

Four standard titration curves:

1. Strong Acid / Strong Base: Sharp vertical equivalence section spans pH ~3 to ~11; equivalence point at pH 7.
2. Weak Acid / Strong Base: Equivalence point is alkaline (\(\text{pH} > 7\)) due to anion hydrolysis; sharp section spans pH ~7 to ~11. Indicator: Phenolphthalein (pH range ~8.3–10.0).
3. Strong Acid / Weak Base: Equivalence point is acidic (\(\text{pH} < 7\)) due to cation hydrolysis; sharp section spans pH ~3 to ~7. Indicator: Methyl Orange (pH range ~3.1–4.4).
4. Weak Acid / Weak Base: No sharp vertical break; standard acid-base indicators cannot be used.

Indicator Rule: A suitable indicator must have a pH transition range that falls completely within the steep vertical equivalence region of the titration curve.

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Section 25.1: Solubility Product (\(K_{sp}\)) (A Level Content)

Definition and Expression

The solubility product, \(K_{sp}\), is the equilibrium constant for a sparingly soluble salt in a saturated aqueous solution.

For a salt \(\text{A}_m\text{B}_n\): \( \text{A}_m\text{B}_n(\text{s}) \rightleftharpoons m\text{A}^{n+}(\text{aq}) + n\text{B}^{m-}(\text{aq}) \) \(\nK_{sp} = [\text{A}^{n+}]^m [\text{B}^{m-}]^n \) Pure solid \(\text{A}_m\text{B}_n\) is omitted from the expression.

Calculations from Solubility (\(S\))

• 1:1 Salt (e.g., \(\text{AgCl}\)): \(K_{sp} = [\text{Ag}^{+}][\text{Cl}^{-}] = (S)(S) = S^2\)
• 1:2 Salt (e.g., \(\text{Mg}(\text{OH})_{2}\)): \(K_{sp} = [\text{Mg}^{2+}][\text{OH}^{-}]^2 = (S)(2S)^2 = 4S^3\)

The Common Ion Effect

The common ion effect is the reduction in solubility of a sparingly soluble salt when a soluble compound containing one of its constituent ions is added.

Adding a common ion increases product ion concentration, causing the equilibrium to shift to the left by Le Chatelier's principle and precipitating out solid salt.

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Section 25.2: Partition Coefficients (\(K_{pc}\)) (A Level Content)

Definition

The partition coefficient (\(K_{pc}\)) is the equilibrium constant that describes the distribution of a solute between two immiscible solvents.

For a solute X distributed between Solvent 1 and Solvent 2: \( \text{X}(\text{Solvent } 1) \rightleftharpoons \text{X}(\text{Solvent } 2) \) \(\nK_{pc} = \frac{[\text{X}(\text{Solvent } 2)]}{[\text{X}(\text{Solvent } 1)]} \)

Condition: The solute must remain in the same physical state (molecular form) in both solvents without undergoing differential dissociation or association.

Polarity and \(K_{pc}\)

The value of \(K_{pc}\) is determined by relative solubilities and polarities ("like dissolves like"). A non-polar solute partitions preferentially into the non-polar solvent, giving a large \(K_{pc}\) relative to an aqueous phase.