IB DP Chemistry - R2.3.2 The equilibrium law and constant - Study Notes - New Syllabus - 2026, 2027 & 2028
IB DP Chemistry – R2.3.2 The equilibrium law and constant – Study Notes – New Syllabus
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Reactivity 2.3.2 – The Equilibrium Law and Deduction of \( K_c \) Expressions
Reactivity 2.3.2 – The Equilibrium Law and Deduction of \( K_c \) Expressions
The equilibrium law defines how the equilibrium constant \( K_c \) is related to the concentrations of reactants and products in a reversible chemical reaction at equilibrium. The expression for \( K_c \) is determined using the balanced chemical equation and its stoichiometric coefficients.
1. What Is the Equilibrium Constant (\( K_c \))?
- \( K_c \) is a numerical value that represents the ratio of the concentrations of products to reactants at equilibrium.
- It provides insight into the position of equilibrium — whether the reaction favors products or reactants.
- \( K_c \) is constant for a given reaction at a specific temperature.
2. General Form of the Equilibrium Expression
For a balanced reaction:
\( aA + bB \rightleftharpoons cC + dD \)
The equilibrium expression is:
\( K_c = \dfrac{[C]^c [D]^d}{[A]^a [B]^b} \)
- Square brackets \([ ]\) represent molar concentrations (mol·dm\(^{-3}\)).
- The powers correspond to the coefficients in the balanced equation.
3. Types of Equilibrium Systems:
- Homogeneous equilibrium: All reactants and products are in the same phase (usually all gases or all aqueous).
- Heterogeneous equilibrium: Reactants and products are in different phases — solids and pure liquids are excluded from the \( K_c \) expression.
4. Steps to Deduce \( K_c \) from a Balanced Equation
- Write the balanced chemical equation.
- Identify which species are in the gas or aqueous phase.
- Write an expression where product concentrations are in the numerator and reactant concentrations in the denominator.
- Use exponents that match each species’ coefficient from the equation.
- Exclude pure solids and pure liquids.
5. Important Notes:
- Pure solids and pure liquids are not included in the equilibrium expression.
- The value of \( K_c \) only changes with temperature.
- If \( K_c \gg 1 \), products dominate at equilibrium. If \( K_c \ll 1 \), reactants dominate.
- The units of \( K_c \) depend on the change in moles of gas or aqueous species and must be derived for each specific reaction.
Example
The following homogeneous equilibrium is established at 450°C:
\( \text{SO}_2(g) + \text{NO}_2(g) \rightleftharpoons \text{SO}_3(g) + \text{NO}(g) \)
All species are gases. Deduce the equilibrium constant expression.
▶️Answer/Explanation
This is a homogeneous gas-phase reaction. All species are included:
\( K_c = \dfrac{[\text{SO}_3][\text{NO}]}{[\text{SO}_2][\text{NO}_2]} \)
Example
The following reversible reaction occurs in aqueous solution:
\( \text{Fe}^{3+}(aq) + \text{SCN}^-(aq) \rightleftharpoons \text{FeSCN}^{2+}(aq) \)
Deduce the equilibrium constant expression.
▶️Answer/Explanation
This is a homogeneous aqueous equilibrium. All species are aqueous ions, so they are included:
\( K_c = \dfrac{[\text{FeSCN}^{2+}]}{[\text{Fe}^{3+}][\text{SCN}^-]} \)
Example
The decomposition of calcium carbonate occurs in a sealed vessel at high temperature:
\( \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \)
Deduce the expression for \( K_c \).
▶️Answer/Explanation
This is a heterogeneous equilibrium. Solids (\( \text{CaCO}_3 \), \( \text{CaO} \)) are excluded from the expression:
\( K_c = [\text{CO}_2] \)
Only the concentration of the gas is included.
Example
A saturated solution of silver chloride establishes the following equilibrium:
\( \text{AgCl}(s) \rightleftharpoons \text{Ag}^+(aq) + \text{Cl}^-(aq) \)
What is the expression for \( K_c \)?
▶️Answer/Explanation
This is a heterogeneous equilibrium involving a solid and aqueous ions. Only the aqueous ions are included:
\( K_c = [\text{Ag}^+][\text{Cl}^-] \)
The solid \( \text{AgCl}(s) \) is excluded.
Example
In the gas-phase equilibrium reaction:
\( \text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g) \)
Deduce the equilibrium expression, clearly using coefficients.
▶️Answer/Explanation
This is a homogeneous gaseous reaction. The exponents reflect the coefficients:
\( K_c = \dfrac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3} \)
The concentration of each gas is raised to the power of its coefficient in the equation.