The Equilibrium Constant Revision Notes for Grade 12 NSC Matric Physical Sciences

The Equilibrium Constant

What is the equilibrium constant?

The equilibrium constant is a fundamental concept in chemistry that helps us understand how far a chemical reaction proceeds before reaching equilibrium. When a chemical reaction reaches dynamic equilibrium, both forwards and reverse reactions continue to occur, but their rates become equal, resulting in no net change in the concentrations of reactants and products.

At equilibrium, although individual molecules continue to react in both directions, the overall concentrations remain constant. This is what we call dynamic equilibrium - the system appears static on a large scale, but molecular activity continues.

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Think of dynamic equilibrium like a busy two-way street where the number of cars travelling in each direction is equal. Even though individual cars are constantly moving, the overall traffic density in each direction stays the same.

Definition: The equilibrium constant (Kc) is the ratio between the concentration of products and reactants in a chemical reaction at equilibrium.

The equilibrium constant formula

For any general reversible reaction:

$aA + bB \rightleftharpoons cC + dD$

The equilibrium constant expression is:

$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Where:

Square brackets [ ] represent molar concentrations (mol·dm⁻³)
Letters a, b, c, d are the coefficients from the balanced equation
These coefficients become the powers in the Kc expression

Important rules for writing Kc expressions

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Essential Rules for Kc Expressions:

Products go on top of the fraction, reactants go on bottom
Coefficients from the balanced equation become powers in the expression
Only include gases and aqueous solutions - pure liquids and solids are omitted
Concentrations must be at equilibrium - not initial or changing values

Example of writing Kc expressions

For the reaction: $2NO(g) + 2H_2(g) \rightleftharpoons N_2(g) + 2H_2O(g)$

The Kc expression becomes: $K_c = \frac{[N_2][H_2O]^2}{[NO]^2[H_2]^2}$

Notice how the coefficient 2 becomes the power 2 for each species.

Calculating equilibrium constants

When calculating Kc values, you need equilibrium concentrations of all species involved. Here's a systematic approach:

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Worked Example 1: Direct Calculation

Question: For the reaction $SO_2(g) + O_2(g) \rightleftharpoons SO_3(g)$ , if Kc = 6 and [SO₃] = 3 mol·dm⁻³ at equilibrium, calculate [O₂].

Solution:

Write the Kc expression: $K_c = \frac{[SO_3]}{[SO_2][O_2]}$
Rearrange to solve for [O₂]: $[O_2] = \frac{[SO_3]}{K_c \times [SO_2]}$
Substitute values: $[O_2] = \frac{3}{6 \times [SO_2]} = 0.5 { mol·dm}^{-3}$

RICE tables for complex calculations

For more complicated equilibrium problems, we use RICE tables - a systematic method for organising information:

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RICE stands for:

Reaction: Write the balanced chemical equation
Initial: Record initial quantities/concentrations
Change: Express changes using algebra (usually involving x)
Equilibrium: Calculate equilibrium quantities/concentrations

How to use RICE tables

The RICE methodology provides a systematic approach to solving complex equilibrium problems. This method ensures you don't miss any important information and helps organise your calculations logically.

Step-by-step process:

Fill in the balanced equation across the top
Record initial molar quantities in the second row
Express changes algebraically using the stoichiometric ratios
Calculate equilibrium quantities by combining initial + change
Convert to concentrations if needed using $C = \frac{n}{V}$

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Worked Example 2: Complete RICE Calculation

Question: 1.4 moles of NH₃(g) decomposes in a 2.0 dm³ container at 600K: $2NH_3(g) \rightleftharpoons N_2(g) + 3H_2(g)$ At equilibrium, [NH₃] = 0.3 mol·dm⁻³. Calculate Kc.

Solution:

Table

Step 1: Set up RICE table with initial conditions

Initial: 1.4 mol NH₃, 0 mol N₂, 0 mol H₂

Table

Step 2: Express changes using stoicheiometry

For every 2 mol NH₃ decomposed, 1 mol N₂ and 3 mol H₂ form
Change: -2x, +x, +3x

Table

Step 3: Calculate equilibrium quantities

NH₃: 1.4 - 2x mol
N₂: x mol
H₂: 3x mol

Step 4: Find x using given equilibrium concentration

$[NH_3] = 0.3 { mol·dm}^{-3} = \frac{1.4 - 2x}{2.0}$
Solving: 0.6 = 1.4 - 2x, so x = 0.4 mol

Table

Step 5: Complete the table and calculate Kc

Equilibrium concentrations: [NH₃] = 0.3, [N₂] = 0.2, [H₂] = 0.6 mol·dm⁻³
$K_c = \frac{[N_2][H_2]^3}{[NH_3]^2} = \frac{(0.2)(0.6)^3}{(0.3)^2} = 0.48$

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Worked Example 3: Another Complete Calculation

Question: $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$ Starting with 0.496 mol H₂ and 0.181 mol I₂ in 1 dm³, equilibrium contains 0.00749 mol I₂. Calculate Kc.

Solution:

Table

Using RICE methodology:

Table

Initial quantities: 0.496 mol H₂, 0.181 mol I₂, 0 mol HI
Changes: -x, -x, +2x (following stoicheiometry)
At equilibrium: I₂ = 0.181 - x = 0.00749 mol
Solving: x = 0.181 - 0.00749 = 0.1735 mol

Table

Final equilibrium concentrations:
- [H₂] = 0.3225 mol·dm⁻³
- [I₂] = 0.00749 mol·dm⁻³
- [HI] = 0.347 mol·dm⁻³
$K_c = \frac{[HI]^2}{[H_2][I_2]} = \frac{(0.347)^2}{(0.3225)(0.00749)} = 49.85$

Interpreting Kc values

The value of Kc tells us important information about the reaction direction and yield:

What Kc values mean:

When Kc > 1:

Equilibrium lies to the right
More products than reactants at equilibrium
High yield of products
Forwards reaction is favoured

When 0 < Kc < 1:

Equilibrium lies to the left
More reactants than products at equilibrium
Low yield of products
Reverse reaction is favoured

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Extreme Kc Values:

When Kc >> 1 (much greater than 1):

Reaction goes almost to completion
Very high product yield

When Kc << 1 (much less than 1):

Very little reaction occurs
Reactants remain mostly unchanged

Exam tips for equilibrium constants

Mastering equilibrium constant problems requires systematic thinking and careful attention to detail. Here are key strategies for exam success:

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Essential Exam Strategies:

Always read the question carefully - make sure you understand what's being asked
Check equilibrium concentrations - Kc expressions only use concentrations at equilibrium, not initial or changing values
Use RICE tables for complex problems - they help organise information systematically
Remember the rules:
- Products on top, reactants on bottom
- Coefficients become powers
- Only include gases and aqueous solutions
- Square brackets mean molar concentration
Check your answer - does the Kc value make sense given the equilibrium position?
Watch units - Kc may have units depending on the reaction, or may be dimensionless

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Key Points to Remember:

The equilibrium constant $K_c$ is the ratio of product concentrations to reactant concentrations, each raised to the power of their stoichiometric coefficients
Dynamic equilibrium means reaction rates are equal in both directions, but concentrations remain constant
RICE tables provide a systematic approach to complex equilibrium calculations: Reaction, Initial, Change, Equilibrium
$K_c > 1$ means the equilibrium favours products; $K_c < 1$ means it favours reactants
Only gases and aqueous solutions are included in $K_c$ expressions - pure liquids and solids are omitted

The Equilibrium Constant (Grade 12 NSC Matric Physical Sciences): Revision Notes