Apply Extent of Chemical Change — Apply Reactivity 2.3

SECTION 1

Historical Context & Motivation

Why don't all chemical reactions simply run to completion? Early chemists assumed that once reactants were mixed, they would convert entirely into products. However, careful experiments in the 1800s revealed something surprising: many reactions appear to stop before all the reactants are consumed. A mixture of reactants and products coexists in a state of dynamic equilibrium, where forward and reverse reactions occur at equal rates. Understanding the extent of chemical change — how far a reaction proceeds toward products — became one of the central questions of physical chemistry.

1803

Berthollet's Reversibility Insight

Claude Louis Berthollet observed that some reactions could run in reverse under different conditions, challenging the idea that reactions always go to completion.

1864

Guldberg & Waage's Law of Mass Action

Cato Guldberg and Peter Waage proposed that the rate of a reaction is proportional to the concentrations of reactants, laying the mathematical foundation for the equilibrium constant.

1884

Le Chatelier's Principle

Henri Le Chatelier published his principle predicting how a system at equilibrium responds to disturbances, giving chemists a powerful qualitative tool.

1901

van 't Hoff's Temperature Dependence

Jacobus van 't Hoff received the first Nobel Prize in Chemistry for his work relating equilibrium constants to temperature through thermodynamics.

These breakthroughs raised a practical question that IB Chemistry still centers on today: given a set of conditions, how far will a particular reaction proceed, and how can we shift the position of equilibrium to favor the products we want? This is precisely what Reactivity 2.3 asks you to apply in problem-solving and explanations.

SECTION 2

Core Principles & Definitions

Before solving any equilibrium problem, you need a solid grasp of the foundational ideas that govern how far a reaction proceeds. These principles connect the macroscopic behavior you observe — such as color changes or pressure shifts — to the molecular-level competition between the forward and reverse reactions.

Dynamic Equilibrium

At equilibrium, the forward and reverse reactions continue at equal rates. Concentrations remain constant, but the system is not static — molecules are constantly reacting in both directions.

Equilibrium Constant (K)

The equilibrium constant K expresses the ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of their stoichiometric coefficients. A large K means products are favored; a small K means reactants dominate.

Reaction Quotient (Q)

The reaction quotient Q has the same form as K but is calculated at any point in the reaction, not just at equilibrium. Comparing Q to K tells you which direction the reaction will shift.

Le Chatelier's Principle

When an external stress — such as a change in concentration, pressure, or temperature — is applied to a system at equilibrium, the system shifts to partially counteract that stress and establish a new equilibrium.

Temperature & K

Temperature is the only factor that changes the value of K itself. For exothermic reactions, increasing temperature decreases K. For endothermic reactions, increasing temperature increases K.

✦ KEY TAKEAWAY

Think of chemical equilibrium like a busy two-way escalator in a shopping mall. People (molecules) are constantly going up (forward reaction) and coming down (reverse reaction). When the number going up equals the number coming down each minute, the crowd on each floor stays the same — that's dynamic equilibrium. The equilibrium constant K tells you which floor has more people — a large K means the upper floor (products) is packed.

SECTION 3

Visualizing Equilibrium: Q vs. K

One of the most powerful tools for predicting the direction of a reaction is comparing the reaction quotient Q with the equilibrium constant K. The diagram below illustrates what happens in each of the three possible scenarios: Q < K, Q = K, and Q > K.

When Q < K, there are too many reactants relative to products, so the reaction shifts to the right (toward products). When Q > K, there are too many products, and the reaction shifts left. At Q = K, the system is at equilibrium and no net change occurs.

Notice that the relative sizes of the reactant and product bars in the diagram reflect the concentrations at each stage. The system always adjusts in the direction that brings Q closer to K. This comparison is one of the most frequently tested skills in IB Chemistry because it combines quantitative calculation with qualitative reasoning about reaction direction.

SECTION 4

Mathematical Framework

The mathematics of equilibrium revolves around writing correct expressions for K and Q, then using algebra and an ICE table to solve for unknown concentrations. Let's build the framework step by step.

EQUILIBRIUM CONSTANT EXPRESSION (Kc)

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

For the general reaction aA + bB ⇌ cC + dD, square brackets denote molar concentrations (mol dm⁻³). The exponents are the stoichiometric coefficients from the balanced equation. Pure solids and pure liquids are omitted.

REACTION QUOTIENT

Qc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ (at any moment)

Q has the same mathematical form as K, but the concentrations are measured at any point during the reaction, not just at equilibrium. If Q < K, the reaction proceeds forward. If Q > K, it proceeds in reverse.

GIBBS FREE ENERGY & EQUILIBRIUM

ΔG° = −RT ln K

R = 8.314 J mol⁻¹ K⁻¹, T is temperature in kelvin. A negative ΔG° means K > 1 (products favored). This equation links thermodynamics directly to the extent of reaction.

📐 ICE Table Method

The ICE table (Initial – Change – Equilibrium) is a systematic way to organize equilibrium calculations. Write initial concentrations, define the change using a variable x and the stoichiometric ratios, then express equilibrium concentrations in terms of x. Substitute into the K expression and solve for x.

SECTION 5

Le Chatelier's Principle in Detail

While Q vs. K is a quantitative approach to predicting the extent of reaction, Le Chatelier's principle gives you a powerful qualitative tool. It states that when a system at equilibrium is disturbed, it will shift in the direction that partially opposes the disturbance. The diagram below summarizes the effects of different stresses on an equilibrium system.

This summary diagram shows how each type of stress affects an equilibrium system. Notice the critical distinction at the bottom: only temperature changes the value of K itself.

A common IB exam mistake is stating that a catalyst shifts the equilibrium toward products. In reality, a catalyst lowers the activation energy for both the forward and reverse reactions by the same amount, so the system reaches equilibrium faster but at the same equilibrium position. Keep this distinction sharp in your explanations.

SECTION 6

Worked Example: ICE Table Calculation

Let's apply everything we've learned to a full ICE table problem. This type of calculation is a staple of IB Chemistry exams and requires you to combine the equilibrium expression with algebraic reasoning.

❓ Problem Statement

Consider the reaction: N₂(g) + 3H₂(g) ⇌ 2NH₃(g). In a 1.00 dm³ container at a certain temperature, 1.00 mol of N₂ and 3.00 mol of H₂ are mixed. At equilibrium, 0.40 mol of NH₃ are present. Calculate K_c.

Calculating Kc Using an ICE Table

Step 1 — Write the balanced equation and K expressionThe balanced equation is N₂(g) + 3H₂(g) ⇌ 2NH₃(g). Therefore K_c = [NH₃]² / ([N₂][H₂]³).

Step 2 — Set up the ICE tableSince the volume is 1.00 dm³, moles equal concentrations. Initial: [N₂] = 1.00, [H₂] = 3.00, [NH₃] = 0. Change: [N₂] decreases by x, [H₂] decreases by 3x, [NH₃] increases by 2x. Equilibrium: [NH₃] = 2x = 0.40, so x = 0.20.

x = 0.20 mol dm⁻³

Step 3 — Calculate equilibrium concentrations[N₂] = 1.00 − 0.20 = 0.80 mol dm⁻³. [H₂] = 3.00 − 3(0.20) = 3.00 − 0.60 = 2.40 mol dm⁻³. [NH₃] = 0.40 mol dm⁻³.

[N₂] = 0.80, [H₂] = 2.40, [NH₃] = 0.40

Step 4 — Substitute into the Kc expressionK_c = (0.40)² / ((0.80) × (2.40)³) = 0.16 / (0.80 × 13.824) = 0.16 / 11.059.

K_c = 0.0145 (3 s.f.)

Step 5 — Interpret the resultSince K_c is much less than 1, the equilibrium lies to the left, meaning the reaction does not proceed far toward products at this temperature. The extent of reaction is small, and reactants are favored.

SECTION 7

Strengths & Limitations of Equilibrium Tools

IB Chemistry provides several tools for analyzing the extent of chemical change. Each has particular strengths and limitations. Understanding when to use each one will improve both your exam technique and your conceptual understanding.

Comparison of equilibrium analysis tools in IB Chemistry

Tool	Strengths	Limitations
Equilibrium Constant K	Quantitative; predicts whether products or reactants are favored; can be used to calculate concentrations.	Only valid at the specific temperature it was measured; requires balanced equation; does not tell you about rate.
Reaction Quotient Q	Can be calculated at any point; directly compared to K to predict direction of shift.	Requires knowledge of all current concentrations or partial pressures; does not tell you the final equilibrium amounts.
Le Chatelier's Principle	Quick qualitative predictions; no calculations needed; applies to any equilibrium system.	Cannot give exact concentrations; can be misapplied (e.g., with catalysts or inert gases at constant volume).
ΔG° = −RT ln K	Connects thermodynamics to equilibrium; explains why K changes with temperature.	Requires temperature and ΔG° data; more complex mathematically; HL topic in depth.

✦ KEY TAKEAWAY

Think of K as your GPS destination — it tells you where the equilibrium lies. Q is your current GPS location — it tells you where you are right now. Le Chatelier's principle is the general rule that says, "If you get pushed off the road, you'll steer back toward it." Each tool gives you a different kind of information, and the best problem solvers know which tool fits the question.

SECTION 8

Connections to Advanced Theory

The ideas you've learned in this lesson form the foundation for more advanced treatments of equilibrium that appear in IB HL Chemistry and university-level courses. Here's a preview of how these concepts extend.

From SL fundamentals to HL and university extensions

SL / Core Treatment	HL / Advanced Extension
K_c written with concentrations	K_p written with partial pressures; relationship K_p = K_c(RT)^Δn
Le Chatelier's qualitative predictions	Quantitative use of Q vs. K with ICE tables involving quadratic equations or simplifying assumptions (the 5% rule)
K changes with temperature (qualitative)	van 't Hoff equation: ln(K₂/K₁) = −ΔH°/R × (1/T₂ − 1/T₁), allowing quantitative calculation of K at different temperatures
ΔG° = −RT ln K as a formula	Full derivation from Gibbs energy; ΔG = ΔG° + RT ln Q used to determine spontaneity at non-standard conditions

Even at the SL level, appreciating that equilibrium is fundamentally a thermodynamic phenomenon will deepen your understanding. The value of K isn't random — it's determined by the relative stability (Gibbs energy) of reactants and products. As you advance in chemistry, you'll use these same ideas to explain acid-base strength, solubility, and electrochemical cell potentials.

SECTION 9

Practice Problems

PROBLEM 1 — CONCEPTUAL

For the reaction 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), K_c = 2.5 × 10² at 700 K. A student claims that since K is large, essentially no SO₂ remains at equilibrium. Is this claim correct? Explain your reasoning.

PROBLEM 2 — BASIC CALCULATION

For the reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), the equilibrium concentrations at a certain temperature are [PCl₅] = 0.15 mol dm⁻³, [PCl₃] = 0.30 mol dm⁻³, and [Cl₂] = 0.20 mol dm⁻³. Calculate K_c.

PROBLEM 3 — INTERMEDIATE

For the equilibrium H₂(g) + I₂(g) ⇌ 2HI(g), K_c = 54 at 698 K. At a given moment, [H₂] = 0.10, [I₂] = 0.20, and [HI] = 0.80 mol dm⁻³. Determine whether the system is at equilibrium. If not, predict the direction of the shift.

PROBLEM 4 — APPLIED

The Haber process (N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹) operates at about 450 °C and 200 atm with an iron catalyst. Using Le Chatelier's principle, explain: (a) why high pressure is used, (b) why the temperature is not lowered further even though the reaction is exothermic, and (c) why a catalyst is used if it doesn't change K.

PROBLEM 5 — CRITICAL THINKING

Consider two reactions at the same temperature. Reaction A has K = 4.0 × 10⁸ and Reaction B has K = 2.5 × 10⁻³. A student states that Reaction A will be faster than Reaction B because it has a larger K. Critically evaluate this statement and explain the relationship — if any — between K and the rate of reaction.

SUMMARY

Lesson Summary

The extent of chemical change is governed by dynamic equilibrium, where forward and reverse reactions proceed at equal rates. The equilibrium constant K quantifies the ratio of product to reactant concentrations at equilibrium: a large K means products are favored, and a small K means reactants dominate. The reaction quotient Q has the same form but is calculated at any instant — comparing Q to K reveals whether the reaction will shift toward products (Q < K), toward reactants (Q > K), or remain unchanged (Q = K). The ICE table provides a systematic algebraic method for calculating equilibrium concentrations when some information is missing.

Le Chatelier's principle predicts that a system at equilibrium will shift to partially counteract any applied stress — whether that's a change in concentration, pressure, or temperature. Crucially, only temperature changes the value of K itself; catalysts, concentration changes, and pressure changes shift the equilibrium position but leave K unchanged. The thermodynamic link ΔG° = −RT ln K connects equilibrium to Gibbs energy, explaining why K depends on temperature. Mastering these tools — both quantitative (K, Q, ICE tables) and qualitative (Le Chatelier) — is essential for IB Chemistry problem-solving and extended-response explanations.