Apply Rate of Chemical Change — Apply Reactivity 2.2—How fast? The rate of chemical change in problem-solving and explanations - IB Chemistry

SECTION 1

Historical Context & Motivation

Understanding how fast a chemical reaction proceeds has been a central question in chemistry for over two centuries. Early chemists noticed that some reactions, such as explosions, happen almost instantaneously, while others, like the rusting of iron, take weeks or even years. The formal study of chemical kinetics — the branch of chemistry concerned with the rates of reactions — grew out of the need to control industrial processes, preserve food, and understand biological metabolism.

1864 • Law of Mass Action

Norwegian scientists Cato Guldberg and Peter Waage proposed that the rate of a reaction depends on the concentrations of the reactants, laying the groundwork for modern rate expressions.

1889 • Arrhenius Equation

Svante Arrhenius quantified how temperature affects reaction rate by introducing the concept of activation energy and the exponential relationship between temperature and rate constant.

1913 • Collision Theory Formalized

Max Trautz and William Lewis independently developed collision theory, explaining that reactant particles must collide with sufficient energy and correct orientation for a reaction to occur.

1935 • Transition State Theory

Henry Eyring and Michael Polanyi developed transition state theory, which describes the high-energy intermediate state that reactants pass through on their way to becoming products.

1970s–Present • Modern Catalysis & Green Chemistry

Advances in catalysis, enzyme kinetics, and computational chemistry allow scientists to design reactions that run faster, cleaner, and more efficiently — from industrial synthesis to pharmaceutical development.

The question at the heart of Reactivity 2.2 is deceptively simple: how fast does a reaction go, and what can we do to change that speed? To answer it, you need to know how to measure rate, express it mathematically, and connect it to the particle-level factors — concentration, temperature, surface area, and catalysts — that govern how quickly reactants become products.

SECTION 2

Core Principles & Definitions

The rate of reaction is defined as the change in concentration of a reactant or product per unit time. It tells you how quickly a reaction is consuming its starting materials or generating its products. Rate is always expressed as a positive quantity; when we track a reactant (whose concentration decreases), we include a negative sign in the expression to make the rate positive. Understanding the following core ideas will equip you to solve any rate problem on the IB exam.

Rate of Reaction

The change in concentration of a reactant or product divided by the change in time: Δ[X]/Δt. Units are typically mol dm⁻³ s⁻¹.

Collision Theory

A reaction occurs only when reactant particles collide with sufficient kinetic energy (≥ activation energy) and proper orientation. Any factor that increases the frequency or energy of effective collisions increases the rate.

Activation Energy (Eₐ)

The minimum energy that colliding particles must possess for a successful reaction. A lower Eₐ means more collisions are effective, so the reaction proceeds faster.

Factors Affecting Rate

Five main factors control rate: concentration of reactants, temperature, surface area of solids, presence of a catalyst, and the nature of the reactants themselves.

Rate Expression (HL Preview)

For many reactions, rate = k[A]ᵐ[B]ⁿ, where k is the rate constant and m, n are the orders of reaction determined experimentally, not from stoichiometry.

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KEY TAKEAWAY

Think of reaction rate like the speed of a car. Just as 'speed' tells you how much distance is covered per unit time, rate of reaction tells you how much concentration changes per unit time. The faster the car, the more distance it covers each second; the faster the reaction, the more product it forms each second. Factors like concentration, temperature, and catalysts are like stepping on the gas pedal — they increase the 'speed' of the reaction.

SECTION 3

Visualizing Rate of Reaction

One of the most important skills in IB Chemistry is reading and interpreting concentration-time graphs. The graph below shows how the concentration of a reactant decreases and the concentration of a product increases over time for a typical reaction. The slope of the tangent to either curve at any point gives you the instantaneous rate at that moment. Notice that the curves flatten over time — the reaction slows down as reactants are used up.

The pink curve shows the reactant concentration decreasing over time, while the cyan curve shows the product concentration increasing. The yellow dashed tangent line at t ≈ 20 s illustrates how to find the instantaneous rate at a specific moment. The steeper the tangent, the faster the reaction is proceeding at that point.

There are two main ways to report rate from a graph. The average rate is calculated by dividing the total change in concentration by the total change in time between two points. The instantaneous rate is found by drawing a tangent to the curve at a specific time and calculating the slope of that tangent. In your IB exam, you may be asked to do either — so be comfortable with both approaches.

SECTION 4

Mathematical Framework

Quantifying the rate of reaction requires several mathematical expressions. At the SL level, you need to master average and instantaneous rate calculations from concentration-time data. At HL, you will also encounter the rate expression and the Arrhenius equation. The equations below form the core mathematical toolkit for Reactivity 2.2.

AVERAGE RATE OF REACTION

Average rate = −Δ[Reactant] / Δt = Δ[Product] / Δt

Δ[Reactant] = change in reactant concentration (mol dm⁻³); Δt = change in time (s). The negative sign ensures the rate is positive when tracking a reactant that is being consumed.

INSTANTANEOUS RATE

Instantaneous rate = −d[Reactant] / dt (slope of tangent at time t)

Draw a tangent line to the concentration-time curve at the desired time. The gradient (rise over run) of that tangent equals the instantaneous rate. In practice, choose two points far apart on the tangent line for accuracy.

RATE EXPRESSION (HL)

Rate = k[A]ᵐ[B]ⁿ

k = rate constant; [A], [B] = concentrations of reactants; m, n = orders of reaction with respect to A and B respectively. The orders must be determined experimentally — they are not taken from the balanced equation.

ARRHENIUS EQUATION (HL)

k = Ae^(−Eₐ / RT)

A = Arrhenius (pre-exponential) factor; Eₐ = activation energy (J mol⁻¹); R = gas constant (8.314 J mol⁻¹ K⁻¹); T = absolute temperature (K). This equation shows that as temperature increases, k increases exponentially.

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IB Exam Tip

When calculating average rate from a data table, always check whether you are given concentration of a reactant or a product. For reactants, include the negative sign so your final rate is positive. For products, the concentration increases, so the rate is already positive without the sign.

SECTION 5

Factors Affecting Rate — A Deeper Look

Every factor that influences reaction rate can be explained through collision theory: either the frequency of collisions changes, the energy of collisions changes, or both. The diagram below summarizes the five key factors, connecting the macroscopic observation (what you see in the lab) to the particle-level explanation (what the molecules are doing).

This diagram maps all five factors affecting rate to their particle-level explanations through collision theory. Notice that temperature is the only factor that increases both collision frequency and the proportion of particles exceeding the activation energy.

Factor	Change	Effect on Rate	Collision Theory Explanation
Concentration	Increase	Rate increases	More particles per unit volume → more frequent collisions
Temperature	Increase by 10 K	Rate approximately doubles	Particles move faster → more frequent collisions AND greater proportion exceed Eₐ
Surface area	Increase (powder vs. lump)	Rate increases	More reactant particles exposed at the surface → more frequent collisions
Catalyst	Add a catalyst	Rate increases	Alternative pathway with lower Eₐ → greater fraction of particles with sufficient energy
Pressure (gases)	Increase	Rate increases	Gas particles compressed into smaller volume → higher effective concentration → more frequent collisions

Summary of factors affecting rate with collision theory explanations

SECTION 6

Worked Example — Calculating Rate from Data

Let's work through a typical IB-style problem step by step. This example requires you to calculate both average rate and to interpret the data using collision theory.

Rate of Decomposition of H₂O₂

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Step 1 — Read the Problem

Hydrogen peroxide decomposes according to the equation: 2H₂O₂(aq) → 2H₂O(l) + O₂(g). The concentration of H₂O₂ was measured at different times: at t = 0 s, [H₂O₂] = 0.80 mol dm⁻³; at t = 40 s, [H₂O₂] = 0.40 mol dm⁻³; at t = 80 s, [H₂O₂] = 0.20 mol dm⁻³. Calculate the average rate over the first 40 s and over the interval 40–80 s. Explain any difference.
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Step 2 — Identify the Formula

Average rate = −Δ[H₂O₂] / Δt. Since H₂O₂ is a reactant, we include the negative sign to ensure a positive rate.
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Step 3 — Calculate Rate for 0–40 s

Rate = −(0.40 − 0.80) / (40 − 0) = −(−0.40) / 40 = 0.40 / 40

Rate (0–40 s) = 0.010 mol dm⁻³ s⁻¹
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Step 4 — Calculate Rate for 40–80 s

Rate = −(0.20 − 0.40) / (80 − 40) = −(−0.20) / 40 = 0.20 / 40

Rate (40–80 s) = 0.0050 mol dm⁻³ s⁻¹
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Step 5 — Explain the Difference

The rate during the first 40 s (0.010 mol dm⁻³ s⁻¹) is double the rate during 40–80 s (0.0050 mol dm⁻³ s⁻¹). This is because the concentration of H₂O₂ is lower during the later interval, meaning fewer reactant particles are available per unit volume. According to collision theory, fewer particles lead to fewer collisions per second, so the rate decreases.

SECTION 7

Experimental Methods — Strengths & Limitations

In the IB syllabus and in your Internal Assessment (IA), you may be asked to choose and evaluate a method for measuring rate. Each experimental technique has its own strengths and limitations, and understanding these will help you write strong evaluations in exam answers and lab reports.

Method	What Is Measured	Strengths	Limitations
Gas syringe / gas collection	Volume of gas produced over time	Continuous monitoring; data easy to graph; no chemicals removed	Only works if a gas is produced; syringe may stick; gas may be soluble in water
Mass loss (balance)	Decrease in mass as gas escapes	Simple setup; continuous data; non-invasive	Less precise for slow reactions; evaporation can cause errors; light gases hard to detect
Colorimetry / spectrophotometry	Absorbance or transmittance of light over time	Very precise; continuous; works for colour changes	Requires a coloured species; calibration curve needed; expensive equipment
Titration (clock method)	Concentration at specific time points	Directly measures concentration; works for many reactions	Discontinuous — only gives snapshots; reaction must be quenched; time-consuming
Disappearing cross / clock reactions	Time for a fixed amount of product to form	Simple; quick; good for initial rate comparisons	Subjective endpoint; measures average initial rate, not continuous rate

Comparison of common experimental methods for measuring rate of reaction

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KEY TAKEAWAY

Choosing the right method to measure rate is like choosing the right tool for a home repair project. A gas syringe is your 'power drill' — great when you're producing a gas, but useless if there's no gas involved. Colorimetry is your 'precision laser level' — highly accurate, but requires a specific condition (a coloured species). In the IB exam, always justify your method choice by explaining why it suits the particular reaction being studied.

SECTION 8

Connection to Rate Expressions & the Arrhenius Equation (HL)

At Standard Level, your focus is on measuring and explaining rate qualitatively using collision theory. At Higher Level, the IB expects you to take the next step: expressing rate quantitatively using the rate expression and the Arrhenius equation. The table below shows how the concepts you've learned in this lesson serve as the foundation for the more advanced treatment.

Concept at SL	Extension at HL
Increasing concentration increases rate	Rate = k[A]ᵐ[B]ⁿ — the rate expression quantifies exactly how rate depends on each reactant's concentration. The exponents m and n are determined experimentally.
Increasing temperature increases rate	The Arrhenius equation k = $Ae^{−Eₐ/RT}$ shows that the rate constant k increases exponentially with temperature. A 10 K rise roughly doubles k for many reactions.
A catalyst provides an alternative pathway	The catalyst lowers Eₐ in the Arrhenius equation, increasing k without raising T. Reaction mechanism involves intermediate steps, each with its own Eₐ.
Average rate from Δ[X]/Δt	Initial rate method: measure rate at t ≈ 0 for different initial concentrations to determine order of reaction and rate constant k.
Rate decreases over time	Half-life (t₁/₂) is constant for first-order reactions. For zero-order reactions, [A] vs. t is linear. Graphical methods distinguish orders.

How SL concepts connect to HL extensions in Reactivity 2.2

Even if you are studying at SL, understanding these connections gives you a deeper appreciation of why you need to master average and instantaneous rates. These calculations are the raw data that HL students use to determine the rate expression. Think of SL content as building the measurement tools, and HL as using those tools to construct a complete mathematical model of the reaction.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

Explain, using collision theory, why grinding a large marble chip into a fine powder increases the rate of its reaction with hydrochloric acid.

Show answer

Grinding the marble chip (CaCO₃) into a powder dramatically increases its surface area. A larger surface area means that more CaCO₃ particles are exposed to HCl molecules at any given moment. According to collision theory, this increases the frequency of collisions between reactant particles, and therefore the frequency of effective collisions (those with energy ≥ Eₐ and correct orientation). As a result, the rate of reaction increases. Importantly, the total amount of product formed remains the same — it is just produced more quickly.

Question 2: BASIC CALCULATION

In a reaction, the concentration of a product increases from 0.00 mol dm⁻³ to 0.15 mol dm⁻³ over 30 seconds. Calculate the average rate of formation of the product.

Show answer

Average rate = Δ[Product] / Δt = (0.15 − 0.00) / (30 − 0) = 0.15 / 30 = 0.0050 mol dm⁻³ s⁻¹. Since we are tracking a product (whose concentration increases), we do not need the negative sign. The rate is 5.0 × 10⁻³ mol dm⁻³ s⁻¹.

Question 3: INTERMEDIATE

The decomposition of N₂O₅ produces NO₂ and O₂: 2N₂O₅(g) → 4NO₂(g) + O₂(g). If the rate of disappearance of N₂O₅ is 4.0 × 10⁻³ mol dm⁻³ s⁻¹, what is the rate of formation of NO₂ and the rate of formation of O₂?

Show answer

Using stoichiometric ratios: for every 2 mol of N₂O₅ consumed, 4 mol of NO₂ are formed and 1 mol of O₂ is formed. Rate of NO₂ formation = (4/2) × 4.0 × 10⁻³ = 8.0 × 10⁻³ mol dm⁻³ s⁻¹. Rate of O₂ formation = (1/2) × 4.0 × 10⁻³ = 2.0 × 10⁻³ mol dm⁻³ s⁻¹. The key is to use the mole ratios from the balanced equation to convert between rates of different species.

Question 4: APPLIED

A student investigates the reaction between magnesium ribbon and sulfuric acid at two temperatures: 25 °C and 35 °C. She finds that the rate at 35 °C is approximately 2.3 times faster than at 25 °C. Using collision theory, explain why a 10 °C increase has such a significant effect. In your answer, distinguish between the two mechanisms by which temperature affects rate.

Show answer

Increasing the temperature from 25 °C (298 K) to 35 °C (308 K) affects the rate through two mechanisms. First, at a higher temperature, particles have greater average kinetic energy and therefore move faster. This increases the frequency of collisions — but this effect alone would only produce a modest increase in rate (roughly 1–2%). The dominant effect is the second one: at a higher temperature, a significantly larger proportion of particles possess kinetic energy equal to or exceeding the activation energy (Eₐ). The Maxwell-Boltzmann distribution shifts so that the area under the curve beyond Eₐ increases substantially — even a small temperature rise can double or triple this fraction. Combined, these two effects explain the 2.3× rate increase observed. This aligns with the general rule that a 10 K temperature increase approximately doubles the rate for many reactions.

Question 5: CRITICAL THINKING

Two students each investigate the reaction between sodium thiosulfate and hydrochloric acid using the 'disappearing cross' method. Student A doubles the concentration of Na₂S₂O₃ and finds the cross disappears in half the time. Student B doubles the concentration of HCl and finds that the time barely changes. Propose an explanation for these different results. What might this suggest about the rate expression for this reaction?

Show answer

The results suggest that the rate of reaction is strongly dependent on the concentration of Na₂S₂O₃ but nearly independent of the concentration of HCl. In the rate expression Rate = k[Na₂S₂O₃]ᵐ[HCl]ⁿ, Student A's result (doubling concentration halves the time, meaning rate doubles) suggests m ≈ 1 (first-order with respect to Na₂S₂O₃). Student B's result (doubling HCl barely changes the rate) suggests n ≈ 0 (zero-order with respect to HCl). This could occur if HCl is present in excess relative to the amount needed in the rate-determining step, or if HCl is not involved in the rate-determining step of the reaction mechanism. This problem illustrates why reaction orders must be determined experimentally and cannot simply be read from the stoichiometric coefficients.

SUMMARY

Lesson Summary

Summary

The rate of chemical change measures how quickly reactant concentrations decrease or product concentrations increase, expressed as Δ[X] / Δt with units of mol dm⁻³ s⁻¹. Collision theory explains rate at the particle level: reactions occur only when particles collide with sufficient energy (≥ Eₐ) and correct orientation. Five key factors affect rate: concentration, temperature, surface area, catalysts, and the nature of the reactants. Each factor works by changing the frequency or energy of effective collisions.

You can determine average rate from a data table using −Δ[Reactant]/Δt, and instantaneous rate by drawing a tangent to a concentration-time graph. Stoichiometric ratios allow you to convert rates between different species in the same reaction. At HL, the rate expression (Rate = k[A]ᵐ[B]ⁿ) and the Arrhenius equation (k = Ae⁻ᴱᵃ/ᴿᵀ) provide the quantitative framework for predicting how changes in conditions affect rate. Master these tools, and you can tackle any rate problem the IB throws at you.