Understand Proton Transfer Reactions — Understand Reactivity 3.1—Proton transfer reactions - IB Chemistry

SECTION 1

Historical Context & Motivation

For centuries, chemists recognized that certain substances taste sour, corrode metals, or feel slippery, but they lacked a unifying explanation. The concept of proton transfer — the idea that a hydrogen ion (H⁺) moves from one molecule to another — eventually became the foundation of modern acid-base chemistry. Understanding how scientists arrived at this elegant picture reveals why proton transfer reactions are so central to the IB Chemistry course and to the natural world around you.

1661 • Boyle's Indicators

Robert Boyle catalogued the properties of acids and bases, noting that acids turn certain plant dyes red and bases turn them blue. This early classification gave chemists a practical way to identify acids and bases, even without knowing what caused their behavior.

1884 • Arrhenius Theory

Svante Arrhenius proposed that acids produce H⁺ ions and bases produce OH⁻ ions when dissolved in water. While groundbreaking, this theory was limited because it only applied to aqueous (water-based) solutions.

1923 • Brønsted–Lowry Theory

Johannes Brønsted and Thomas Lowry independently redefined acids as proton donors and bases as proton acceptors. This broader definition allowed chemists to explain acid-base reactions in any solvent — or even in the gas phase.

1923 • Lewis Theory

Gilbert N. Lewis expanded the concept further by defining acids as electron-pair acceptors and bases as electron-pair donors. While Lewis theory is broader, the Brønsted–Lowry model remains the go-to framework for understanding proton transfer reactions in IB Chemistry.

The central question that drove this progression was deceptively simple: What actually happens at the molecular level when an acid reacts with a base? The Brønsted–Lowry answer — a proton physically transfers from one species to another — is the focus of IB Reactivity 3.1 and the key to unlocking everything from buffer chemistry to biological enzyme reactions.

SECTION 2

Core Principles & Definitions

The Brønsted–Lowry model rests on a beautifully simple idea: every acid-base reaction is a competition for a proton. One species donates H⁺ (the acid) and another accepts it (the base). This single concept generates several important definitions that you need to master for the IB exam.

Brønsted–Lowry Acid

A proton donor — any species that can give away an H⁺ ion to another molecule. Examples include HCl, H₂SO₄, and CH₃COOH.

Brønsted–Lowry Base

A proton acceptor — any species with a lone pair of electrons available to bond with an incoming H⁺. Examples include NH₃, OH⁻, and CO₃²⁻.

Conjugate Acid-Base Pair

Two species that differ by exactly one proton. When an acid donates H⁺, it becomes its conjugate base; when a base accepts H⁺, it becomes its conjugate acid.

Amphiprotic Species

A molecule that can act as either an acid or a base depending on the reaction partner. Water (H₂O) is the classic example — it can donate or accept a proton.

Autoionization of Water

Water molecules transfer protons among themselves: H₂O + H₂O ⇌ H₃O⁺ + OH⁻. This equilibrium defines the ion product constant K_w = 1.00 × 10⁻¹⁴ at 25 °C.

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KEY TAKEAWAY

Think of a proton transfer reaction like passing a ball in a relay race. The acid is the runner handing off the ball (H⁺), and the base is the runner receiving it. Once the hand-off occurs, each runner has a new identity — the former acid is now a conjugate base (it lost the ball), and the former base is now a conjugate acid (it gained the ball). Every proton transfer creates two conjugate pairs, always.

SECTION 3

Visual Explanation — Proton Transfer in Action

The diagram below shows the classic proton transfer reaction between hydrochloric acid (HCl) and water (H₂O). Pay close attention to how the proton leaves one species and bonds to another, and how conjugate pairs are formed on both sides of the equation.

The pink boxes represent the acid and its conjugate base (HCl / Cl⁻), while the cyan boxes show the base and its conjugate acid (H₂O / H₃O⁺). The golden arrow traces the path of the proton from the donor to the acceptor.

Notice that the H⁺ doesn't float freely in solution — it is always transferred directly from one molecule to another. In this reaction, HCl gives its proton to the lone pair on the oxygen atom of water. The result is a hydronium ion (H₃O⁺) and a chloride ion (Cl⁻). The two conjugate pairs — HCl/Cl⁻ and H₂O/H₃O⁺ — are always present in any Brønsted–Lowry reaction.

SECTION 4

Mathematical Framework — pH, pOH, and Kw

Proton transfer reactions are quantified using the pH scale, which expresses the concentration of hydronium ions in solution. Because these concentrations span many orders of magnitude, chemists use a logarithmic scale to keep the numbers manageable.

DEFINITION OF pH

pH = −log₁₀[H₃O⁺]

where [H₃O⁺] is the molar concentration of hydronium ions in mol dm⁻³ (M). A low pH means a high [H₃O⁺] (acidic), and a high pH means a low [H₃O⁺] (basic).

DEFINITION OF pOH

pOH = −log₁₀[OH⁻]

where [OH⁻] is the molar concentration of hydroxide ions. In any aqueous solution at 25 °C, pH + pOH = 14.00.

ION PRODUCT OF WATER

Kw = [H₃O⁺][OH⁻] = 1.00 × 10⁻¹⁴ (at 25 °C)

K_w is the ion product constant of water. This value increases with temperature because the autoionization of water is endothermic.

RELATIONSHIP BETWEEN Ka AND Kb

Ka × Kb = Kw

For any conjugate acid-base pair, the product of the acid dissociation constant (K_a) and the base dissociation constant (K_b) equals K_w. A strong acid (large K_a) has a weak conjugate base (small K_b), and vice versa.

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IB Exam Tip

The IB data booklet provides the formula pH = −log[H⁺] and the value of K_w. You are expected to rearrange these to find [H₃O⁺] from pH: [H₃O⁺] = 10^−pH. Practice this operation on your calculator before the exam.

SECTION 5

Strong vs. Weak Acids and Bases

Not all proton transfer reactions go to completion. Strong acids like HCl, HNO₃, and H₂SO₄ completely donate their protons to water — the reaction essentially goes 100% to products. Weak acids like CH₃COOH (acetic acid) only partially donate their protons, establishing an equilibrium between reactants and products. The same distinction applies to bases: NaOH is a strong base that fully dissociates, while NH₃ is a weak base that only partially accepts protons from water.

The bar charts show relative concentrations of species in solution. For the strong acid (left), virtually all HCl has ionized into H₃O⁺ and Cl⁻. For the weak acid (right), most molecules remain as undissociated CH₃COOH. The pH scale below compares the two solutions at the same initial concentration.

Property	Strong Acid / Base	Weak Acid / Base
Degree of ionization	Complete (≈ 100%)	Partial (often < 5%)
Equilibrium arrow	→ (forward only)	⇌ (equilibrium)
K_a / K_b value	Very large (≫ 1)	Small (≪ 1)
Conjugate strength	Conjugate is very weak	Conjugate has moderate strength
Examples (acids)	HCl, HNO₃, H₂SO₄	CH₃COOH, HF, H₂CO₃

Key differences between strong and weak acids/bases

SECTION 6

Worked Example — Identifying Conjugate Pairs & Calculating pH

Let's work through a complete IB-style problem that combines identification of conjugate pairs with a pH calculation.

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Problem

A 0.050 mol dm⁻³ solution of nitric acid (HNO₃) is prepared. (a) Write the equation for the proton transfer reaction with water and identify both conjugate acid-base pairs. (b) Calculate the pH of the solution.

Solution

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Step 1 — Write the Balanced Equation

Nitric acid is a strong acid, so it completely transfers its proton to water. The equation uses a forward arrow (→) because ionization is complete:

HNO₃(aq) + H₂O(l) → H₃O⁺(aq) + NO₃⁻(aq)
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Step 2 — Identify Conjugate Pair 1

HNO₃ donates a proton and becomes NO₃⁻. These two species differ by exactly one proton, making them a conjugate acid-base pair.

Conjugate Pair 1: HNO₃ (acid) / NO₃⁻ (conjugate base)
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Step 3 — Identify Conjugate Pair 2

H₂O accepts a proton and becomes H₃O⁺. Again, these differ by one proton.

Conjugate Pair 2: H₂O (base) / H₃O⁺ (conjugate acid)
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Step 4 — Determine [H₃O⁺]

Since HNO₃ is a strong acid, it ionizes completely. Every mole of HNO₃ produces one mole of H₃O⁺. Therefore:

[H₃O⁺] = 0.050 mol dm⁻³
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Step 5 — Calculate pH

Apply the pH formula: pH = −log₁₀[H₃O⁺] = −log₁₀(0.050). Using your calculator:

pH = 1.30

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Check Your Answer

Does the answer make sense? A 0.050 M strong acid should have a pH between 1 and 2, so pH = 1.30 is reasonable. If you got a pH above 7, double-check your calculator — you may have forgotten the negative sign in the formula.

SECTION 7

Comparing Acid-Base Models

The Brønsted–Lowry model is the primary framework for IB Reactivity 3.1, but it's useful to see how it compares to the Arrhenius and Lewis models. Each successive theory is broader than the last, but the Brønsted–Lowry approach remains the most practical for explaining proton transfer reactions.

Feature	Arrhenius	Brønsted–Lowry	Lewis
Definition of acid	Produces H⁺ in water	Donates H⁺ (proton)	Accepts an electron pair
Definition of base	Produces OH⁻ in water	Accepts H⁺ (proton)	Donates an electron pair
Solvent required?	Yes (water only)	No — works in any solvent or gas phase	No — works in any context
Scope	Narrowest	Moderate	Broadest
Explains NH₃ as a base?	Not directly (no OH⁻ in formula)	Yes — NH₃ accepts H⁺ from water	Yes — NH₃ donates a lone pair

Comparison of the three major acid-base models

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KEY TAKEAWAY

Think of the three acid-base models as increasingly powerful telescopes. The Arrhenius model is a basic pair of binoculars — it works but only shows you water-based reactions. The Brønsted–Lowry model is a proper telescope that reveals proton transfers in any environment. The Lewis model is the Hubble Space Telescope — it can see electron-pair interactions everywhere, even where no protons are involved. For IB Reactivity 3.1, the Brønsted–Lowry telescope is your go-to tool.

SECTION 8

Connection to Advanced Theory — Buffer Systems & Biological pH

Proton transfer reactions are not just a classroom concept — they are essential to life itself. Your blood, for example, is maintained at a pH of about 7.4 by a buffer system involving the conjugate pair H₂CO₃ / HCO₃⁻ (carbonic acid / hydrogen carbonate). When you exercise and produce CO₂, this buffer absorbs excess H⁺ through proton transfer reactions, preventing dangerous changes in blood pH.

Topic	Reactivity 3.1 (This Lesson)	Advanced / HL Extension
Equilibrium	Recognize ⇌ for weak acids/bases	Calculate Ka, Kb, and use ICE tables
Buffers	Understand conjugate pairs exist	Use Henderson–Hasselbalch equation to design buffers
Titrations	Identify the proton transfer in neutralization	Interpret titration curves and select indicators
pH calculations	pH of strong acids and bases	pH of weak acids, polyprotic acids, and salt solutions

How Reactivity 3.1 connects to higher-level topics

As you progress through the IB Chemistry course, you will see that conjugate pair relationships underpin titration analysis, buffer design, and even the regulation of ocean pH (ocean acidification). Mastering the basics of proton transfer now will give you a solid foundation for these more complex applications.

SECTION 9

Practice Problems

Question 1: CONCEPTUAL

In the reaction NH₃(aq) + H₂O(l) ⇌ NH₄⁺(aq) + OH⁻(aq), identify the Brønsted–Lowry acid and the Brønsted–Lowry base. Then state both conjugate acid-base pairs.

Show answer

Water (H₂O) acts as the Brønsted–Lowry acid because it donates a proton to ammonia. Ammonia (NH₃) acts as the Brønsted–Lowry base because it accepts the proton. Conjugate pair 1 is H₂O / OH⁻ (H₂O loses H⁺ to become OH⁻). Conjugate pair 2 is NH₃ / NH₄⁺ (NH₃ gains H⁺ to become NH₄⁺). This reaction also illustrates the amphiprotic nature of water, which acts as an acid here but acts as a base when reacting with HCl.

Question 2: BASIC CALCULATION

Calculate the pH of a 0.0020 mol dm⁻³ solution of hydrochloric acid (HCl). State any assumption you make.

Show answer

HCl is a strong acid, so it ionizes completely: [H₃O⁺] = 0.0020 mol dm⁻³. Applying the pH formula: pH = −log₁₀(0.0020) = −log₁₀(2.0 × 10⁻³) = −(log 2.0 + log 10⁻³) = −(0.301 + (−3)) = 2.70. The assumption is that HCl ionizes 100%, which is valid for strong acids. You can verify: 10⁻²·⁷⁰ = 0.0020, confirming the answer.

Question 3: INTERMEDIATE

A solution has a pOH of 3.40 at 25 °C. Calculate (a) the pH, (b) the [H₃O⁺], and (c) determine whether the solution is acidic, neutral, or basic.

Show answer

(a) At 25 °C, pH + pOH = 14.00, so pH = 14.00 − 3.40 = 10.60. (b) [H₃O⁺] = 10⁻ᵖᴴ = 10⁻¹⁰·⁶⁰ = 2.51 × 10⁻¹¹ mol dm⁻³. (c) Since the pH is greater than 7 (or equivalently, pOH < 7), the solution is basic. You could also check: [OH⁻] = 10⁻³·⁴⁰ = 3.98 × 10⁻⁴ mol dm⁻³, which is much greater than [H₃O⁺], confirming that hydroxide ions dominate and the solution is indeed basic.

Question 4: APPLIED

Gastric juice in the human stomach has a pH of approximately 1.5. Calculate the concentration of hydronium ions in gastric juice. If 250 cm³ of gastric juice is neutralized by an antacid containing Mg(OH)₂, write the balanced proton transfer equation and determine the moles of Mg(OH)₂ required.

Show answer

[H₃O⁺] = 10⁻¹·⁵ = 0.0316 mol dm⁻³. The volume is 250 cm³ = 0.250 dm³, so moles of H₃O⁺ = 0.0316 × 0.250 = 7.91 × 10⁻³ mol. The balanced equation is: Mg(OH)₂(s) + 2 H₃O⁺(aq) → Mg²⁺(aq) + 4 H₂O(l). Alternatively, it can be written as Mg(OH)₂ + 2 HCl → MgCl₂ + 2 H₂O, but the proton transfer form shows H₃O⁺ directly. From stoichiometry, 1 mol Mg(OH)₂ neutralizes 2 mol H₃O⁺, so moles of Mg(OH)₂ = 7.91 × 10⁻³ / 2 = 3.95 × 10⁻³ mol ≈ 3.96 × 10⁻³ mol.

Question 5: CRITICAL THINKING

Hydrogen fluoride (HF) is a weak acid with K_a = 6.8 × 10⁻⁴, while hydrochloric acid (HCl) is a strong acid. Both are hydrogen halides. Explain, using the concept of conjugate pairs and proton transfer, why a 0.10 M HF solution has a higher pH than a 0.10 M HCl solution. Predict which conjugate base — F⁻ or Cl⁻ — would be more effective at accepting a proton in a reverse reaction, and justify your answer.

Show answer

HCl is a strong acid and ionizes completely, so [H₃O⁺] = 0.10 M and pH = 1.00. HF is a weak acid and only partially ionizes: the small Ka means the equilibrium HF + H₂O ⇌ H₃O⁺ + F⁻ lies far to the left, producing [H₃O⁺] much less than 0.10 M, and therefore a higher pH (approximately 2.1). Because Ka × Kb = Kw, a weak acid (small Ka) has a relatively strong conjugate base (larger Kb). Therefore, F⁻ is a stronger base than Cl⁻ and is more effective at accepting a proton in the reverse reaction. Cl⁻ is the conjugate base of a strong acid and is essentially inert — it has virtually no tendency to accept a proton. This illustrates the inverse relationship: the weaker the acid, the stronger its conjugate base, and vice versa.

SUMMARY

Lesson Summary

Summary

A proton transfer reaction occurs when a Brønsted–Lowry acid donates an H⁺ ion to a Brønsted–Lowry base. This process always produces two conjugate acid-base pairs — the acid becomes its conjugate base and the base becomes its conjugate acid. Strong acids transfer their protons completely (→), while weak acids establish equilibrium (⇌) with only partial ionization. The strength of an acid and its conjugate base are inversely related through K_a × K_b = K_w.

The pH scale (pH = −log₁₀[H₃O⁺]) quantifies the hydronium ion concentration in solution, and pH + pOH = 14 at 25 °C. Amphiprotic species like water can act as either acids or bases. The autoionization of water (K_w = 1.00 × 10⁻¹⁴) provides the link between [H₃O⁺] and [OH⁻] and underpins all aqueous acid-base calculations you will encounter in IB Chemistry.