English:Acid-Base Equilibria
Acid-Base Equilibria
Introduction
Acid-base equilibria connect chemical equilibrium, acids, bases, pH, buffers, and titrations. In this aiMOOC for Grades 11–13, you will move from qualitative ideas about proton transfer to quantitative calculations with equilibrium constants. You will also learn how chemists measure pH, design buffers, interpret titration curves, and decide when an approximation is justified.
An acid-base system at equilibrium is dynamic: forward and reverse proton-transfer reactions continue, but macroscopic concentrations remain constant. This idea explains why a weak acid may be only partly ionized while a strong acid is essentially fully ionized in dilute aqueous solution.
The pH scale is logarithmic. A change of one pH unit corresponds to a tenfold change in hydrogen-ion activity. In routine school calculations with dilute solutions, you usually approximate activity by molar concentration.
Learning Goals
By the end of this course, you should be able to explain acid-base models, identify conjugate acid-base pairs, write and interpret equilibrium expressions, calculate pH and pOH, use Ka, Kb, and Kw, design and analyze buffers, interpret titration curves, select suitable indicators, and justify the assumptions used in your calculations.
You should also be able to connect acid-base equilibria to laboratory analysis, biological systems, environmental chemistry, and industrial processes.
Foundations of Acid-Base Chemistry
Arrhenius, Brønsted–Lowry, and Lewis Models
The Arrhenius model describes an acid as a substance that increases the concentration of H₃O⁺ in water and a base as a substance that increases the concentration of OH⁻ in water. It is useful for aqueous chemistry but does not cover every acid-base reaction.
The Brønsted–Lowry model is especially important for equilibrium work. A Brønsted–Lowry acid donates a proton, H⁺, and a Brønsted–Lowry base accepts a proton. Consider:
HA + H₂O ⇌ A⁻ + H₃O⁺
Here, HA is the acid and H₂O is the base. A⁻ is the conjugate base of HA, while H₃O⁺ is the conjugate acid of H₂O. Conjugate partners differ by exactly one proton.
The Lewis model is broader. A Lewis acid accepts an electron pair, while a Lewis base donates an electron pair. Lewis acid-base chemistry is important in coordination chemistry and organic mechanisms, but this aiMOOC focuses mainly on proton-transfer equilibria in water.
Amphiprotic Species and Water
A species is amphiprotic if it can either donate or accept a proton. Water is the most familiar example. In one reaction, H₂O may accept H⁺ and become H₃O⁺; in another, it may donate H⁺ and become OH⁻.
Other common amphiprotic species include HCO₃⁻ and H₂PO₄⁻. Recognizing amphiprotic species helps you predict acid-base behavior in multistep systems.
Predicting the Direction of Proton Transfer
Acid-base equilibria tend to favor the side containing the weaker acid and the weaker base. A useful quantitative guide is pKa: lower pKa means a stronger acid.
For the reaction
HA + B ⇌ A⁻ + HB⁺
the equilibrium constant can be related approximately to acid strengths by:
K ≈ 10pKa(HB⁺) − pKa(HA)
If the product acid HB⁺ has a much higher pKa than the reactant acid HA, the forward reaction is strongly favored.
Acid and Base Dissociation Constants
The Acid Dissociation Constant Ka
For a weak monoprotic acid:
HA + H₂O ⇌ H₃O⁺ + A⁻
the acid dissociation constant is:
Ka = [H₃O⁺][A⁻] / [HA]
In dilute school-level calculations, the square brackets represent equilibrium molar concentrations. A larger Ka generally means greater ionization and therefore a stronger acid in the same solvent and under comparable conditions.
The logarithmic form is:
pKa = −log₁₀(Ka)
A stronger acid therefore has a lower pKa.
The Base Dissociation Constant Kb
For a weak base B:
B + H₂O ⇌ BH⁺ + OH⁻
the base dissociation constant is:
Kb = [BH⁺][OH⁻] / [B]
A larger Kb corresponds to a stronger base in the same solvent and under comparable conditions.
For a conjugate acid-base pair at a fixed temperature:
Ka × Kb = Kw
At 25 °C, Kw is approximately 1.0 × 10−14, so pKa + pKb ≈ 14.00.
Strong Is Not the Same as Concentrated
Strength describes the extent of ionization or proton transfer. Concentration describes how much solute is present per unit volume. A dilute strong acid can contain less acid per litre than a concentrated weak acid. Keeping these ideas separate prevents many pH errors.
Water, Kw, pH, and pOH
Water undergoes self-ionization:
2 H₂O ⇌ H₃O⁺ + OH⁻
The ionic product of water is:
Kw = [H₃O⁺][OH⁻]
At 25 °C, Kw ≈ 1.0 × 10−14. In pure water at this temperature, [H₃O⁺] = [OH⁻] ≈ 1.0 × 10−7 mol L⁻¹.
The pH and pOH scales are defined by:
pH = −log₁₀[H₃O⁺]
pOH = −log₁₀[OH⁻]
At 25 °C, pH + pOH ≈ 14.00. A neutral solution has equal hydronium and hydroxide activities. At 25 °C this corresponds approximately to pH 7, but the neutral pH changes with temperature because Kw changes.
Strictly, pH is defined using hydrogen-ion activity rather than concentration. At Grades 11–13, concentration is a useful approximation for sufficiently dilute solutions. Very concentrated solutions can also have pH values below 0 or above 14, so the familiar 0–14 range is not a universal physical limit.
Measuring pH
Indicators provide an approximate pH range through colour changes. A calibrated pH meter can provide a more precise measurement by comparing electrode potentials.
Good laboratory practice includes calibrating the meter with suitable buffer standards, rinsing the electrode between samples, avoiding contamination, recording temperature when relevant, and never allowing a glass electrode to dry out if its storage instructions require it to remain hydrated.
Calculating the pH of Weak Acids and Bases
ICE-Table Reasoning
For a weak acid HA with initial concentration C, let x be the amount that ionizes:
HA ⇌ H⁺ + A⁻
Initial: C, 0, 0
Change: −x, +x, +x
Equilibrium: C − x, x, x
Then:
Ka = x² / (C − x)
You can solve the resulting quadratic equation exactly. If x is much smaller than C, you may approximate C − x ≈ C, giving x ≈ √(KaC). You should check afterward that the approximation was reasonable.
Worked Weak-Acid Example
Suppose a 0.100 mol L⁻¹ solution of a monoprotic weak acid has Ka = 1.8 × 10−5. The exact equilibrium equation is:
1.8 × 10−5 = x² / (0.100 − x)
Solving gives [H₃O⁺] ≈ 1.33 × 10−3 mol L⁻¹ and pH ≈ 2.88. The approximation x ≈ √(KaC) gives a very similar answer because the fraction ionized is small.
Worked Weak-Base Example
For 0.100 mol L⁻¹ NH₃ with Kb ≈ 1.8 × 10−5 at 25 °C, the same method gives [OH⁻] ≈ 1.33 × 10−3 mol L⁻¹, pOH ≈ 2.88, and pH ≈ 11.12.
The numerical similarity occurs because the chosen Kb and concentration match the weak-acid example; the chemical systems themselves are different.
Percent Ionization and the Common-Ion Effect
Percent ionization can be written as:
percent ionization = equilibrium amount ionized / initial amount × 100%
Weak acids are usually more strongly ionized when diluted. If you add a source of the conjugate base A⁻ to HA, the equilibrium shifts toward HA. This is the common-ion effect, an application of Le Châtelier's principle.
Buffer Solutions
A buffer resists large pH changes when small amounts of strong acid or strong base are added. A typical acidic buffer contains a weak acid HA and a significant amount of its conjugate base A⁻.
When added H₃O⁺ enters the buffer, A⁻ consumes much of it:
A⁻ + H₃O⁺ → HA + H₂O
When added OH⁻ enters the buffer, HA consumes much of it:
HA + OH⁻ → A⁻ + H₂O
A buffer does not keep pH perfectly constant. It has a finite buffer capacity that depends strongly on the total amount of buffer components present.
Henderson–Hasselbalch Equation
Starting from the Ka expression, you can rearrange to obtain:
pH ≈ pKa + log₁₀([A⁻]/[HA])
This is the Henderson–Hasselbalch approximation. It is most useful when both conjugate partners are present in appreciable amounts and concentration is a reasonable approximation for activity.
If [A⁻] = [HA], then log₁₀(1) = 0 and pH ≈ pKa. A commonly useful buffer range is about pKa ± 1, corresponding roughly to conjugate-base-to-acid ratios between 0.1 and 10.
For example, if pKa = 4.76 and [A⁻]/[HA] = 2.0:
pH ≈ 4.76 + log₁₀(2.0) ≈ 5.06
Buffer Capacity
Two buffers can have the same pH but different capacities. A buffer containing 1.0 mol L⁻¹ of each component can neutralize more added strong acid or base than a buffer containing 0.010 mol L⁻¹ of each component, even though both have the same acid-to-base ratio.
When designing a buffer, choose a conjugate pair with pKa close to the target pH, then select a suitable total concentration and ratio while considering safety, solubility, ionic strength, and the needs of the system.
Acid-Base Titrations
An acid-base titration uses a solution of accurately known concentration to determine the amount or concentration of an acid or base. A burette delivers the titrant while pH or an indicator response is monitored.
The equivalence point is the stoichiometric point at which chemically equivalent amounts of acid and base have reacted. The endpoint is the observed signal used to estimate that point, such as an indicator colour change. Good experimental design minimizes the difference between endpoint and equivalence point.
Strong Acid–Strong Base Titration
For a strong monoprotic acid titrated with a strong base, the pH changes slowly at first and then rises sharply near equivalence. At 25 °C, the equivalence-point pH is approximately 7 when the salt formed does not appreciably react with water.
Weak Acid–Strong Base Titration
A weak acid titrated with a strong base shows a buffer region before equivalence. At the half-equivalence point, equal amounts of HA and A⁻ are present, so:
pH ≈ pKa
At equivalence, the conjugate base A⁻ hydrolyzes water, making the solution basic relative to the neutral point.
Choosing an Indicator
An acid-base indicator is itself a weak acid or weak base whose protonated and deprotonated forms have different colours. You should choose an indicator whose transition range lies within the steep part of the titration curve near the equivalence point. The same indicator is not automatically suitable for every acid-base titration.
A pH meter can provide a full titration curve and is especially useful when the endpoint is difficult to see or when several equivalence regions occur.
Polyprotic Acids and Multiple Equilibria
A polyprotic acid can donate more than one proton in successive steps. For a diprotic acid H₂A:
H₂A ⇌ H⁺ + HA⁻
HA⁻ ⇌ H⁺ + A²⁻
Each step has its own dissociation constant. Usually Ka1 > Ka2 because removing a proton from an increasingly negative species becomes less favorable.
If successive pKa values are sufficiently separated, a titration curve may show distinct buffer regions and equivalence points. In more advanced work, you may need mass-balance, charge-balance, and equilibrium equations to describe the complete species distribution.
Linking Equilibria to Real Systems
Biological Systems
Biological fluids rely on coupled acid-base equilibria. The carbonic-acid/bicarbonate system is one important example in blood, where chemical equilibria interact with respiration and physiological regulation. A chemical buffer alone does not explain the entire living system, but equilibrium principles help you understand why pH can be stabilized.
Environmental Chemistry
Natural waters contain carbonate species, dissolved carbon dioxide, minerals, and organic acids. Changes in these equilibria affect alkalinity, aquatic chemistry, soil chemistry, and the behavior of nutrients and metals. Measuring pH without considering buffering capacity can therefore give an incomplete picture of a water system.
Analytical and Industrial Chemistry
Acid-base titrations are used in quality control, food chemistry, pharmaceuticals, water analysis, and manufacturing. Buffer design is also important wherever reactions, enzymes, dyes, or materials depend strongly on pH.
Laboratory Safety and Good Practice
Wear appropriate eye protection and follow your laboratory's rules whenever you work with acids, bases, indicators, or titration equipment. Use only teacher-approved concentrations and procedures. Never taste chemicals, do not pipette by mouth, label solutions clearly, clean spills according to local procedures, and dispose of chemicals as instructed.
When collecting quantitative data, record uncertainties, rinse volumetric glassware correctly, read the burette at eye level, remove air bubbles from the burette tip, and repeat measurements until your results are sufficiently consistent.
Interactive Tasks
Quiz: Test Your Knowledge
Which statement best describes a Brønsted–Lowry acid? (It donates a proton) (!It accepts an electron pair only) (!It always contains hydroxide) (!It must be fully ionized)
What does a larger K_a usually indicate for comparable acids in the same solvent? (A stronger acid) (!A weaker acid) (!A lower equilibrium concentration of products) (!A stronger conjugate base)
At 25 degrees Celsius, what is the approximate value of K_w in dilute aqueous solution? (1 times 10 to the minus 14) (!1 times 10 to the minus 7) (!7) (!14)
Which relationship applies to a conjugate acid-base pair at 25 degrees Celsius? (K_a times K_b equals K_w) (!K_a plus K_b equals K_w) (!K_a equals K_b for every pair) (!K_a divided by K_b always equals one)
What happens at the half-equivalence point when a weak monoprotic acid is titrated by a strong base? (pH equals pK_a) (!pH must equal seven) (!The acid concentration is zero) (!The buffer capacity is zero)
Which mixture is most directly able to act as an acidic buffer? (A weak acid and its conjugate base) (!A strong acid and a strong base in equal amounts) (!Pure water and sodium chloride) (!A strong acid without its conjugate base)
What does buffer capacity describe? (The amount of added acid or base a buffer can absorb before pH changes substantially) (!The exact pH value of every buffer) (!The colour range of an indicator) (!The speed of a titration)
Why is the equivalence point of a weak acid titrated with strong base usually basic at 25 degrees Celsius? (The conjugate base reacts with water to produce hydroxide) (!The strong base is always in excess at equivalence) (!The weak acid becomes a strong acid) (!Water stops self-ionizing)
Which statement correctly distinguishes acid strength from concentration? (Strength concerns ionization while concentration concerns amount per volume) (!Strength and concentration always mean the same thing) (!Only strong acids can be concentrated) (!Weak acids always have high pH)
When is a small-x approximation most defensible in a weak-acid calculation? (When the calculated ionization is only a small fraction of the initial concentration) (!Whenever the initial concentration is exactly one molar) (!Whenever pH is below seven) (!Whenever the acid contains one proton)
Memory Game
| Conjugate base | Species formed when an acid donates a proton |
| Hydronium | H₃O⁺ ion produced when water accepts a proton |
| Buffer capacity | Measure of how much added acid or base can be resisted before a substantial pH change |
| Equivalence point | Stoichiometric point in a titration where chemically equivalent amounts have reacted |
| Amphiprotic | Able to donate or accept a proton |
| Common-ion effect | Suppression of ionization caused by adding an ion already present in the equilibrium |
Drag and Drop
| Match the correct terms. | Topic |
|---|---|
| Proton donor | Brønsted–Lowry acid |
| Proton acceptor | Brønsted–Lowry base |
| Weak acid plus conjugate base | Buffer system |
| Stoichiometric neutralization point | Equivalence point |
| Negative logarithm of acid dissociation constant | pK_a |
...
Crossword Puzzle
| Buffer | What solution resists a large pH change after small acid or base additions? |
| Hydronium | What ion is commonly written as H₃O⁺? |
| Equilibrium | What dynamic state has equal forward and reverse reaction rates? |
| Indicator | What weak acid or base can signal pH by a colour change? |
| Amphiprotic | What word describes a species that can both donate and accept a proton? |
| Titration | What analytical method gradually adds a known solution to determine an unknown amount? |
LearningApps
Cloze Text
Open-Ended Tasks
Easy
- pH Infographic: Create a one-page infographic that explains the logarithmic pH scale, includes at least four everyday examples from reliable sources, and clearly distinguishes acidic, neutral, and basic conditions.
- Conjugate Pair Cards: Design a set of cards showing at least six conjugate acid-base pairs and use arrows to show which member gains or loses a proton.
- Indicator Demonstration: With teacher-approved household materials, produce a short photo sequence or video showing how a safe indicator changes across acidic and basic samples, and explain that colour gives a range rather than an exact pH.
- Laboratory Interview: Interview a chemistry teacher, laboratory technician, or other qualified practitioner about how pH is measured accurately and summarize three sources of experimental error.
Standard
- Buffer Investigation: Compare the pH change of a teacher-approved buffer with that of water after small controlled additions of dilute acid or base, graph your results, and explain the difference using equilibrium.
- Titration Curve Project: Use supervised experimental data or a trusted simulation to create a pH-versus-volume graph, label its major regions, and identify the equivalence point.
- pK_a Identification: Analyze a weak-acid titration data set, estimate the pK_a from the half-equivalence point, and explain why the method works.
- Water-Quality Visit: Visit a school laboratory, water-treatment facility, environmental monitoring site, or a verified virtual tour and document how pH and buffering are relevant to water quality.
Advanced
- Exact-versus-Approximate Model: Build a spreadsheet or small program that solves a weak-acid equilibrium both with the quadratic equation and the small-x approximation, then map where the approximation begins to fail.
- Polyprotic Species Study: Choose a diprotic or triprotic acid system, research reliable pK_a values, and create a diagram showing which protonation state dominates across different pH regions.
- Indicator Selection Challenge: Compare several hypothetical titration curves and justify the best indicator transition range for each, including cases where a pH meter would be preferable.
- Research Video: Produce a three-to-five-minute evidence-based video explaining one real system such as carbonate chemistry, food acidity, industrial pH control, or physiological buffering, and distinguish chemical equilibrium from broader system regulation.
Learning Assessment
- Equilibrium Reasoning: Given two proton-transfer reactions and relevant pK_a data, predict the favored direction of each equilibrium and justify your prediction quantitatively.
- Buffer Design: Design a buffer for a specified target pH, choose an appropriate conjugate pair, calculate the required ratio, and explain how concentration affects capacity.
- Titration Analysis: Interpret an unfamiliar titration curve, identify the likely acid-base combination, locate buffer and equivalence regions, and justify a suitable indicator.
- Approximation Validity: Compare an exact weak-acid calculation with a small-x approximation and decide whether the approximation is acceptable using a stated criterion.
- Environmental Transfer: Explain why two lakes with the same measured pH could respond very differently to acid input, using buffer capacity and equilibrium ideas.
Evidence of Learning
- Knowledge: You can explain conjugate pairs, K_a, K_b, K_w, pH, pOH, buffers, titration regions, and the difference between strength and concentration.
- Skills: You can write equilibrium expressions, solve weak-acid and weak-base problems, test approximations, calculate buffer pH, analyze titration data, and communicate uncertainty.
- Products: You can produce graphs, equilibrium models, laboratory records, infographics, calculation reports, and short scientific presentations or videos.
- Transfer: You can apply acid-base equilibrium reasoning to unfamiliar biological, environmental, analytical, and industrial contexts and state the limitations of your model.
OERs on the Topic
For further open study, explore Acid dissociation constant, Buffer solution, Self-ionization of water, Acid–base titration, and Chemical equilibrium. Chemistry LibreTexts also provides openly accessible explanations and worked examples on buffer chemistry and the Henderson–Hasselbalch approximation.
Linked Learning Areas
