What you'll learn

By the end of these study notes, you will be able to:

• Identify Brønsted–Lowry acids, bases, and conjugate acid–base pairs in equilibria.
• Calculate the pH of strong acids, strong bases, weak acids, and buffer solutions.
• Explain buffer action qualitatively and quantitatively, including the carbonic acid–hydrogencarbonate blood buffer system.
• Sketch and interpret pH titration curves, choose suitable indicators, and describe pH meter calibration procedures.

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1. Brønsted–Lowry Acids, Bases and Conjugate Pairs

In your earlier studies, you defined an acid simply as a substance that releases hydrogen ions, $H^{+}$, in solution. At A-Level, we use a more refined model called the Brønsted–Lowry theory to describe acid–base behaviour in aqueous systems.

Conjugate Acid–Base Pairs

When an acid loses a proton, it forms its conjugate base. When a base gains a proton, it forms its conjugate acid. These two species, which differ by exactly one proton ($H^{+}$), are called a conjugate acid–base pair.

Consider the equilibrium between ethanoic acid and water:

$${CH}_{3}COOH(aq)+H_{2}O(l)\rightleftharpoons {CH}_3{COO}^{-}(aq)+H_3{O}^{+}(aq)$$

In the forward reaction:

• ${CH}_{3}COOH$ donates a proton to $H_{2}O$. Therefore, ${CH}_{3}COOH$ is Acid 1, and ${CH}_3{COO}^{-}$ is its Conjugate Base 1.
• $H_{2}O$ accepts a proton from ${CH}_{3}COOH$. Therefore, $H_{2}O$ is Base 2, and $H_3{O}^{+}$ (the hydronium ion) is its Conjugate Acid 2.

Acid Classification: Monobasic, Dibasic, and Tribasic

Acids are classified by the number of protons they can donate per molecule:

• Monobasic acids can donate only one proton per molecule (e.g., $HCl$, ${HNO}_3$, ${CH}_{3}COOH$).
• Dibasic acids can donate two protons per molecule in two successive steps (e.g., $H_2{SO}_4$).
• Tribasic acids can donate three protons per molecule in three successive steps (e.g., $H_3{PO}_4$).

Reactions of Acids

The reactions of acids with metals and bases depend entirely on the active role of the hydrogen ion, $H^{+}(aq)$. You must be able to write full balanced equations and simplified ionic equations for these reactions.

1. Acid + Reactive Metal $\to$ Salt + Hydrogen

$$Mg(s)+2HCl(aq)\to {MgCl}_2(aq)+H_2(g)$$

*Ionic Equation:*

$$Mg(s)+2H^{+}(aq)\to {Mg}^{2+}(aq)+H_2(g)$$

2. Acid + Alkali $\to$ Salt + Water

$$NaOH(aq)+{HNO}_3(aq)\to {NaNO}_3(aq)+H_{2}O(l)$$

*Ionic Equation:*

$${OH}^{-}(aq)+H^{+}(aq)\to H_{2}O(l)$$

3. Acid + Metal Oxide $\to$ Salt + Water

$$CuO(s)+2HCl(aq)\to {CuCl}_2(aq)+H_{2}O(l)$$

*Ionic Equation:*

$$CuO(s)+2H^{+}(aq)\to {Cu}^{2+}(aq)+H_{2}O(l)$$

4. Acid + Carbonate $\to$ Salt + Water + Carbon Dioxide

$${Na}_2{CO}_3(aq)+2HCl(aq)\to 2NaCl(aq)+H_{2}O(l)+{CO}_2(g)$$

*Ionic Equation:*

$${CO}_3^{2-}(aq)+2H^{+}(aq)\to H_{2}O(l)+{CO}_2(g)$$

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2. The pH Scale and Strong Acids and Bases

Because the concentration of hydrogen ions, $[H^{+}(aq)]$, in aqueous solutions can span many orders of magnitude (from over 1.0 mol dm⁻³ to less than $10^{-14}{mol\; dm}^{-3}$), the Danish biochemist Søren Sørensen developed the pH scale as a convenient way to compare acidity.

Strong Monobasic Acids

A strong acid fully dissociates in aqueous solution. For a strong monobasic acid, $HA$, the acid dissociation is complete:

$$HA(aq)\to H^{+}(aq)+A^{-}(aq)$$

Therefore, the concentration of hydrogen ions is equal to the initial concentration of the acid:

$$[H^{+}(aq)]=[HA]$$

The Ionic Product of Water, $K_w$

Water molecules dissociate slightly to establish a dynamic equilibrium:

$$H_{2}O(l)\rightleftharpoons H^{+}(aq)+{OH}^{-}(aq)$$

The equilibrium constant for this reaction can be written as:

$$K_c=\frac{[H^{+}][{OH}^{-}]}{[H_{2}O]}$$

Because water is in such a vast excess, its concentration $[H_{2}O]$ is effectively constant ($55.6{mol\; dm}^{-3}$). We can multiply $K_c$ by $[H_{2}O]$ to define a new constant, the ionic product of water, $K_w$:

• In pure water (or any neutral solution), $[H^{+}]=[{OH}^{-}]$. Therefore:

$$K_w=[H^{+}{]}^2⟹[H^{+}]=\sqrt{K_w}=1.00\times 10^{-7}{mol\; dm}^{-3}$$

This gives pure water a pH of 7.00 at 298 K.

Strong Bases

A strong base fully dissociates in aqueous solution to release ${OH}^{-}$ ions (e.g., $NaOH$, $KOH$). To find the pH of a strong base:

1. Identify the hydroxide ion concentration, $[{OH}^{-}]$, from the base concentration.
2. Use $K_w$ to calculate $[H^{+}]$.
3. Convert $[H^{+}]$ into pH.

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3. Weak Acids and the Acid Dissociation Constant ($K_a$)

Unlike strong acids, weak acids only partially dissociate in aqueous solution:

$$HA(aq)\rightleftharpoons H^{+}(aq)+A^{-}(aq)$$

We quantify the position of this equilibrium using the acid dissociation constant, $K_a$.

Weak Acid pH Calculations and Approximations

To calculate the pH of a weak acid, we make two simplifying approximations to avoid solving a quadratic equation:

1. Approximation 1: The dissociation of water is negligible, so all $H^{+}$ ions come solely from the dissociation of the weak acid $HA$. Therefore:

$$[H^{+}(aq)]\approx [A^{-}(aq)]$$

This simplifies the numerator of the expression:

$$K_a\approx \frac{[H^{+}{]}^2}{[HA{]}_{eq}}$$

2. Approximation 2: The extent of dissociation is very small, so the equilibrium concentration of the undissociated acid is virtually identical to its initial concentration:

$$[HA{]}_{eq}\approx [HA{]}_{initial}$$

This gives the simplified expression:

$$K_a\approx \frac{[H^{+}{]}^2}{[HA{]}_{initial}}$$

We can rearrange this formula to find $[H^{+}]$ directly:

$$[H^{+}]\approx \sqrt{K_a\times [HA{]}_{initial}}$$

When Do These Approximations Fail?

As an A-Level chemist, you must understand the limitations of these approximations:

• Approximation 1 fails in extremely dilute solutions (e.g., concentrations below $10^{-6}{mol\; dm}^{-3}$) because the dissociation of water becomes significant and contributes a non-negligible concentration of $H^{+}$ ions.
• Approximation 2 fails if the weak acid is relatively "strong" (having a high $K_a$ value) or highly dilute. Under these conditions, a significant fraction of $HA$ dissociates, making the assumption $[HA{]}_{eq}\approx [HA{]}_{initial}$ invalid. Typically, if the dissociation is greater than 5%, you would need to use a quadratic equation to obtain an accurate pH.

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4. Buffer Solutions

How Buffers Are Made

An acidic buffer solution contains a mixture of a weak acid ($HA$) and its conjugate base ($A^{-}$) in high concentrations. There are two chemical routes to prepare one:

1. Direct Method: Mix a weak acid directly with a soluble salt of its conjugate base (e.g., ethanoic acid, ${CH}_{3}COOH$, and sodium ethanoate, ${CH}_{3}COONa$).
2. Partial Neutralisation Method: Mix an excess of a weak acid with a strong alkali (e.g., reacting excess ${CH}_{3}COOH$ with $NaOH$). The alkali completely reacts with some of the weak acid to produce the conjugate base ${CH}_3{COO}^{-}$, leaving a mixture of unreacted weak acid and its newly formed conjugate base.

Explanation of Buffer Action

The conjugate acid–base pair controls the pH by shifting the position of the equilibrium in response to external changes:

$$HA(aq)\rightleftharpoons H^{+}(aq)+A^{-}(aq)$$

• When a small amount of acid ($H^{+}$) is added: The added $H^{+}$ ions react with the conjugate base $A^{-}$ to form the weak acid molecules:

$$A^{-}(aq)+H^{+}(aq)\to HA(aq)$$

The equilibrium shifts to the left, removing the added $H^{+}$ ions and keeping the pH virtually constant.

• When a small amount of alkali (${OH}^{-}$) is added: The added ${OH}^{-}$ ions react with the small concentration of $H^{+}$ ions to form water:

$$H^{+}(aq)+{OH}^{-}(aq)\to H_{2}O(l)$$

To restore the lost $H^{+}$ ions, the weak acid $HA$ dissociates:

$$HA(aq)\to H^{+}(aq)+A^{-}(aq)$$

Overall, the added hydroxide ions are neutralised by the weak acid:

$$HA(aq)+{OH}^{-}(aq)\to A^{-}(aq)+H_{2}O(l)$$

The equilibrium shifts to the right, maintaining a stable pH.

Controlling Blood pH

In human blood plasma, the pH must be maintained precisely between 7.35 and 7.45. This narrow range is controlled by the carbonic acid–hydrogencarbonate buffer system:

$$H_2{CO}_3(aq)\rightleftharpoons H^{+}(aq)+{HCO}_3^{-}(aq)$$

• Carbonic acid, $H_2{CO}_3$, acts as the weak acid (proton donor).
• Hydrogencarbonate, ${HCO}_3^{-}$, acts as the conjugate base (proton acceptor).
• If blood becomes too acidic, the excess $H^{+}$ reacts with ${HCO}_3^{-}$ to form $H_2{CO}_3$. The body converts excess carbonic acid into dissolved carbon dioxide, which is exhaled by the lungs:

$$H_2{CO}_3(aq)\rightleftharpoons H_{2}O(l)+{CO}_2(g)$$

• If blood becomes too alkaline, the carbonic acid dissociates to release more $H^{+}$, neutralising the added base.

Buffer Calculations

To calculate the pH of a buffer, we rearrange the $K_a$ expression:

$$K_a=\frac{[H^{+}][A^{-}]}{[HA]}⟹[H^{+}]=K_a\times \frac{[HA]}{[A^{-}]}$$

Take the negative logarithm of both sides to get the Henderson–Hasselbalch equation (which you can use, but OCR spec calculates via $[H^{+}]$):

$$pH=p{K}_a+\log \left(\frac{[A^{-}]}{[HA]}\right)$$

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5. pH Titration Curves and Indicators

A pH titration curve tracks the pH of an acid as a base is progressively added (or vice versa).

Features of Titration Curves

• Starting pH: Tells you whether the substance in the flask is a strong acid (pH ~ 1), weak acid (pH ~ 3), weak base (pH ~ 11), or strong base (pH ~ 13).
• Buffer Region: For weak acid titrations, the initial rise is shallow because a buffer system ($HA/A^{-}$) forms dynamically as base is added.
• Equivalence Point: The center of the vertical section of the curve, representing the volume of base at which stoichiometric neutralisation is complete.
• Vertical Section: A region of rapid pH change.
  • Strong Acid - Strong Base: Vertical section spans from pH ~ 3 to 11. Equivalence point is exactly at pH 7.0.
  • Weak Acid - Strong Base: Vertical section spans from pH ~ 7 to 11. Equivalence point is $>7$ (typically around pH 8.7).
  • Strong Acid - Weak Base: Vertical section spans from pH ~ 3 to 7. Equivalence point is $<7$ (typically around pH 5.2).
  • Weak Acid - Weak Base: No sharp vertical section is observed. The pH changes gradually throughout.

Theory of Acid–Base Indicators

An indicator is itself a weak acid, which we can represent as $HIn$. It dissociates in aqueous solution to establish an equilibrium where the acid and conjugate base have distinctly different colours:

$$HIn(aq)\rightleftharpoons H^{+}(aq)+{In}^{-}(aq)$$ $$(Colour\; A)(Colour\; B)$$

• When acid ($H^{+}$) is added: The equilibrium shifts to the left. The concentration of $HIn$ increases, and the solution exhibits Colour A.
• When alkali (${OH}^{-}$) is added: The added base reacts with $H^{+}$ to form water. This shifts the equilibrium to the right to replace the lost $H^{+}$. The concentration of ${In}^{-}$ increases, and the solution exhibits Colour B.

Choosing a Suitable Indicator

An indicator changes colour over a specific range called its pH transition interval.

• Methyl Orange (pH range 3.1–4.4) is suitable for titrations with a vertical section in the acidic region (Strong Acid–Strong Base, Strong Acid–Weak Base).
• Phenolphthalein (pH range 8.3–10.0) is suitable for titrations with a vertical section in the alkaline region (Strong Acid–Strong Base, Weak Acid–Strong Base).
• Weak Acid - Weak Base titrations have no sharp vertical section. Consequently, no indicator is suitable for a weak acid–weak base titration, and a pH meter must be used instead.

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6. PAG 11: Calibration and Use of a pH Meter

Using a pH probe connected to a digital meter provides a more precise and continuous measurement of pH than universal indicator paper. However, pH meters must be calibrated before use to ensure accuracy.

Calibration Procedure

1. Rinse the probe thoroughly with deionised water.
2. Calibrate using buffer solutions of known, fixed pH.
   • Dip the probe into a pH 7.00 buffer and adjust the reading on the meter to match.
   • Rinse the probe and repeat this process with a second buffer (e.g., pH 4.00 for acidic titrations, or pH 10.00 for alkaline titrations). This calibration line corrects for systemic instrument drift (creating a calibration curve).
3. Rinse the probe again with deionised water before taking measurements of your test solutions.

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