Chemistry | Acid-base Equilibria

🧪 Welcome to Acid-Base Equilibria!

Hello future chemist! This chapter, Acid-Base Equilibria, might seem a bit abstract, but it’s crucial for understanding how reactions work in solution—from your stomach acid to the delicate balance of pH in your blood.
Don't worry if terms like \(K_a\) and buffers sound intimidating right now. We're going to break everything down into easy steps. By the end, you'll be a master of pH calculations and buffer chemistry!

1. Defining Acids and Bases: The Brønsted-Lowry Theory

While you might have learned simple definitions before, the modern definition used in A-Level Chemistry (and almost always in equilibria) is the Brønsted-Lowry Theory.

1.1 Protons, Donors, and Acceptors

In this theory, an acid-base reaction is a simple transfer of a proton (\(H^+\)). Since a hydrogen atom is just one proton and one electron, an \(H^+\) ion is often referred to simply as a proton.

• Brønsted-Lowry Acid: A species that is a proton donor.
• Brønsted-Lowry Base: A species that is a proton acceptor.

Memory Aid: Acid DONOR, Base ACCEPTS. A for Acid, D for Donor (alphabetically close).

1.2 Conjugate Acid-Base Pairs

When an acid donates a proton, the species it forms is now capable of accepting a proton back. This creates a reversible relationship called a conjugate pair.

\(\text{Acid}_1 + \text{Base}_2 \rightleftharpoons \text{Conjugate Base}_1 + \text{Conjugate Acid}_2\)

Example: Hydrochloric acid reacting with water.

\(HCl(aq) + H_2O(l) \longrightarrow Cl^-(aq) + H_3O^+(aq)\)

• Acid (\(HCl\)): Donates \(H^+\), forming its Conjugate Base (\(Cl^-\)).
• Base (\(H_2O\)): Accepts \(H^+\), forming its Conjugate Acid (\(H_3O^+\), the hydronium ion).

Did you know? Water (\(H_2O\)) can act as both an acid and a base (it’s amphiprotic). It can donate a proton (acting as an acid) or accept one (acting as a base).

2. Strong vs. Weak Acids and Bases

The terms 'strong' and 'weak' do not refer to concentration; they refer to the extent of ionisation in water.

2.1 Strong Acids and Bases

Strong Acid: Dissociates completely in water.
Example: \(HCl(aq) \longrightarrow H^+(aq) + Cl^-(aq)\)

Because strong acids dissociate 100%, the concentration of hydrogen ions (\([H^+]\)) is equal to the initial concentration of the acid.

• Examples of Strong Acids: HCl, HBr, HI, \(HNO_3\), \(H_2SO_4\) (only the first proton).
• Examples of Strong Bases: Group 1 Hydroxides (NaOH, KOH) and some Group 2 Hydroxides.

2.2 Weak Acids and Bases

Weak Acid: Dissociates partially in water, setting up an equilibrium.
Example: Ethanoic acid (acetic acid):

\(CH_3COOH(aq) \rightleftharpoons H^+(aq) + CH_3COO^-(aq)\)

In a weak acid solution, most of the original acid molecules (\(CH_3COOH\)) remain undissociated. This is why we use the equilibrium arrow (\(\rightleftharpoons\)).

Common Mistake Alert: Students often confuse "dilute strong acid" with "concentrated weak acid." They are fundamentally different. A strong acid is always strong, regardless of dilution.

3. The Ionisation of Water, pH, and \(K_w\)

3.1 The pH Scale

The pH scale is a logarithmic scale used to measure the concentration of hydrogen ions (\([H^+]\)) in a solution.

The definition of pH is:

\(\text{pH} = -\log_{10}[H^+]\)

Conversely, if you know the pH, you can find the concentration:

\([H^+] = 10^{-\text{pH}}\)

3.2 The Ion Product of Water (\(K_w\))

Even pure water undergoes a very slight ionisation:

\(H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)\)

The equilibrium constant for this reaction is called the Ion Product of Water, \(K_w\).

\(K_w = [H^+][OH^-]\)

• At \(298\ K\) (25°C), the standard value for \(K_w\) is \(1.00 \times 10^{-14} \text{ mol}^2\text{ dm}^{-6}\).
• Since pure water is neutral, \([H^+] = [OH^-]\). Therefore, \([H^+] = \sqrt{K_w}\), which is \(1.00 \times 10^{-7}\text{ mol dm}^{-3}\).
• This gives pure water a pH of 7.00 at 25°C.

Important Note: The value of \(K_w\) changes with temperature. If the temperature increases, \(K_w\) increases (the reaction is endothermic), and the pH of neutral water drops below 7. However, the water remains neutral because \([H^+]\) still equals \([OH^-]\).

3.3 Calculating the pH of Strong Acids and Bases

Strong Acid Calculation

1. Determine \([H^+]\) directly from the acid concentration (due to 100% dissociation).
2. Use \(\text{pH} = -\log_{10}[H^+]\).
Example: 0.010 mol dm\(^{-3}\) HCl. \([H^+] = 0.010\). \(\text{pH} = -\log(0.010) = 2.00\).

Strong Base Calculation (The Two-Step Process)

Calculating the pH of a strong base (like NaOH) requires using \(K_w\):

1. Find the concentration of hydroxide ions, \([OH^-]\). (For NaOH, \([OH^-] = [\text{NaOH}]\)).
2. Use \(K_w = [H^+][OH^-]\) to calculate \([H^+]\). \([H^+] = \frac{K_w}{[OH^-]}\)
3. Calculate the pH using the new \([H^+]\) value.

Encouragement: If you struggle with rearranging equations, remember this relationship: \(K_w\) is always \(1.00 \times 10^{-14}\) at 25°C. Just plug in the known concentration and solve for the unknown.

4. Weak Acids and the Equilibrium Constant (\(K_a\))

Since weak acids set up an equilibrium, we need an equilibrium constant to describe their degree of dissociation. This constant is the Acid Dissociation Constant, \(K_a\).

4.1 The \(K_a\) Expression and \(\text{p}K_a\)

For a general weak acid, \(HA\):

\(HA(aq) \rightleftharpoons H^+(aq) + A^-(aq)\)

The \(K_a\) expression is:

\(K_a = \frac{[H^+][A^-]}{[HA]}\)

• A larger \(K_a\) means a stronger weak acid (more dissociation).
• A smaller \(K_a\) means a weaker weak acid (less dissociation).

Because \(K_a\) values are often very small, chemists use the logarithmic scale \(\text{p}K_a\) for simplicity:

\(\text{p}K_a = -\log_{10}K_a\)

Interpretation: A low \(\text{p}K_a\) value indicates a strong acid (like a low pH indicates a high \([H^+]\)).

4.2 Calculating pH of Weak Acids

When calculating the pH of a weak acid solution, we make two important simplifying assumptions:

1. Assumption 1: Since the dissociation is very small, we assume that the equilibrium concentration of the unionised acid, \([HA]\), is approximately the same as the initial concentration: \([HA]_{\text{eq}} \approx [HA]_{\text{initial}}\).
2. Assumption 2: We assume that the only source of \(H^+\) ions is the acid itself (ignoring the tiny contribution from water). Therefore, \([H^+] \approx [A^-]\).

Using these assumptions, the \(K_a\) expression simplifies to:

\(K_a \approx \frac{[H^+]^2}{[HA]_{\text{initial}}}\)

We can then rearrange this to solve for \([H^+]\):

\([H^+] = \sqrt{K_a \times [HA]_{\text{initial}}}\)

Step-by-step for Weak Acid pH:

1. Write down the \(K_a\) expression.
2. Apply the assumptions to get \([H^+] = \sqrt{K_a \times [HA]}\).
3. Calculate \([H^+]\).
4. Calculate pH using \(\text{pH} = -\log_{10}[H^+]\).

5. Buffer Solutions: Controlling pH

Biological systems (like your blood) and many industrial processes rely on maintaining a stable pH, even if small amounts of acid or base are added. This is the job of a buffer solution.

5.1 What is a Buffer Solution?

A buffer solution is a system that resists changes in pH when small amounts of acid or base are added.

There are two main types of buffer:

1. Acidic Buffer: Made from a weak acid and its salt (which provides the conjugate base).
   Example: Ethanoic acid (\(CH_3COOH\)) and Sodium ethanoate (\(CH_3COONa\)).
2. Basic Buffer: Made from a weak base and its salt (which provides the conjugate acid).
   Example: Ammonia (\(NH_3\)) and Ammonium chloride (\(NH_4Cl\)).

5.2 The Mechanism of Buffer Action (The pH Shock Absorber)

Consider an acidic buffer containing the equilibrium:

\(HA(aq) \rightleftharpoons H^+(aq) + A^-(aq)\) (The conjugate base, \(A^-\), is present in high concentration because it comes from the fully dissociated salt.)

A. Response to Added Acid (\(H^+\)):

• The high concentration of the conjugate base (\(A^-\)) reacts with the added \(H^+\).
• The equilibrium shifts to the left to use up the added \(H^+\).
• \([H^+]\) returns almost to its original value, so the pH hardly changes.

\(H^+ + A^- \longrightarrow HA\)

B. Response to Added Base (\(OH^-\)):

• The added \(OH^-\) reacts with the small amount of \(H^+\) already present, forming water.
• This reduces \([H^+]\), causing the weak acid (\(HA\)) to dissociate further (shift to the right) to replace the lost \(H^+\).
• Again, \([H^+]\) remains nearly constant.

\(OH^- + HA \longrightarrow A^- + H_2O\)

5.3 Calculating the pH of a Buffer

Buffer pH calculations use the \(K_a\) expression, but modified to account for the high concentration of the salt/conjugate base.

Starting with the \(K_a\) expression: \(K_a = \frac{[H^+][A^-]}{[HA]}\)

Rearranging to find \([H^+]\):

\([H^+] = K_a \times \frac{[HA]}{[A^-]}\)

Since the salt is fully dissociated, \([A^-]\) is equal to the concentration of the salt added. \([HA]\) is the initial concentration of the weak acid.

The Henderson-Hasselbalch Equation (or using the log version):

\(\text{pH} = \text{p}K_a + \log_{10} \frac{[\text{Salt}]}{[\text{Acid}]}\)

Maximum Buffering Capacity: A buffer works most effectively when the concentration of the weak acid equals the concentration of its conjugate base (i.e., \([\text{Acid}] = [\text{Salt}]\)). In this case, \(\log_{10}(1) = 0\), so \(\text{pH} = \text{p}K_a\).

6. Titration Curves and Indicators

A titration curve plots the pH of a solution against the volume of titrant (the solution added from the burette). These curves are essential for understanding acid-base reactions and selecting the correct analytical tool.

6.1 Interpreting Titration Curves

There are four main types of curves you need to recognise:

1. Strong Acid / Strong Base (e.g., HCl / NaOH):
   • Starts at a very low pH (e.g., pH 1).
   • The equivalence point (the point where moles of acid = moles of base) is exactly at pH 7.0.
   • The vertical steep change is very long (pH 3 to 11).
2. Weak Acid / Strong Base (e.g., \(CH_3COOH\) / NaOH):
   • Starts at a higher pH (e.g., pH 3).
   • A buffer region is seen before the equivalence point.
   • The equivalence point is above pH 7.0 (basic). This is because the strong base creates the salt of the weak acid, which hydrolyses the water.
3. Strong Acid / Weak Base (e.g., HCl / \(NH_3\)):
   • Starts at a low pH (e.g., pH 1).
   • The equivalence point is below pH 7.0 (acidic). This is because the strong acid creates the salt of the weak base, which hydrolyses the water.
4. Weak Acid / Weak Base:
   • Rarely used in analysis.
   • There is no sharp vertical change, making the equivalence point difficult to identify.

The Equivalence Point vs. The End Point:
The Equivalence Point is the theoretical point where neutralisation is complete (moles are equal).
The End Point is the point where the indicator changes colour. We choose indicators so the end point is as close as possible to the equivalence point.

6.2 Choosing the Correct Indicator

An indicator is itself a weak acid or weak base where the acid form (\(HIn\)) has a different colour from the base form (\(In^-\)).

For an indicator to work effectively, its colour change interval (range) must fall entirely within the steep vertical region of the titration curve. This ensures that the colour change is sudden and sharp, exactly when the equivalence point is reached.

Titration Type	Equivalence Point pH	Suitable Indicator	Indicator pH Range
Strong Acid / Strong Base	pH 7	Methyl Orange or Phenolphthalein	(3.1–4.4) or (8.3–10.0)
Weak Acid / Strong Base	pH > 7 (Basic)	Phenolphthalein	(8.3–10.0)
Strong Acid / Weak Base	pH < 7 (Acidic)	Methyl Orange	(3.1–4.4)

Analogy: Choosing the right indicator is like setting a trap door. You want the trap door (the indicator's colour change range) to be positioned exactly across the cliff edge (the steep pH change). If the cliff is pH 3 to 11, both indicators work. If the cliff is small (pH 7 to 10), only phenolphthalein will work effectively.