Acids and Bases: Mastering Equilibrium in Aqueous Solutions (9620 Physical Chemistry A2)
Hello future chemists! Welcome to the fascinating world of Acids and Bases. This chapter is vital because these concepts govern everything from industrial processes and drug manufacturing to the pH of your blood and the acidity of rainwater.
Don't worry if the calculations seem intimidating—we'll break down the logarithmic pH scale, the equilibrium constants \(K_w\) and \(K_a\), and titration curves into clear, manageable steps. Let's dive in and master this essential section of Physical Chemistry!
3.1.10.1 The Brønsted-Lowry Theory: Defining Acids and Bases
The core definitions we use at A-level focus on proton transfer. A proton in chemistry is simply a hydrogen ion, \(\text{H}^+\).
- Acid: A substance that is a proton donor.
- Base: A substance that is a proton acceptor.
Analogy: Imagine an acid has a proton (a basketball) it wants to give away. A base is waiting patiently to catch (accept) that basketball.
Acid-base reactions are essentially acid-base equilibria involving the transfer of protons in aqueous solution. For example, when hydrochloric acid reacts with water:
\( \text{HCl} + \text{H}_2\text{O} \rightarrow \text{H}_3\text{O}^+ + \text{Cl}^- \)
In this reaction, HCl donated a proton to become \(\text{Cl}^-\) (its conjugate base), and \(\text{H}_2\text{O}\) accepted a proton to become \(\text{H}_3\text{O}^+\) (the hydronium ion, which we usually just represent as \(\text{H}^+\)).
Key Takeaway
Acids give away \(\text{H}^+\); bases accept \(\text{H}^+\). All acid-base reactions involve proton transfer.
3.1.10.2 Measuring Acidity: The pH Scale
The concentration of hydrogen ions (\([\text{H}^+]\)) in solution can vary over an enormous range. To make these numbers easier to handle, chemists use the logarithmic pH scale.
Definition of pH
pH is the measure of hydrogen ion concentration in a solution.
$$ \text{pH} = -\log_{10}[\text{H}^+] $$
Conversely, if you know the pH and want the concentration:
$$ [\text{H}^+] = 10^{-\text{pH}} $$
Strong Acids vs. Weak Acids
This section focuses primarily on strong acids. A strong acid (like HCl or \(\text{HNO}_3\)) dissociates completely in water.
If you have a 0.10 mol \(\text{dm}^{-3}\) solution of HCl, then because it fully dissociates, the concentration of \(\text{H}^+\) ions is also 0.10 mol \(\text{dm}^{-3}\).
Step-by-step calculation for a Strong Acid:
- Determine the concentration of the strong monoprotic acid, \([\text{Acid}]\).
- Assume full dissociation: \([\text{H}^+] = [\text{Acid}]\).
- Calculate pH using \(\text{pH} = -\log_{10}[\text{H}^+]\).
Example: What is the pH of 0.005 mol \(\text{dm}^{-3}\) \(\text{HNO}_3\)?
\([\text{H}^+] = 0.005 \text{ mol dm}^{-3}\)
\(\text{pH} = -\log_{10}(0.005) = 2.30\)
Quick Review: Logarithms
Don't worry about the mathematical origins! Just remember:
- A decrease of 1 on the pH scale means a 10-fold increase in \([\text{H}^+]\). (e.g., pH 3 is ten times more acidic than pH 4).
- The negative sign in the pH equation means that as \([\text{H}^+]\) increases, the pH value decreases (more acidic).
3.1.10.3 The Ionic Product of Water, \(K_w\)
Water is not just a passive solvent; it undergoes a slight reversible dissociation (auto-ionisation):
$$ \text{H}_2\text{O} \rightleftharpoons \text{H}^+ + \text{OH}^- $$
The equilibrium constant for this dissociation is called the ionic product of water, \(K_w\). Since the concentration of water is effectively constant, we include it in the constant:
$$ K_w = [\text{H}^+][\text{OH}^-] $$
- At the standard temperature of 298 K (\(25^\circ \text{C}\)), \(K_w = 1.00 \times 10^{-14} \text{ mol}^2 \text{dm}^{-6}\).
- In pure water, \([\text{H}^+] = [\text{OH}^-]\). Therefore, in neutral water at 298 K, \([\text{H}^+] = \sqrt{1.00 \times 10^{-14}} = 1.00 \times 10^{-7} \text{ mol dm}^{-3}\), giving a pH of 7.00.
- Important Note: The value of \(K_w\) varies with temperature. As temperature increases, the dissociation is favoured (it's an endothermic process), so \(K_w\) increases, and the pH of neutral water decreases (it remains neutral, but the concentration of ions increases).
Calculating the pH of Strong Bases
Strong bases (like NaOH or KOH) fully dissociate to produce hydroxide ions, \(\text{OH}^-\). We use \(K_w\) to find the pH.
Step-by-step calculation for a Strong Base:
- Determine the concentration of the base, \([\text{Base}]\).
- Assume full dissociation: \([\text{OH}^-] = [\text{Base}]\).
- Use \(K_w\) to find the hydrogen ion concentration: \( [\text{H}^+] = \frac{K_w}{[\text{OH}^-]} \). (Remember to use \(K_w = 1.00 \times 10^{-14}\) unless a different temperature is specified).
- Calculate pH using \(\text{pH} = -\log_{10}[\text{H}^+]\).
Example: What is the pH of 0.010 mol \(\text{dm}^{-3}\) NaOH at 298 K?
\([\text{OH}^-] = 0.010 \text{ mol dm}^{-3}\)
\([\text{H}^+] = \frac{1.00 \times 10^{-14}}{0.010} = 1.00 \times 10^{-12} \text{ mol dm}^{-3}\)
\(\text{pH} = -\log_{10}(1.00 \times 10^{-12}) = 12.00\)
Key Takeaway
The ionic product \(K_w\) links \([\text{H}^+]\) and \([\text{OH}^-]\) concentrations. You must use \(K_w\) to calculate the pH of strong bases.
3.1.10.4 Weak Acids and the Dissociation Constant, \(K_a\)
Unlike strong acids, weak acids (like ethanoic acid, \(\text{CH}_3\text{COOH}\)) only partially dissociate in aqueous solution. This means an equilibrium is established.
$$ \text{HA} \rightleftharpoons \text{H}^+ + \text{A}^- $$
The Acid Dissociation Constant, \(K_a\)
The equilibrium constant for this dissociation is called \(K_a\):
$$ K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} $$
- The larger the value of \(K_a\), the stronger the acid (more dissociation).
- The syllabus specifies that weak bases also dissociate slightly, though explicit calculations for \(K_b\) are not required.
Using \(pK_a\)
Just like pH, we use a logarithmic scale for \(K_a\):
$$ \text{p}K_a = -\log_{10} K_a $$
- The smaller the value of \(\text{p}K_a\), the stronger the acid.
- You must be able to convert between \(K_a\) and \(\text{p}K_a\) and vice versa.
Calculating the pH of a Weak Acid
To calculate the pH of a weak acid solution (monoprotic), we often make two key assumptions to simplify the calculation:
- The contribution of \(\text{H}^+\) ions from the dissociation of water is negligible.
- Since the acid is weak, the amount that dissociates is very small, so the equilibrium concentration of the undissociated acid, \([\text{HA}]\), is approximately equal to its initial concentration.
- Since the acid is monoprotic and dissociates into a 1:1 ratio, we assume \([\text{H}^+] = [\text{A}^-]\).
Using these assumptions, \(K_a\) simplifies to:
$$ K_a = \frac{[\text{H}^+]^2}{[\text{HA}]} $$
We can rearrange this to find the hydrogen ion concentration:
$$ [\text{H}^+] = \sqrt{K_a \times [\text{HA}]} $$
Once \([\text{H}^+]\) is known, calculate pH using \( \text{pH} = -\log_{10}[\text{H}^+] \).
Common Mistake Alert! Always remember that for strong acids, \([\text{H}^+] = [\text{Acid}]\), but for weak acids, you must use the \(K_a\) expression and the square root calculation.
Key Takeaway
\(K_a\) quantifies how much a weak acid dissociates. A lower \(\text{p}K_a\) means a stronger weak acid.
3.1.10.5 Titrations, pH Curves, and Indicators
Titrations allow us to determine the concentration of an unknown solution by reacting it exactly with a solution of known concentration. Plotting the pH against the volume of titrant added gives a pH curve.
Understanding pH Curves
pH curves have a characteristic 'S' shape, featuring a rapid change in pH around the equivalence point (the point where the acid and base have reacted completely according to the stoichiometric equation).
The syllabus requires you to sketch and explain the shapes of four main types of titration curves:
- Strong Acid vs. Strong Base (e.g., HCl vs. NaOH):
- Starts very low pH (\(\approx 1\)).
- The steep vertical region (equivalence point) is long and spans pH \(\approx 3\) to \(\approx 11\).
- Equivalence point is exactly at pH 7.
- Weak Acid vs. Strong Base (e.g., \(\text{CH}_3\text{COOH}\) vs. NaOH):
- Starts higher pH (\(\approx 3-5\)).
- The curve has a buffer region (a shallow slope) before the equivalence point.
- The steep vertical region is shorter.
- Equivalence point is basic (\(> 7\)).
- Strong Acid vs. Weak Base (e.g., HCl vs. \(\text{NH}_3\)):
- Starts low pH (\(\approx 1\)).
- The curve has a buffer region after the equivalence point.
- The steep vertical region is shorter.
- Equivalence point is acidic (\(< 7\)).
- Weak Acid vs. Weak Base (e.g., \(\text{CH}_3\text{COOH}\) vs. \(\text{NH}_3\)):
- Starts higher pH, ends lower pH (or vice versa).
- No steep vertical region—the pH changes gradually throughout. This makes it impossible to locate the equivalence point accurately with a simple indicator.
Did You Know? The equivalence point for weak acid/strong base titrations is basic because the salt formed (the conjugate base) hydrolyses water, producing \(\text{OH}^-\) ions.
Selecting the Right Indicator
An indicator is a weak acid or weak base that changes colour over a specific pH range. To be effective in a titration, the indicator's colour change must occur entirely within the steep vertical region of the pH curve.
- For Strong/Strong titrations, most indicators (like Methyl Orange or Phenolphthalein) work fine.
- For Weak/Strong titrations, you must choose an indicator carefully:
- Strong Base titrations (e.g., WA vs SB) require an indicator that changes colour in the basic region (e.g., Phenolphthalein, range 8.3–10.0).
- Strong Acid titrations (e.g., SA vs WB) require an indicator that changes colour in the acidic region (e.g., Methyl Orange, range 3.1–4.4).
- For Weak/Weak titrations, indicators are generally unsuitable because there is no sharp pH break.
Key Takeaway
The shape of the pH curve dictates the feasibility of the titration and the choice of indicator. Always match the indicator's colour range to the vertical part of the curve.
3.1.10.6 Buffer Action and Calculations
Imagine you pour a tiny bit of acid into pure water; the pH plummets! A buffer solution is a chemical safety net—it maintains an approximately constant pH even when small amounts of acid or base are added, or upon dilution.
Composition of Buffer Solutions
A buffer system requires two components: a weak partner and its conjugate salt.
- Acidic Buffer: Contains a weak acid and the salt of that weak acid (e.g., Ethanoic acid, \(\text{CH}_3\text{COOH}\), and Sodium ethanoate, \(\text{CH}_3\text{COONa}\)).
- Basic Buffer: Contains a weak base and the salt of that weak base (e.g., Ammonia, \(\text{NH}_3\), and Ammonium chloride, \(\text{NH}_4\text{Cl}\)).
Qualitative Explanation of Buffer Action (Acidic Buffer)
Consider the equilibrium in an acidic buffer (\(\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-\)):
- If a small amount of strong acid (\(\text{H}^+\)) is added: The excess \(\text{H}^+\) is removed by reacting with the abundant conjugate base (\(\text{A}^-\)) from the salt, shifting the equilibrium to the left. The concentration of \(\text{H}^+\) barely changes.
\( \text{H}^+ + \text{A}^- \rightarrow \text{HA} \)
- If a small amount of strong base (\(\text{OH}^-\)) is added: The \(\text{OH}^-\) is removed by reacting with the weak acid (\(\text{HA}\)), shifting the equilibrium to the right.
\( \text{OH}^- + \text{HA} \rightarrow \text{A}^- + \text{H}_2\text{O} \)
Because the added acid or base is converted into harmless, neutral species (\(\text{H}_2\text{O}\)) or very weak species (\(\text{HA}\) or \(\text{A}^-\)), the pH remains stable.
Analogy: Think of the buffer like a chemical sponge. When acid is added, the base component soaks it up. When base is added, the acid component soaks it up.
Calculating the pH of Acidic Buffers
The calculation for an acidic buffer uses the \(K_a\) expression, rearranged to separate the concentrations of the acid and its salt (conjugate base).
Starting with: \( K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]} \)
Rearranged for \([\text{H}^+]\):
$$ [\text{H}^+] = K_a \times \frac{[\text{Acid}]}{[\text{Salt}]} $$
(Where \([\text{Salt}]\) is approximately equal to the concentration of the conjugate base, \([\text{A}^-]\)).
Taking the negative logarithm of both sides gives the famous Henderson-Hasselbalch equation (though you may not be required to name it):
$$ \text{pH} = \text{p}K_a + \log_{10} \frac{[\text{Salt}]}{[\text{Acid}]} $$
Step-by-step for Buffer pH Calculation:
- Identify the weak acid (\([\text{Acid}]\)) and the salt (\([\text{Salt}]\)) concentrations.
- Find \(K_a\) (or calculate it from \(\text{p}K_a\)).
- Use the rearranged \(K_a\) equation to calculate \([\text{H}^+]\).
- Calculate the pH.
Applications: Buffer solutions are essential in biology (maintaining blood pH at 7.4) and industry (controlling fermentation and dyeing processes).
Key Takeaway
Buffers work by having large reservoirs of both the weak acid and its conjugate base. Calculations for acidic buffers rely on the ratio of \([\text{Acid}]\) to \([\text{Salt}]\) combined with \(K_a\).