Welcome to Acids, Bases, and Buffers!
In this chapter, we are going to dive deep into the world of protons (H+ ions). While you might remember acids being "sour" or "corrosive" from earlier years, at A Level, we look at the math and the equilibrium behind them. We will learn how our blood stays at a perfect pH to keep us alive and how to calculate the exact acidity of almost any solution. Don't worry if the math seems a bit heavy at first—we will take it one step at a time!
1. The Brønsted–Lowry Theory
At A Level, we define acids and bases by what they do with protons (\( H^+ \)).
Brønsted–Lowry Acid: A species that donates a proton (\( H^+ \)).
Brønsted–Lowry Base: A species that accepts a proton (\( H^+ \)).
Memory Aid: The "BAD" Mnemonic
Bases Accept, Donate Acids (well, Acids Donate!). Just remember: B.A.A.D.
Conjugate Acid–Base Pairs
In a reaction, when an acid gives away a proton, what's left behind could potentially take that proton back. This creates a "pair."
\( HA + B \rightleftharpoons A^- + BH^+ \)
In this example:
1. \( HA \) is the acid (it gives away \( H^+ \)). Its partner \( A^- \) is the conjugate base.
2. \( B \) is the base (it takes the \( H^+ \)). Its partner \( BH^+ \) is the conjugate acid.
Monobasic, Dibasic, and Tribasic Acids
This simply refers to how many protons one molecule of the acid can donate.
Example: HCl is monobasic (donates 1 \( H^+ \)).
Example: \( H_2SO_4 \) is dibasic (donates 2 \( H^+ \)).
Example: \( H_3PO_4 \) is tribasic (donates 3 \( H^+ \)).
Quick Review: An acid is a proton donor. Every acid has a conjugate base partner. Monobasic acids donate one proton per molecule.
2. The pH Scale and Strong Acids
pH is a way of measuring the concentration of \( H^+ \) ions. Because these concentrations are usually tiny (like \( 0.00001 \)), we use a logarithmic scale to make the numbers easier to handle.
The Formulas
To find pH: \( pH = -\log[H^+] \)
To find \( [H^+] \): \( [H^+] = 10^{-pH} \)
Calculating pH for Strong Acids
Strong acids (like HCl or \( HNO_3 \)) completely dissociate in water. This means if you have 0.1 mol dm\(^{-3}\) of HCl, you effectively have 0.1 mol dm\(^{-3}\) of \( H^+ \) ions.
Step-by-Step Example: Calculate the pH of 0.05 mol dm\(^{-3}\) \( HNO_3 \).
1. Since it's a strong monobasic acid, \( [H^+] = [HNO_3] = 0.05 \).
2. \( pH = -\log(0.05) \)
3. \( pH = 1.30 \)
Common Mistake: For a strong dibasic acid like \( H_2SO_4 \), remember that \( [H^+] \) will be double the concentration of the acid!
3. The Ionic Product of Water (\( K_w \))
Even pure water dissociates slightly: \( H_2O \rightleftharpoons H^+ + OH^- \).
The equilibrium constant for this is called \( K_w \).
\( K_w = [H^+][OH^-] \)
At 25°C (298K), \( K_w = 1.00 \times 10^{-14} \) mol\(^2\) dm\(^{-6}\).
Calculating pH for Strong Bases
Strong bases like NaOH fully release \( OH^- \) ions. To find the pH, we use \( K_w \) to find the \( [H^+] \) first.
Step-by-Step Example: Find the pH of 0.1 mol dm\(^{-3}\) NaOH.
1. \( [OH^-] = 0.1 \)
2. Use \( K_w \): \( [H^+] = \frac{K_w}{[OH^-]} = \frac{1 \times 10^{-14}}{0.1} = 1 \times 10^{-13} \)
3. \( pH = -\log(1 \times 10^{-13}) = 13 \)
Key Takeaway: pH is a log scale. For strong acids, \( [H^+] \) is basically the acid concentration. For strong bases, use \( K_w \) to bridge the gap between \( OH^- \) and \( H^+ \).
4. Weak Acids and the \( K_a \) Constant
Weak acids (like ethanoic acid, \( CH_3COOH \)) only partially dissociate. Most of the acid stays as molecules, and only a tiny bit turns into ions.
We use the acid dissociation constant, \( K_a \), to measure how weak/strong they are:
\( K_a = \frac{[H^+][A^-]}{[HA]} \)
\( pK_a \): Making the numbers pretty
Just like pH, we use \( pK_a \) to avoid long decimals.
\( pK_a = -\log(K_a) \)
\( K_a = 10^{-pK_a} \)
Crucial Rule: A smaller \( K_a \) (or a larger \( pK_a \)) means the acid is weaker.
Calculating pH of Weak Acids
To make the math easier for weak acids, we use two approximations:
1. We assume \( [H^+] \approx [A^-] \), so the top of our formula becomes \( [H^+]^2 \).
2. We assume the concentration of the acid at equilibrium is the same as it was at the start (because so little reacts).
Formula: \( K_a = \frac{[H^+]^2}{[HA]} \)
Don't worry if this seems tricky! Just remember you need to rearrange it to find \( [H^+] \):
\( [H^+] = \sqrt{K_a \times [HA]} \)
When do these approximations fail?
If the acid is "too strong" for a weak acid (high \( K_a \)) or very dilute, the amount that dissociates is significant, and our "initial concentration = equilibrium concentration" assumption breaks down.
Summary: Weak acids use \( K_a \). Higher \( pK_a \) = Weaker acid. We use approximations to simplify the math into \( [H^+] = \sqrt{K_a \times [HA]} \).
5. Buffer Solutions
A buffer is a chemical "shock absorber." It minimizes pH changes when small amounts of acid or base are added.
How to make a buffer
1. Weak acid + its salt: e.g., Ethanoic acid and Sodium ethanoate.
2. Partial Neutralisation: Adding a small amount of strong base to an excess of weak acid.
How a Buffer Works
Imagine the equilibrium: \( CH_3COOH \rightleftharpoons CH_3COO^- + H^+ \)
- Add \( H^+ \): The large reservoir of conjugate base (\( CH_3COO^- \)) reacts with the extra \( H^+ \), shifting the equilibrium to the left.
- Add \( OH^- \): The \( OH^- \) reacts with \( H^+ \) to make water. The reservoir of weak acid (\( CH_3COOH \)) dissociates to replace the lost \( H^+ \), shifting equilibrium to the right.
Calculating Buffer pH
You cannot use the "weak acid approximation" here because you have added extra salt!
Formula: \( [H^+] = K_a \times \frac{[HA]}{[A^-]} \)
Real-World Example: Blood pH
Your blood must stay between pH 7.35 and 7.45. It uses the carbonic acid–hydrogencarbonate buffer system:
\( H_2CO_3 \rightleftharpoons H^+ + HCO_3^- \)
Key Takeaway: Buffers contain a weak acid and its conjugate base. They shift equilibrium to neutralize added \( H^+ \) or \( OH^- \).
6. Titration Curves and Indicators
A titration curve shows how pH changes as you add an alkali to an acid.
The Four Shapes
1. Strong Acid / Strong Base: pH starts at 1, ends at 13. Large vertical section.
2. Weak Acid / Strong Base: pH starts higher (approx 3). Vertical section is shorter and above pH 7.
3. Strong Acid / Weak Base: pH ends lower (approx 10-11). Vertical section is below pH 7.
4. Weak Acid / Weak Base: No clear vertical section. Very hard to titrate!
Equivalence Point vs. End Point
- Equivalence Point: The volume where the acid and base have reacted in the exact molar ratio (the center of the vertical section).
- End Point: When the indicator changes color.
Choosing an Indicator
Indicators are actually weak acids themselves that have a different color than their conjugate base partner (\( HIn \rightleftharpoons H^+ + In^- \)).
For an indicator to be useful, its color change range must fall within the vertical section of the titration curve.
Did you know? Methyl orange is great for strong acid/weak base titrations because it changes color in the acidic range (pH 3.1–4.4), which matches that curve's vertical section!
Quick Review: Match the indicator's range to the vertical part of your curve. Equivalence point is the theoretical neutralisation; End point is the visible color change.
7. Final Tips for Success
- Check your units: Concentration is usually mol dm\(^{-3}\).
- pH Meter: In practical work, use a pH meter for more accuracy than indicator paper. Always calibrate it first using "buffer tablets" of known pH.
- Temperature: Remember that \( K_w \) and \( K_a \) change with temperature. If the temperature isn't 25°C, the neutral pH might not be exactly 7.00!
You've got this! Acids and bases are all about tracking where the protons go. Keep practicing the rearrangements of the \( K_a \) and \( pH \) formulas, and it will become second nature.