AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/8/8-1)
Unit 8 · Topic 8.1
8.1 Introduction to Acids and Bases
Even pure water contains a tiny amount of H₃O⁺ and OH⁻, because water molecules transfer protons to each other. Their product is the constant Kw, which is 1.0 × 10⁻¹⁴ at 25 °C, and pH and pOH are log scales that make these tiny concentrations easy to work with.
Key terms
- autoionization of water
- Kw
- pH
- pOH
- hydronium ion (H₃O⁺)
- neutral solution
Water ionizes itself
In pure water, a very small fraction of molecules act as an acid and give a proton (H⁺) to another water molecule, which acts as a base: H₂O(l) + H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq). This is called autoionization.
H₃O⁺ is the hydronium ion. You'll also see it written as H⁺(aq); the exam accepts both, though H₃O⁺ is preferred.
The equilibrium constant is Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. Water is a pure liquid, so it doesn't appear in the expression.
Kw links H₃O⁺ and OH⁻
Kw holds in every aqueous solution, not just pure water. If you know one concentration, you can always find the other: [OH⁻] = Kw / [H₃O⁺].
In pure water the two are equal, so each is √(1.0 × 10⁻¹⁴) = 1.0 × 10⁻⁷ M at 25 °C. Add acid and [H₃O⁺] goes up while [OH⁻] goes down, keeping the product fixed.
A solution is acidic when [H₃O⁺] > [OH⁻], basic when [OH⁻] > [H₃O⁺], and neutral when they're equal.
pH and pOH
pH = −log[H₃O⁺] and pOH = −log[OH⁻]. Because of the minus sign, a higher [H₃O⁺] means a lower pH. Each 1-unit drop in pH means [H₃O⁺] is 10 times larger.
Taking −log of Kw gives pKw = pH + pOH. At 25 °C, pKw = 14.00, so pH + pOH = 14.00. Neutral water at 25 °C has pH = pOH = 7.00.
To go backward, [H₃O⁺] = 10^(−pH) and [OH⁻] = 10^(−pOH).
Significant figures: the number of decimal places in a pH equals the number of significant figures in the concentration. [H₃O⁺] = 2.5 × 10⁻⁴ M (two sig figs) gives pH = 3.60 (two decimal places).
Neutral isn't always pH 7
Kw depends on temperature. Autoionization is endothermic, so Kw gets larger as water warms. At 50 °C, Kw is about 5.5 × 10⁻¹⁴, so neutral water has [H₃O⁺] = √(5.5 × 10⁻¹⁴) and a pH of about 6.63.
That water is still neutral, because [H₃O⁺] still equals [OH⁻]. Neutral means equal concentrations, not 'pH 7'. The rule pH + pOH = 14.00 is only true at 25 °C.
Working from [OH⁻]
Basic solutions are often described by [OH⁻]. If [OH⁻] = 1.0 × 10⁻³ M at 25 °C, then pOH = 3.00 and pH = 14.00 − 3.00 = 11.00. You can also get there through Kw: [H₃O⁺] = (1.0 × 10⁻¹⁴) ÷ (1.0 × 10⁻³) = 1.0 × 10⁻¹¹ M, and −log of that is 11.00. Both routes always agree at 25 °C.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
From [H₃O⁺] to everything else
A solution at 25 °C has [H₃O⁺] = 2.5 × 10⁻⁴ M. Find its pH, [OH⁻] and pOH. Is it acidic or basic?
Show the solutionHide the solution
- Step 1: pH = −log(2.5 × 10⁻⁴) = 3.60.
- Step 2: [OH⁻] = Kw / [H₃O⁺] = (1.0 × 10⁻¹⁴) ÷ (2.5 × 10⁻⁴) = 4.0 × 10⁻¹¹ M.
- Step 3: pOH = −log(4.0 × 10⁻¹¹) = 10.40. Check: 3.60 + 10.40 = 14.00.
- Step 4: [H₃O⁺] > [OH⁻], so the solution is acidic.
Answer: pH = 3.60; [OH⁻] = 4.0 × 10⁻¹¹ M; pOH = 10.40; acidic
- Example 2Calculator allowed
Trap: neutral water that isn't pH 7
At 50 °C, Kw = 5.5 × 10⁻¹⁴. A student measures the pH of pure water at 50 °C as 6.63 and concludes the water is acidic. Is the student right?
Show the solutionHide the solution
- Step 1: In pure water, [H₃O⁺] = [OH⁻] = √Kw = √(5.5 × 10⁻¹⁴) = 2.3 × 10⁻⁷ M.
- Step 2: pH = −log(2.3 × 10⁻⁷) = 6.63. The pOH is also 6.63, and pH + pOH = 13.26 (which is pKw at 50 °C, not 14).
- Step 3: Since [H₃O⁺] equals [OH⁻], the water is neutral. pH 7 marks neutral only at 25 °C.
Answer: No. The water is neutral: [H₃O⁺] = [OH⁻], even though the pH is 6.63.
Common mistakes
- Assuming pH 7 is neutral at every temperature. Neutral means [H₃O⁺] = [OH⁻].
- Using pH + pOH = 14 at temperatures other than 25 °C.
- Forgetting the minus sign in pH = −log[H₃O⁺], which gives negative pH values for ordinary solutions.
- Reporting the wrong number of decimal places in pH. Match the significant figures of the concentration.
On the exam
- Many acid–base calculations end with a pH conversion. Practice moving quickly between [H₃O⁺], [OH⁻], pH and pOH.
- Questions about Kw at other temperatures test whether you know the definition of neutral. Be ready to explain it in a sentence.
Connected topics
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Check yourself
4 questions on 8.1 Introduction to Acids and Bases. Pick an answer to see if you got it, and why.
At 50 °C, Kw = 5.5 × 10⁻¹⁴. Which of the following correctly describes pure water at 50 °C?
A solution at 25 °C has a pH of 3.00. What is [OH⁻] in the solution?
At 25 °C, solution X has a pH of 3.0 and solution Y has a pH of 5.0. Which of the following correctly compares [H₃O⁺] in the two solutions?
A solution at 25 °C has [H₃O⁺] = 2.5 × 10⁻⁹ M. Which of the following correctly describes the solution?
0 of 4 answered