Unit 8 · Acids and Bases

AP Chemistry pH Scale

What pH and pOH measure, how they connect through K_w, why each pH unit is a factor of 10, and why neutral is not always pH 7, in four worked examples.

pH is the number every acid-base question eventually asks for. It is a compact way to write the hydronium ion concentration, which can range across more than fourteen powers of ten. This page covers the scale itself: the definitions, the links between pH, pOH, and K_w, and the conversions you need before moving on to strong acids and bases and weak acids.

What pH Measures and What the p Means

In chemistry, a lowercase p in front of a quantity means “negative base-10 logarithm of.” So pH is the negative log of the hydronium ion concentration:

pH = −log[H₃O⁺]   and   [H₃O⁺] = 10^−pH

• Acidic: [H₃O⁺] > [OH⁻], pH below 7 at 25°C.
• Neutral: [H₃O⁺] = [OH⁻], pH 7.00 at 25°C.
• Basic: [OH⁻] > [H₃O⁺], pH above 7 at 25°C.

Because of the minus sign, a lower pH means more H₃O⁺. H⁺ and H₃O⁺ are used interchangeably; a free proton in water is always attached to a water molecule, as described in Brønsted-Lowry acids and bases.

How pH, pOH, and K_w Fit Together

Water transfers protons to itself to a tiny extent, which links [H₃O⁺] and [OH⁻] in every aqueous solution:

2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq)    K_w = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25°C

• pOH = −log[OH⁻], defined the same way as pH.
• pH + pOH = 14.00 at 25°C, which is pK_w.
• From any one of pH, pOH, [H₃O⁺], or [OH⁻], you can find the other three.

The pH of Common Substances

Typical values from the open-access textbook Beginning Chemistry (Ball), Table 12.3; real samples vary with conditions. The 1.0 M HCl value is calculated.

Why Each pH Unit Is a Factor of 10

pH is a logarithmic scale, so moving down one pH unit means ten times more H₃O⁺, and two units means one hundred times more. Lemon juice (pH 2.2) has 10^{5.0 − 2.2} ≈ 630 times the hydronium concentration of black coffee (pH 5.0), even though the numbers differ by less than 3.

The log also sets the significant-figure rule: the number of decimal places in a pH equals the number of significant figures in the concentration. That rule and calculator-free log estimates are covered in scientific notation.

Worked Example 1: Converting Between pH and [H₃O⁺]

(a) Find the pH of a solution with [H₃O⁺] = 3.2 × 10⁻⁴ M. (b) Find [H₃O⁺] in a solution with pH 9.25.

(a) pH = −log(3.2 × 10⁻⁴) = 3.49. Two significant figures in the concentration give two decimal places.
(b) [H₃O⁺] = 10^−9.25 = 5.6 × 10⁻¹⁰ M. The solution is basic.

A quick sense check: a pH between 3 and 4 must come from a concentration between 10⁻³ and 10⁻⁴ M, and 3.2 × 10⁻⁴ fits.

Worked Example 2: Going From [OH⁻] to pOH and pH

A solution has [OH⁻] = 2.5 × 10⁻³ M at 25°C. Find pOH, pH, and [H₃O⁺].

pOH: −log(2.5 × 10⁻³) = 2.60.
pH: 14.00 − 2.60 = 11.40.
[H₃O⁺]: K_w / [OH⁻] = (1.0 × 10⁻¹⁴) / (2.5 × 10⁻³) = 4.0 × 10⁻¹² M, and −log(4.0 × 10⁻¹²) = 11.40 confirms the pH.

Two routes giving the same pH is a useful check on a free-response answer.

Worked Example 3: Comparing Acidity Across pH Values

(a) How many times greater is [H₃O⁺] at pH 3.00 than at pH 5.00? (b) 0.010 M HCl is diluted tenfold. What happens to its pH?

(a) The difference is 2 pH units, so the ratio is 10² = 100 times.
(b) Before: [H₃O⁺] = 0.010 M, pH 2.00. After: 0.0010 M, pH 3.00. A tenfold dilution of a strong acid raises the pH by exactly 1.

Part (b) works only for strong acids, which ionize completely. Diluting a weak acid tenfold raises its pH by less than 1, because a larger fraction of it ionizes, as shown in weak acids, K_a, and pK_a.

Worked Example 4: Why Neutral Water Is Not pH 7 at 50°C

At 50°C, K_w = 5.5 × 10⁻¹⁴. Find the pH of pure water at this temperature and say whether it is acidic, basic, or neutral.

In pure water: [H₃O⁺] = [OH⁻] = x, so x² = 5.5 × 10⁻¹⁴.
Solve: x = 2.3 × 10⁻⁷ M, so pH = 6.63.
Classify: neutral, because [H₃O⁺] still equals [OH⁻].

Water’s self-ionization is endothermic, so K_w grows as the temperature rises and the neutral pH drops below 7. At 50°C, a solution with pH 7.00 would actually be slightly basic. The rule “pH 7 is neutral” holds only at 25°C.

Five pH Practice Questions With Answers

1. What is the pH of a solution with [H₃O⁺] = 1.0 × 10⁻⁵ M?
   Show answer

   pH = 5.00.
2. Find [H₃O⁺] for a solution with pH 4.50.
   Show answer

   10^−4.50 = 3.2 × 10⁻⁵ M.
3. A solution has [OH⁻] = 1.0 × 10⁻³ M at 25°C. Find pOH and pH.
   Show answer

   pOH = 3.00 and pH = 14.00 − 3.00 = 11.00.
4. How many times greater is [H₃O⁺] at pH 2 than at pH 6?
   Show answer

   10⁴ = 10,000 times.
5. Blood has a pH of 7.4. What is its [H₃O⁺], and is it acidic, basic, or neutral at body temperature if neutral water there has pH 6.8?
   Show answer

   [H₃O⁺] = 10^−7.4 = 4 × 10⁻⁸ M. It is slightly basic, because its pH is above the neutral value at that temperature.

Common pH Mistakes

• Reading the scale backward. A lower pH means more H₃O⁺ and a more acidic solution.
• Treating pH as linear. One pH unit is a factor of 10, not a small step.
• Using pH + pOH = 14 at any temperature. It is pK_w, which equals 14.00 only at 25°C.
• Calling pH 7 neutral at every temperature. Neutral means [H₃O⁺] = [OH⁻].
• Mixing up pH and pOH. pOH comes from [OH⁻]; convert before reporting a pH.
• Reporting the wrong number of decimal places. Decimal places in a pH match the significant figures in the concentration.

pH conversions are the entry point to every Unit 8 calculation, and Unit 8 is the second-heaviest unit on the multiple-choice section. To see how stronger acid-base answers would move your overall estimate, try the AP Chem Score Calculator.

Related Resources

• AP Chem Score Calculator
• Unit 8 Review: Acids and Bases
• AP Chemistry Strong Acids and Bases
• AP Chemistry Weak Acids, Ka, and pKa
• AP Chemistry Bronsted-Lowry Acids and Bases
• AP Chemistry Scientific Notation
• AP Chemistry Buffers
• AP Chemistry Study Guide

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