Unit 8 · Topic 8.2 Beta

pH and pOH of Strong Acids and Bases

Strong acids and strong bases ionize fully, so [H₃O⁺] or [OH⁻] comes straight from the concentration (doubled for hydroxides such as Ba(OH)₂).

Practice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

A drop of concentrated hydrochloric acid and a spoonful of drain cleaner do opposite things to water, but both are easy to calculate. A strong acid or strong base breaks apart fully, so once you know how much you dissolved, you know exactly how many hydronium or hydroxide ions are in the solution.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. What is the pH of a solution with [H₃O⁺] = 1.0 × 10⁻³ M?

  1. 3.00
  2. 11.00
  3. −3.00
  4. 0.0010
Show the answer

pH = −log(1.0 × 10⁻³) = 3.00.

  • Correct: 3.00:
  • 11.00:
  • −3.00:
  • 0.0010:

2. How many moles of solute are in 25.0 mL of 0.200 M solution?

  1. 0.00500 mol
  2. 5.00 mol
  3. 0.125 mol
  4. 0.0080 mol
Show the answer

Moles = 0.0250 L × 0.200 mol/L = 0.00500 mol. Convert mL to L first.

  • Correct: 0.00500 mol:
  • 5.00 mol:
  • 0.125 mol:
  • 0.0080 mol:

3. In a net ionic equation for HCl(aq) + NaOH(aq), which ions are spectators?

  1. Na⁺ and Cl⁻
  2. H₃O⁺ and OH⁻
  3. H₃O⁺ and Cl⁻
  4. Na⁺ and OH⁻
Show the answer

The net reaction is H₃O⁺ + OH⁻ → 2 H₂O; Na⁺ and Cl⁻ are unchanged.

  • Correct: Na⁺ and Cl⁻:
  • H₃O⁺ and OH⁻:
  • H₃O⁺ and Cl⁻:
  • Na⁺ and OH⁻:

Part 4 · See it

See it first

Left: four HCl molecules put in water become four hydronium ions and four chloride ions, with no HCl molecules left, because a strong acid ionizes completely. Right: mixing 0.0050 mol hydronium with 0.0030 mol hydroxide leaves 0.0020 mol hydronium in 0.0500 L, 0.040 M, pH 1.40.
A strong acid leaves no whole molecules behind, so [H₃O⁺] is the acid concentration. When strong acid meets strong base, find what is left over. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. A strong acid gives its proton to water essentially every timeno acid molecules remain, and [H₃O⁺] equals the acid concentration
  2. A strong base such as Ba(OH)₂ dissociates fully[OH⁻] equals the base concentration times the OH⁻ per formula unit
  3. H₃O⁺ and OH⁻ react to form water whenever they meetmixing strong acid and strong base leaves only the excess of whichever had more moles
  4. The excess is spread through the whole mixed volumeits concentration, and then the pH, comes from the excess moles over the total volume

Part 6 · Key ideas

Key ideas

  • Strong acids: HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄ (first proton). Strong bases: group 1 hydroxides, Ca(OH)₂, Sr(OH)₂, Ba(OH)₂.
  • Strong acid: [H₃O⁺] = C. Strong base: [OH⁻] = C × (number of OH⁻ per formula unit), then pOH, then pH.
  • Mixing: moles first, subtract, divide the excess by the total volume, then take the log.
  • At equivalence, strong acid + strong base gives a neutral salt solution: pH 7.00 at 25 °C.

Part 7 · Misconception

A common mistake

The wrong idea: A 1.0 × 10⁻⁸ M HCl solution has pH 8.

What actually happens: An acid cannot make water basic. At that tiny concentration, water's own 1.0 × 10⁻⁷ M H₃O⁺ is larger than the acid's, so the pH is just under 7 (about 6.98).

Part 8 · Check yourself

Check yourself

Exam-style questions. Anything you miss goes into your review queue.

Data table

Four stock solutions

A prep room stocks these solutions at 25 °C. Each solute is a strong acid or a strong base.

Solute and concentration
BottleSoluteConcentration (M)
1HNO₃0.0250
2Ba(OH)₂0.0150
3KOH0.0040
4HCl1.0 × 10⁻⁸

1. What is the pH of Bottle 1?

Type a number.

Show the answer

HNO₃ ionizes fully, so [H₃O⁺] = 0.0250 M. pH = −log(0.0250) = 1.6021, which is 1.602: three significant figures in the concentration give three decimal places.

  • Answer: 1.602

2. What is the pH of Bottle 2?

Type a number.

Show the answer

Ba(OH)₂ → Ba²⁺ + 2 OH⁻, so [OH⁻] = 2 × 0.0150 = 0.0300 M. pOH = −log(0.0300) = 1.5229; pH = 14.000 − 1.523 = 12.477.

  • Answer: 12.477

3. Which bottle has the highest pH?

  1. Bottle 2
  2. Bottle 3
  3. Bottle 4
  4. Bottle 1
Show the answer

The highest pH goes with the highest [OH⁻]. Bottle 2 has 0.0300 M OH⁻ (pH 12.48); Bottle 3 has 0.0040 M (pH 11.60).

  • Correct: Bottle 2: Right: two OH⁻ per formula unit makes its [OH⁻] the largest.
  • Bottle 3: KOH gives one OH⁻ per formula unit, so [OH⁻] = 0.0040 M, less than Bottle 2's 0.0300 M.
  • Bottle 4: A very dilute HCl solution is still slightly acidic; its pH is just under 7, not 8.
  • Bottle 1: Bottle 1 is an acid, so its pH is the lowest of the four.

Experimental setup

Mixing an acid and a base

A student adds 15.0 mL of 0.150 M NaOH to 25.0 mL of 0.120 M HCl in a flask and swirls. Assume the volumes add and the temperature is 25 °C.

4. How many moles of H₃O⁺ are left over after the reaction?

Type a number in mol.

Show the answer

HCl: 0.0250 L × 0.120 mol/L = 0.00300 mol H₃O⁺. NaOH: 0.0150 L × 0.150 mol/L = 0.00225 mol OH⁻. They react 1:1, leaving 0.00300 − 0.00225 = 7.5 × 10⁻⁴ mol H₃O⁺. Both amounts are known to the 0.00001 mol place, so the difference, 0.00075 mol, has two significant figures.

  • Answer: 7.5 × 10-4 mol

5. What is the pH of the mixture?

Type a number.

Show the answer

[H₃O⁺] = 7.5 × 10⁻⁴ mol / 0.0400 L = 0.0188 M. pH = −log(0.0188) = 1.727, which is 1.73 (two significant figures in the leftover moles).

  • Answer: 1.73

Particle view

Four mixtures of HCl and NaOH

WH₃O⁺H₃O⁺Na⁺Na⁺Na⁺Cl⁻Cl⁻Cl⁻Cl⁻Cl⁻XNa⁺Na⁺Na⁺Na⁺Cl⁻Cl⁻Cl⁻Cl⁻YOH⁻OH⁻Na⁺Na⁺Na⁺Na⁺Na⁺Cl⁻Cl⁻Cl⁻ZH₃O⁺H₃O⁺OH⁻OH⁻Na⁺Na⁺Na⁺Na⁺Cl⁻Cl⁻Cl⁻Cl⁻

Key: H₃O⁺ hydronium; OH⁻ hydroxide; Na⁺ sodium ion; Cl⁻ chloride ion. Water molecules are not drawn; at this scale the H₃O⁺ and OH⁻ from water itself are too few to show.

6. Five HCl and three NaOH formula units were mixed. Which box shows the result?

  1. W
  2. X
  3. Y
  4. Z
Show the answer

Five HCl give 5 H₃O⁺ and 5 Cl⁻; three NaOH give 3 Na⁺ and 3 OH⁻. Three H₃O⁺ react with the three OH⁻, leaving 2 H₃O⁺, 5 Cl⁻ and 3 Na⁺: Box W.

  • Correct: W: Right: 2 H₃O⁺ left over, and the spectator ions keep their counts.
  • X: Box X is the equivalence point: equal numbers of acid and base.
  • Y: Box Y has excess OH⁻, which needs more NaOH than HCl.
  • Z: H₃O⁺ and OH⁻ cannot stay side by side in these amounts: they react until one is used up.

7. Which box cannot represent a real mixture, and why?

  1. Z, because H₃O⁺ and OH⁻ would react until one of them was nearly gone
  2. X, because a solution needs H₃O⁺ ions to conduct electricity
  3. Y, because there are more Na⁺ ions than Cl⁻ ions
  4. W, because there are more Cl⁻ ions than Na⁺ ions
Show the answer

Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ is tiny, so large amounts of both ions cannot coexist. They react to make water until the product falls to Kw.

  • Correct: Z, because H₃O⁺ and OH⁻ would react until one of them was nearly gone: Right: neutralization goes essentially to completion.
  • X, because a solution needs H₃O⁺ ions to conduct electricity: Na⁺ and Cl⁻ conduct electricity on their own; X is a neutral salt solution.
  • Y, because there are more Na⁺ ions than Cl⁻ ions: Excess NaOH gives more Na⁺ than Cl⁻; Y is a real mixture with base left over.
  • W, because there are more Cl⁻ ions than Na⁺ ions: Excess HCl gives more Cl⁻ than Na⁺; W is a real mixture with acid left over.

Part 9 · Summary

Summary

Strong acids and strong bases ionize fully, so [H₃O⁺] or [OH⁻] comes straight from the concentration (doubled for hydroxides such as Ba(OH)₂). When they are mixed, the H₃O⁺ and OH⁻ cancel mole for mole; the pH comes from whatever is left over, divided by the total volume.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections