Unit 8 · Topic 8.1 Beta

Introduction to Acids and Bases

Water ionizes itself slightly, so every water solution holds both H₃O⁺ and OH⁻, tied together by Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C.

Practice 1: Models and RepresentationsPractice 5: Mathematical Routines

Question set for this topic

Part 1 · Hook

Why this matters

Black coffee sits around pH 5 and household ammonia around pH 11. That gap of six units means the coffee has a million times more hydronium ions per liter. Even the purest water holds a few of these ions, and that tiny amount is the starting point for every acid and base in this unit.

Part 2 · Before you start

What this builds on

Part 3 · Prerequisite check

Quick check before you start

1. What is log(1 × 10⁻⁵)?

  1. −5
  2. 5
  3. 0.00001
  4. −0.00001
Show the answer

The base-10 log of a power of ten is the exponent: log(10⁻⁵) = −5.

  • Correct: −5:
  • 5:
  • 0.00001:
  • −0.00001:

2. In the reaction H₂O + H₂O ⇌ H₃O⁺ + OH⁻, what does the first water molecule do?

  1. Accepts a proton
  2. Donates a proton
  3. Gains an electron
  4. Loses an oxygen atom
Show the answer

It becomes H₃O⁺ by gaining H⁺, so it acts as a Brønsted-Lowry base; the other water molecule donates the proton.

  • Correct: Accepts a proton:
  • Donates a proton:
  • Gains an electron:
  • Loses an oxygen atom:

3. Which species are left out of an equilibrium constant expression?

  1. Pure liquids and solids
  2. Gases
  3. Dissolved ions
  4. Products
Show the answer

Pure liquids and solids have constant concentrations, so they are left out. That is why water does not appear in Kw.

  • Correct: Pure liquids and solids:
  • Gases:
  • Dissolved ions:
  • Products:

Part 4 · See it

See it first

The pH scale from 0 to 14 at 25 °C. Hydronium concentration falls from 1 M at pH 0 to 10 to the minus 14 M at pH 14, while hydroxide concentration rises the other way. Below pH 7 is acidic, pH 7 is neutral, above 7 is basic. One pH unit is a factor of ten in hydronium concentration; pH plus pOH is 14.00 at 25 °C.
The pH scale at 25 °C. Hydronium and hydroxide concentrations run in opposite directions, and their product stays 1.0 × 10⁻¹⁴. LevlPrep original diagram.

Part 5 · Step by step

How it works, step by step

  1. Water molecules collide and a few transfer a proton to a neighborpure water always holds equal, tiny amounts of H₃O⁺ and OH⁻
  2. That self-ionization is an equilibriumKw = [H₃O⁺][OH⁻] has one value at a given temperature: 1.0 × 10⁻¹⁴ at 25 °C
  3. Adding acid raises [H₃O⁺]some of the added H₃O⁺ reacts with OH⁻ until the product is back to Kw, so [OH⁻] falls
  4. Concentrations span many powers of tenchemists report them as pH = −log[H₃O⁺], where each unit is a factor of ten
  5. Self-ionization absorbs heatwarm water has a larger Kw, so neutral water there has a pH below 7

Part 6 · Key ideas

Key ideas

  • Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C, in every water solution. Know one ion and you know the other.
  • pH = −log[H₃O⁺] and pOH = −log[OH⁻]; at 25 °C pH + pOH = 14.00. One pH unit is ten times the [H₃O⁺].
  • Acidic: [H₃O⁺] > [OH⁻]. Basic: [OH⁻] > [H₃O⁺]. Neutral: equal. Neutral is pH 7.00 only at 25 °C.
  • Significant figures: the pH gets as many decimal places as the concentration has significant figures.

Part 7 · Misconception

A common mistake

The wrong idea: Water at pH 6.6 must be acidic, because neutral is pH 7.

What actually happens: Neutral means [H₃O⁺] = [OH⁻]. Pure water is neutral at every temperature; at 50 °C, where Kw is larger, neutral water has a pH of about 6.6.

Part 8 · Check yourself

Check yourself

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

Data table

Four solutions at 25 °C

A student records one measured quantity for each of four aqueous solutions, all at 25 °C.

One known quantity per solution
SolutionQuantity measuredValue
A[H₃O⁺]3.2 × 10⁻⁴ M
B[OH⁻]2.5 × 10⁻³ M
CpH9.15
DpOH11.62

1. Find the pH of Solution A from its measured hydronium concentration.

Type a number.

Show the answer

pH = −log(3.2 × 10⁻⁴) = 3.495. The concentration has two significant figures, so the pH gets two decimal places: 3.49.

  • Answer: 3.49

2. What is the pH of Solution B?

Type a number.

Show the answer

pOH = −log(2.5 × 10⁻³) = 2.602; pH = 14.00 − 2.60 = 11.40. Two significant figures in [OH⁻] give two decimal places.

  • Answer: 11.40

3. Which solution has the highest concentration of H₃O⁺?

  1. Solution D, with a pOH of 11.62
  2. Solution A, with [H₃O⁺] = 3.2 × 10⁻⁴ M
  3. Solution B, with [OH⁻] = 2.5 × 10⁻³ M
  4. Solution C, with a pH of 9.15
Show the answer

Convert each to pH: A 3.49, B 11.40, C 9.15, D 14.00 − 11.62 = 2.38. The lowest pH, D, has the most H₃O⁺.

  • Correct: Solution D, with a pOH of 11.62: Right: a large pOH means little OH⁻, so pH = 2.38, the lowest of the four.
  • Solution A, with [H₃O⁺] = 3.2 × 10⁻⁴ M: Solution A is acidic (pH 3.49), but D's pH of 2.38 is lower, so D has more H₃O⁺. A was the only one stated as [H₃O⁺], which is not the same as having the most.
  • Solution B, with [OH⁻] = 2.5 × 10⁻³ M: This reads [OH⁻] as if it were [H₃O⁺]. A large [OH⁻] means a basic solution, pH 11.40, with very little H₃O⁺.
  • Solution C, with a pH of 9.15: A larger pH number means less H₃O⁺, not more: pH 9.15 is basic.

Particle view

Ions in four samples of water

Box 1H₃O⁺H₃O⁺OH⁻OH⁻Box 2H₃O⁺H₃O⁺H₃O⁺H₃O⁺OH⁻Box 3H₃O⁺OH⁻OH⁻OH⁻OH⁻Box 4H₃O⁺H₃O⁺H₃O⁺OH⁻OH⁻OH⁻

Key: H₃O⁺ hydronium ion; OH⁻ hydroxide ion. Water molecules and any other ions are not drawn. Boxes 1, 2 and 3 are at the same temperature; Box 4 is pure water at a different temperature.

4. Which box represents a basic solution?

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

A solution is basic when [OH⁻] > [H₃O⁺]. Only Box 3 has more hydroxide (4) than hydronium (1).

  • Correct: Box 3: Right: 4 OH⁻ to 1 H₃O⁺.
  • Box 1: Box 1 has equal numbers of the two ions, so it is neutral.
  • Box 2: Box 2 has more H₃O⁺ than OH⁻, so it is acidic.
  • Box 4: Box 4 has equal numbers of the two ions, so it is neutral even though it holds more ions than Box 1.

5. In Boxes 1, 2 and 3 the product (number of H₃O⁺) × (number of OH⁻) is the same. What does this show?

  1. [H₃O⁺][OH⁻] is fixed at a given temperature, so raising one lowers the other
  2. Each solution contains the same total number of ions
  3. Adding acid to water adds OH⁻ ions as well as H₃O⁺ ions
  4. The pH of each of the three solutions is the same
Show the answer

Each box has 2 × 2 = 4 × 1 = 1 × 4 = 4. This mirrors Kw = [H₃O⁺][OH⁻], which has one value at a given temperature: more H₃O⁺ means less OH⁻.

  • Correct: [H₃O⁺][OH⁻] is fixed at a given temperature, so raising one lowers the other: Right: the product is the model of Kw.
  • Each solution contains the same total number of ions: The totals differ: 4, 5 and 5 ions. It is the product that stays the same.
  • Adding acid to water adds OH⁻ ions as well as H₃O⁺ ions: Box 2 has fewer OH⁻ than Box 1. Added H₃O⁺ reacts with OH⁻, which lowers [OH⁻].
  • The pH of each of the three solutions is the same: The boxes have different [H₃O⁺], so different pH values; only the product is the same.

6. A solution at 25 °C has [H₃O⁺] = 4.0 × 10⁻³ M. What is [OH⁻]? Include the unit.

Type a number and its unit.

Show the answer

[OH⁻] = Kw / [H₃O⁺] = (1.0 × 10⁻¹⁴) / (4.0 × 10⁻³) = 2.5 × 10⁻¹² M.

  • Answer: 2.5 × 10-12 M

7. A solution has [H₃O⁺] = 0.0050 M. How should its pH be reported?

  1. 2.30
  2. 2.3
  3. 2.301
  4. 2.3010
Show the answer

0.0050 has two significant figures, so the pH gets two decimal places: −log(0.0050) = 2.3010 → 2.30. The digits before the decimal point only give the power of ten.

  • Correct: 2.30: Right: two significant figures, two decimal places.
  • 2.3: One decimal place throws away a measured digit: 0.0050 has two significant figures.
  • 2.301: Three decimal places claim more precision than the two significant figures measured.
  • 2.3010: Four decimal places treat the trailing zero of 2.3010 as measured, which it is not.

Part 9 · Summary

Summary

Water ionizes itself slightly, so every water solution holds both H₃O⁺ and OH⁻, tied together by Kw = [H₃O⁺][OH⁻] = 1.0 × 10⁻¹⁴ at 25 °C. pH and pOH are base-10 logarithm scales of the two concentrations, adding to 14.00 at 25 °C. Neutral means equal concentrations, which falls at pH 7 only at 25 °C.

Part 10 · Up next

What comes next

Part 11 · Connections

Connections