# Acids, bases and pH

Canonical: https://duckyhelper.com/learn/chemistry/acids-bases-and-ph/
Updated: 2026-10-01

An acid gives away hydrogen ions (\(\mathrm{H^+}\)), which in water form \(\mathrm{H_3O^+}\). A base accepts \(\mathrm{H^+}\) or adds hydroxide ions (\(\mathrm{OH^-}\)). pH measures how acidic a solution is: \(\mathrm{pH} = -\log[\mathrm{H_3O^+}]\). At 25 °C, a pH below 7 is acidic, 7 is neutral and above 7 is basic. Each pH unit is a tenfold change, so pH 3 has 10 times more \(\mathrm{H_3O^+}\) than pH 4.

## Key ideas

- **Arrhenius definition.** An acid makes \(\mathrm{H^+}\) in water (HCl). A base makes \(\mathrm{OH^-}\) in water (NaOH).
- **Brønsted-Lowry definition.** An acid is a proton (\(\mathrm{H^+}\)) donor. A base is a proton acceptor. This one also covers bases like \(\mathrm{NH_3}\) that have no OH in their formula.
- **Conjugate pairs.** When an acid gives away \(\mathrm{H^+}\), what is left is its conjugate base. When a base takes \(\mathrm{H^+}\), it becomes its conjugate acid. A pair differs by exactly one \(\mathrm{H^+}\).
- **Strong vs weak.** Strong acids (HCl, HBr, HI, \(\mathrm{HNO_3}\), \(\mathrm{H_2SO_4}\), \(\mathrm{HClO_4}\)) ionize completely in water. Weak acids, like acetic acid in vinegar, ionize only a little. Strong bases include NaOH, KOH and \(\mathrm{Ba(OH)_2}\).

$$
\mathrm{pH} = -\log[\mathrm{H_3O^+}] \qquad \mathrm{pOH} = -\log[\mathrm{OH^-}]
$$

$$
\mathrm{pH} + \mathrm{pOH} = 14.00 \qquad [\mathrm{H_3O^+}][\mathrm{OH^-}] = K_w = 1.0 \times 10^{-14} \quad (25\ ^{\circ}\text{C})
$$

- \([\mathrm{H_3O^+}]\) and \([\mathrm{OH^-}]\) are concentrations in moles per liter (M). Square brackets mean molar concentration.
- \(\log\) is the base-10 logarithm. To go back from pH to concentration, use \([\mathrm{H_3O^+}] = 10^{-\mathrm{pH}}\).
- \(K_w\) is the ion product of water. pH and pOH have no units.

**Approximate pH of some solutions (OpenStax Chemistry 2e, Figure 14.2)**

| Solution | pH | Type |
| --- | --- | --- |
| 1 M HCl | 0 | Strongly acidic |
| Lime juice | about 2 | Acidic |
| Coffee | about 5 | Weakly acidic |
| Pure water | 7 | Neutral |
| Milk of magnesia | about 10.5 | Basic |
| Household ammonia | about 12 | Basic |
| 1 M NaOH | 14 | Strongly basic |

> **Tip: Significant figures in pH**
>
> The number of decimal places in a pH equals the number of significant figures in the concentration. \([\mathrm{H_3O^+}] = 1.0 \times 10^{-3}\) M has 2 significant figures, so pH = 3.00.

## Worked examples

**Example 1: pH of a strong acid**

Problem: What is the pH of 0.0010 M HCl?

1. HCl is a strong acid, so it ionizes completely. \([\mathrm{H_3O^+}] = 0.0010\) M \(= 1.0 \times 10^{-3}\) M.
2. Take the negative log.

   $$
   \mathrm{pH} = -\log(1.0 \times 10^{-3}) = 3.00
   $$
3. 2 significant figures in the concentration means 2 decimal places in the pH.

Answer: pH = 3.00

**Example 2: pH of a strong base**

Problem: What is the pH of 0.050 M NaOH?

1. NaOH is a strong base, so \([\mathrm{OH^-}] = 0.050\) M.
2. Find pOH first.

   $$
   \mathrm{pOH} = -\log(0.050) = 1.30
   $$
3. Then pH.

   $$
   \mathrm{pH} = 14.00 - 1.30 = 12.70
   $$

Answer: pH = 12.70

**Example 3: concentration from pH**

Problem: A rainwater sample has a pH of 4.25. What is \([\mathrm{H_3O^+}]\)?

1. Undo the log.

   $$
   [\mathrm{H_3O^+}] = 10^{-4.25} = 5.62 \times 10^{-5}\ \text{M}
   $$
2. The pH has 2 decimal places, so the concentration gets 2 significant figures.

Answer: \(5.6 \times 10^{-5}\) M

**Example 4: name the conjugate pairs**

Problem: Label the acid, base, conjugate acid and conjugate base: \(\mathrm{NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-}\)

1. Follow the \(\mathrm{H^+}\). Water loses one H and becomes \(\mathrm{OH^-}\), so water is the acid (proton donor).
2. Ammonia gains that H and becomes \(\mathrm{NH_4^+}\), so ammonia is the base (proton acceptor).
3. Pair each one with what it turns into. \(\mathrm{NH_4^+}\) is the conjugate acid of \(\mathrm{NH_3}\), and \(\mathrm{OH^-}\) is the conjugate base of \(\mathrm{H_2O}\).

Answer: Base \(\mathrm{NH_3}\), acid \(\mathrm{H_2O}\), conjugate acid \(\mathrm{NH_4^+}\), conjugate base \(\mathrm{OH^-}\)

## Common mistakes and how to fix them

- **Forgetting the minus sign.** \(\log(10^{-3}) = -3\), so pH = +3. Fix: a normal pH is between 0 and 14, so a negative answer for a dilute solution is a red flag.
- **Using pOH as the pH for a base.** Fix: for a base you usually find pOH first, then subtract from 14.00.
- **Thinking pH 4 is twice as acidic as pH 2.** It is the other way, and the gap is 100 times, not 2. Fix: each unit is a factor of 10, and a lower pH is more acidic.
- **Too many decimal places.** Fix: decimal places in pH = significant figures in the concentration.
- **Mixing up strong with concentrated.** Strong means it ionizes completely. Concentrated means there is a lot of it. Dilute HCl is still a strong acid.

**Practice problems**

1. What is the pH of \(1.0 \times 10^{-5}\) M \(\mathrm{HNO_3}\)?

   Answer: pH = 5.00. \(\mathrm{HNO_3}\) is a strong acid, so \([\mathrm{H_3O^+}] = 1.0 \times 10^{-5}\) M and \(\mathrm{pH} = -\log(1.0 \times 10^{-5}) = 5.00\).

2. Which solution is the most acidic?
   A. pH 2
   B. pH 5
   C. pH 7
   D. pH 11

   Answer: pH 2. Lower pH means more \(\mathrm{H_3O^+}\). pH 7 is neutral and pH 11 is basic.

3. How many times more \(\mathrm{H_3O^+}\) does a pH 3 solution have than a pH 6 solution?
   A. 3 times
   B. 30 times
   C. 300 times
   D. 1000 times

   Answer: 1000 times. The pH values differ by 3 units, and each unit is a factor of 10: \(10^3 = 1000\).

4. A solution has \([\mathrm{OH^-}] = 1.0 \times 10^{-4}\) M. What is its pH?

   Answer: pH = 10.00. \(\mathrm{pOH} = -\log(1.0 \times 10^{-4}) = 4.00\). Then \(\mathrm{pH} = 14.00 - 4.00 = 10.00\).

5. What is the conjugate base of sulfuric acid, \(\mathrm{H_2SO_4}\)?
   A. \(\mathrm{HSO_4^-}\)
   B. \(\mathrm{SO_4^{2-}}\)
   C. \(\mathrm{H_3SO_4^+}\)
   D. \(\mathrm{H_2O}\)

   Answer: \(\mathrm{HSO_4^-}\). Remove one \(\mathrm{H^+}\): one fewer H and one more negative charge. \(\mathrm{SO_4^{2-}}\) has lost two.

## Frequently asked questions

### Can pH be negative or above 14?

Yes, for very concentrated solutions. 10 M HCl has a pH of about \(-1\). The 0 to 14 range covers most solutions you will meet, because it matches concentrations from 1 M acid to 1 M base at 25 °C.

### Why is pure water neutral at pH 7?

Water splits into \(\mathrm{H_3O^+}\) and \(\mathrm{OH^-}\) in equal amounts. At 25 °C, \(K_w = 1.0 \times 10^{-14}\), so each one is \(1.0 \times 10^{-7}\) M and the pH is 7.00. At other temperatures \(K_w\) changes, so neutral is not exactly 7.

### What is the difference between a strong acid and a weak acid?

A strong acid ionizes completely, so its \([\mathrm{H_3O^+}]\) equals the acid's concentration. A weak acid ionizes only partly, so its \([\mathrm{H_3O^+}]\) is much smaller and you need an equilibrium constant, \(K_a\), to find the pH. That is a common AP Chemistry topic.

### What happens when an acid and a base react?

They neutralize each other and make water and a salt: \(\mathrm{HCl + NaOH \rightarrow NaCl + H_2O}\). Measuring how much base it takes to neutralize an acid is called a titration, and the math uses [molarity](https://duckyhelper.com/learn/chemistry/molarity-and-dilution/).

## Sources

- [OpenStax Chemistry 2e, 14.1 Brønsted-Lowry Acids and Bases](https://openstax.org/books/chemistry-2e/pages/14-1-bronsted-lowry-acids-and-bases), accessed 2026-10-01
- [OpenStax Chemistry 2e, 14.2 pH and pOH](https://openstax.org/books/chemistry-2e/pages/14-2-ph-and-poh), accessed 2026-10-01

## Related

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- [Types of chemical reactions](https://duckyhelper.com/learn/chemistry/types-of-chemical-reactions/)
- [Stoichiometry: how much reacts and how much forms](https://duckyhelper.com/learn/chemistry/stoichiometry/)
- [Chemistry study guides](https://duckyhelper.com/learn/chemistry/)

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