Chemistry

Acids, bases and pH

An acid gives away hydrogen ions (H+\mathrm{H^+}), which in water form H3O+\mathrm{H_3O^+}. A base accepts H+\mathrm{H^+} or adds hydroxide ions (OH−\mathrm{OH^-}). pH measures how acidic a solution is: pH=−log⁡[H3O+]\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 H3O+\mathrm{H_3O^+} than pH 4.

Updated

On this page

Key ideas

  • Arrhenius definition. An acid makes H+\mathrm{H^+} in water (HCl). A base makes OH−\mathrm{OH^-} in water (NaOH).
  • Brønsted-Lowry definition. An acid is a proton (H+\mathrm{H^+}) donor. A base is a proton acceptor. This one also covers bases like NH3\mathrm{NH_3} that have no OH in their formula.
  • Conjugate pairs. When an acid gives away H+\mathrm{H^+}, what is left is its conjugate base. When a base takes H+\mathrm{H^+}, it becomes its conjugate acid. A pair differs by exactly one H+\mathrm{H^+}.
  • Strong vs weak. Strong acids (HCl, HBr, HI, HNO3\mathrm{HNO_3}, H2SO4\mathrm{H_2SO_4}, HClO4\mathrm{HClO_4}) ionize completely in water. Weak acids, like acetic acid in vinegar, ionize only a little. Strong bases include NaOH, KOH and Ba(OH)2\mathrm{Ba(OH)_2}.
pH=−log⁡[H3O+]pOH=−log⁡[OH−]\mathrm{pH} = -\log[\mathrm{H_3O^+}] \qquad \mathrm{pOH} = -\log[\mathrm{OH^-}]
pH+pOH=14.00[H3O+][OH−]=Kw=1.0×10−14(25 ∘C)\mathrm{pH} + \mathrm{pOH} = 14.00 \qquad [\mathrm{H_3O^+}][\mathrm{OH^-}] = K_w = 1.0 \times 10^{-14} \quad (25\ ^{\circ}\text{C})
  • [H3O+][\mathrm{H_3O^+}] and [OH−][\mathrm{OH^-}] are concentrations in moles per liter (M). Square brackets mean molar concentration.
  • log⁡\log is the base-10 logarithm. To go back from pH to concentration, use [H3O+]=10−pH[\mathrm{H_3O^+}] = 10^{-\mathrm{pH}}.
  • KwK_w is the ion product of water. pH and pOH have no units.
Approximate pH of some solutions (OpenStax Chemistry 2e, Figure 14.2)
SolutionpHType
1 M HCl0Strongly acidic
Lime juiceabout 2Acidic
Coffeeabout 5Weakly acidic
Pure water7Neutral
Milk of magnesiaabout 10.5Basic
Household ammoniaabout 12Basic
1 M NaOH14Strongly basic

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. [H3O+]=0.0010[\mathrm{H_3O^+}] = 0.0010 M =1.0×10−3= 1.0 \times 10^{-3} M.
  2. Take the negative log.
    pH=−log⁡(1.0×10−3)=3.00\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 [OH−]=0.050[\mathrm{OH^-}] = 0.050 M.
  2. Find pOH first.
    pOH=−log⁡(0.050)=1.30\mathrm{pOH} = -\log(0.050) = 1.30
  3. Then pH.
    pH=14.00−1.30=12.70\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 [H3O+][\mathrm{H_3O^+}]?

  1. Undo the log.
    [H3O+]=10−4.25=5.62×10−5 M[\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 5.6×10−55.6 \times 10^{-5} M

Example 4: name the conjugate pairs

Problem Label the acid, base, conjugate acid and conjugate base: NH3+H2O⇌NH4++OH−\mathrm{NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^-}

  1. Follow the H+\mathrm{H^+}. Water loses one H and becomes OH−\mathrm{OH^-}, so water is the acid (proton donor).
  2. Ammonia gains that H and becomes NH4+\mathrm{NH_4^+}, so ammonia is the base (proton acceptor).
  3. Pair each one with what it turns into. NH4+\mathrm{NH_4^+} is the conjugate acid of NH3\mathrm{NH_3}, and OH−\mathrm{OH^-} is the conjugate base of H2O\mathrm{H_2O}.

Answer Base NH3\mathrm{NH_3}, acid H2O\mathrm{H_2O}, conjugate acid NH4+\mathrm{NH_4^+}, conjugate base OH−\mathrm{OH^-}

Common mistakes and how to fix them

  • Forgetting the minus sign. log⁡(10−3)=−3\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 1.0×10−51.0 \times 10^{-5} M HNO3\mathrm{HNO_3}?

    Show answer

    Answer: pH = 5.00

    HNO3\mathrm{HNO_3} is a strong acid, so [H3O+]=1.0×10−5[\mathrm{H_3O^+}] = 1.0 \times 10^{-5} M and pH=−log⁡(1.0×10−5)=5.00\mathrm{pH} = -\log(1.0 \times 10^{-5}) = 5.00.

  2. Which solution is the most acidic?

    1. pH 2
    2. pH 5
    3. pH 7
    4. pH 11
    Show answer

    Answer: pH 2

    Lower pH means more H3O+\mathrm{H_3O^+}. pH 7 is neutral and pH 11 is basic.

  3. How many times more H3O+\mathrm{H_3O^+} does a pH 3 solution have than a pH 6 solution?

    1. 3 times
    2. 30 times
    3. 300 times
    4. 1000 times
    Show answer

    Answer: 1000 times

    The pH values differ by 3 units, and each unit is a factor of 10: 103=100010^3 = 1000.

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

    Show answer

    Answer: pH = 10.00

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

  5. What is the conjugate base of sulfuric acid, H2SO4\mathrm{H_2SO_4}?

    1. HSO4−\mathrm{HSO_4^-}
    2. SO42−\mathrm{SO_4^{2-}}
    3. H3SO4+\mathrm{H_3SO_4^+}
    4. H2O\mathrm{H_2O}
    Show answer

    Answer: HSO4−\mathrm{HSO_4^-}

    Remove one H+\mathrm{H^+}: one fewer H and one more negative charge. SO42−\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 −1-1. 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 H3O+\mathrm{H_3O^+} and OH−\mathrm{OH^-} in equal amounts. At 25 °C, Kw=1.0×10−14K_w = 1.0 \times 10^{-14}, so each one is 1.0×10−71.0 \times 10^{-7} M and the pH is 7.00. At other temperatures KwK_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 [H3O+][\mathrm{H_3O^+}] equals the acid's concentration. A weak acid ionizes only partly, so its [H3O+][\mathrm{H_3O^+}] is much smaller and you need an equilibrium constant, KaK_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: HCl+NaOH→NaCl+H2O\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.

Sources

  1. OpenStax Chemistry 2e, 14.1 Brønsted-Lowry Acids and Bases, accessed October 1, 2026
  2. OpenStax Chemistry 2e, 14.2 pH and pOH, accessed October 1, 2026

Try asking Ducky

  • “Check my pH answers on this worksheet. Am I using the right number of decimal places?”
  • “I keep mixing up the conjugate acid and conjugate base. Quiz me on five reactions.”
  • “Walk me through number 4. It gives pOH and I don't know where to start.”

Free to start. The web app works in any browser, Chromebooks included; the Mac app can also draw on your real screen.

Try it free in your browserGet the Mac app
DuckyHelper
The AI tutor that shows you
FREE TO TRY
Try it free