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pH and the pH Scale

What is pH and how do you calculate it?

IntermediateAcids & BasesLast reviewed 3 October 2026
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What is it?

pH is a number that tells you how acidic or basic a solution is. It is based on the concentration of hydronium ions, HX3OX+\ce{H3O+}:

pH=−log⁡[HX3OX+]\text{pH} = -\log[\ce{H3O+}]

where [HX3OX+][\ce{H3O+}] is the concentration in mol/L.

At 25 °C:

  • pH < 7: acidic
  • pH = 7: neutral
  • pH > 7: basic (also called alkaline)

Key idea

The pH scale is logarithmic: each change of 1 pH unit means a 10-fold change in [HX3OX+][\ce{H3O+}]. A solution at pH 3 has 1000 times more HX3OX+\ce{H3O+} than one at pH 6.

Why does it matter?

  • Living things depend on it. Human blood is kept between about pH 7.35 and 7.45; a change of a few tenths can be dangerous.
  • Chemistry depends on it. The speed and outcome of many reactions, and how well many substances dissolve, change with pH.
  • Everyday life depends on it. Soil pH affects which crops grow, swimming pools and drinking water are kept within set pH ranges, and many food and cleaning products are designed around their pH.

How does it work?

1. Water always contains a little H₃O⁺ and OH⁻

Water reacts with itself very slightly:

2 HX2O⇌HX3OX++OHX−\ce{2H2O <=> H3O+ + OH-}

At 25 °C, the product of the two concentrations is always the same constant, KwK_\text{w}:

Kw=[HX3OX+][OHX−]=1.0×10−14K_\text{w} = [\ce{H3O+}][\ce{OH-}] = 1.0 \times 10^{-14}

In pure water both concentrations are 1.0×10−71.0 \times 10^{-7} M, so the pH is 7.00. Adding acid raises [HX3OX+][\ce{H3O+}] and lowers [OHX−][\ce{OH-}], and adding base does the opposite.

pOH=−log⁡[OHX−]\text{pOH} = -\log[\ce{OH-}]

and, at 25 °C,

pH+pOH=14.00\text{pH} + \text{pOH} = 14.00

3. Strong acids and bases

A strong acid ionizes completely, so [HX3OX+][\ce{H3O+}] equals the acid’s concentration (for acids that give one HX+\ce{H+}, such as HCl and HNO₃). Likewise, for a strong base, [OHX−][\ce{OH-}] comes straight from its concentration, remembering how many OH⁻ each formula unit releases (2 for Ca(OH)X2\ce{Ca(OH)2}).

4. Going back from pH to concentration

[HX3OX+]=10−pH[\ce{H3O+}] = 10^{-\text{pH}}

Think of it like this

Think of prices that each have one more zero: 10, 100, 1,000, 10,000. Each step is ten times the last. The pH scale counts those zeros: each step down in pH means ten times more H₃O⁺. So pH 4 isn’t twice as acidic as pH 8. It has 10,000 times more H₃O⁺.

More precisely

KwK_\text{w} changes with temperature, so neutral water has pH 7.00 only at 25 °C (at higher temperatures, neutral pH is a little lower). pH can also be below 0 or above 14 for very concentrated acids or bases. For very dilute acids, the HX3OX+\ce{H3O+} from water itself can’t be ignored: 1×10−81 \times 10^{-8} M HCl is slightly acidic, not pH 8. Strictly, pH is defined using activity rather than concentration, but concentration works well for dilute solutions.

Visualise it

The pH scale at 25 degrees Celsius, from 0 to 14. Acidic below 7, neutral at 7, basic above 7. Approximate everyday values: lemon juice about 2, black coffee about 5, pure water 7, blood about 7.4, household ammonia about 11. Each step of one pH unit is a ten-fold change in hydronium ion concentration.
The pH scale. Each step is a 10× change in [H₃O⁺].

Worked example

Worked example: pH of a strong acid

Question: What is the pH of 0.050 M hydrochloric acid?

  1. HCl is a strong acid, so [HX3OX+]=0.050[\ce{H3O+}] = 0.050 M.
  2. pH=−log⁡(0.050)=1.30\text{pH} = -\log(0.050) = 1.30

Worked example: pH of a strong base

Question: What is the pH of 0.020 M calcium hydroxide, Ca(OH)X2\ce{Ca(OH)2}?

  1. Each Ca(OH)X2\ce{Ca(OH)2} releases two OHX−\ce{OH-} ions: [OHX−]=2×0.020=0.040[\ce{OH-}] = 2 \times 0.020 = 0.040 M
  2. pOH=−log⁡(0.040)=1.40\text{pOH} = -\log(0.040) = 1.40
  3. pH=14.00−1.40=12.60\text{pH} = 14.00 - 1.40 = 12.60

Worked example: Concentration from pH

Question: A solution has pH 4.50. What is [HX3OX+][\ce{H3O+}]?

[HX3OX+]=10−4.50=3.2×10−5[\ce{H3O+}] = 10^{-4.50} = 3.2 \times 10^{-5} M

Common mistake

Common mistake: Thinking the pH scale is linear

pH 4 is not twice as acidic as pH 8. Each pH unit is a factor of 10, so the difference is 10410^4 = 10,000 times.

Common mistake: Forgetting the number of OH⁻ ions

For Ca(OH)X2\ce{Ca(OH)2} or Ba(OH)X2\ce{Ba(OH)2}, [OHX−][\ce{OH-}] is twice the concentration of the base. Using 0.020 M instead of 0.040 M in the example gives pH 12.30 instead of 12.60.

Common mistake: Mixing up pH and pOH

For a base, you usually calculate pOH first from [OHX−][\ce{OH-}], then convert: pH = 14.00 − pOH. Reporting the pOH as the pH is a very common slip.

Notation note

  • [HX+][\ce{H+}] and [HX3OX+][\ce{H3O+}] are used interchangeably in pH calculations.
  • Significant figures: the number of decimal places in a pH equals the number of significant figures in the concentration. 0.050 M (2 s.f.) gives pH 1.30 (2 decimal places).
  • “log” here means the base-10 logarithm (the “log” key on a calculator, not “ln”).

Remember this

Remember this

  • pH = −log[H₃O⁺]; [H₃O⁺] = 10⁻ᵖᴴ.
  • At 25 °C: pH < 7 acidic, = 7 neutral, > 7 basic; pH + pOH = 14.00.
  • 1 pH unit = 10× change in [H₃O⁺].
  • Strong acids/bases: concentration of H₃O⁺ or OH⁻ comes straight from the formula (count the OH⁻!).

Test yourself

Check your understanding before moving on.

Flashcards

10 cards

  1. Question
    What is the definition of pH?
    Answer

    pH=−log⁡[HX3OX+]\text{pH} = -\log[\ce{H3O+}]

  2. Question
    At 25 °C, what pH values are acidic, neutral and basic?
    Answer

    Below 7 acidic, exactly 7 neutral, above 7 basic.

  3. Question
    What is KwK_\text{w} at 25 °C?
    Answer

    Kw=[HX3OX+][OHX−]=1.0×10−14K_\text{w} = [\ce{H3O+}][\ce{OH-}] = 1.0 \times 10^{-14}

  4. Question
    What is the relationship between pH and pOH at 25 °C?
    Answer

    pH + pOH = 14.00

  5. Question
    How many times more HX3OX+\ce{H3O+} does a pH 3 solution have than a pH 6 solution?
    Answer

    1000 times (10310^3): each pH unit is a factor of 10.

  6. Question
    What is the pH of 0.010 M HCl?
    Answer

    −log⁡(0.010)=2.00-\log(0.010) = 2.00

  7. Question
    What is the pH of 0.0010 M NaOH?
    Answer

    pOH = 3.00, so pH = 14.00 − 3.00 = 11.00

  8. Question
    How do you find [HX3OX+][\ce{H3O+}] from the pH?
    Answer

    [HX3OX+]=10−pH[\ce{H3O+}] = 10^{-\text{pH}}

  9. Question
    What is [OHX−][\ce{OH-}] in 0.020 M Ca(OH)X2\ce{Ca(OH)2}?
    Answer

    0.040 M: each formula unit releases two OHX−\ce{OH-} ions.

  10. Question
    How many decimal places should a pH have?
    Answer

    As many as the significant figures in the concentration (0.050 M → pH 1.30).

Quiz

7 questions

  1. Question 1EasyAt 25 °C, a solution has pH 9. It is…
    Show answer

    Answer: basic

    At 25 °C, pH above 7 is basic, below 7 is acidic, and exactly 7 is neutral.

  2. Question 2MediumWhat is the pH of 0.0025 M nitric acid, HNOX3\ce{HNO3} (a strong acid)?
    Show answer

    Answer: 2.60

    Strong acid, so [HX3OX+]=0.0025[\ce{H3O+}] = 0.0025 M and pH = −log(0.0025) = 2.60. The answer 11.40 is the pOH.

  3. Question 3MediumWhat is the pH of 0.15 M KOH (a strong base)?
    Show answer

    Answer: 13.18

    [OHX−]=0.15[\ce{OH-}] = 0.15 M, so pOH = −log(0.15) = 0.82, and pH = 14.00 − 0.82 = 13.18. The answer 0.82 reports the pOH as the pH.

  4. Question 4MediumSolution A has pH 4 and solution B has pH 8. How do their HX3OX+\ce{H3O+} concentrations compare?
    Show answer

    Answer: A has 10,000 times more

    A difference of 4 pH units is a factor of 10410^4 = 10,000, and the lower pH has the higher [HX3OX+][\ce{H3O+}].

  5. Question 5HardA solution has [OHX−]=2.5×10−4[\ce{OH-}] = 2.5 \times 10^{-4} M at 25 °C. What is its pH?
    Show answer

    Answer: 10.40

    pOH = −log(2.5 × 10⁻⁴) = 3.60, so pH = 14.00 − 3.60 = 10.40. (Equivalently, [HX3OX+]=1.0×10−14÷2.5×10−4=4.0×10−11[\ce{H3O+}] = 1.0 \times 10^{-14} \div 2.5 \times 10^{-4} = 4.0 \times 10^{-11} M.)

  6. Question 6HardWhat is the pH of 0.020 M Ca(OH)X2\ce{Ca(OH)2}?
    Show answer

    Answer: 12.60

    Each Ca(OH)X2\ce{Ca(OH)2} gives two OHX−\ce{OH-}: [OHX−]=0.040[\ce{OH-}] = 0.040 M, pOH = 1.40, pH = 12.60. The answer 12.30 forgets the factor of 2.

  7. Question 7Medium0.10 M HCl (pH 1.00) is diluted 10 times with water. What is the new pH?
    Show answer

    Answer: 2.00

    Diluting 10 times gives 0.010 M HCl, and pH = −log(0.010) = 2.00. A 10-fold dilution of a strong acid raises the pH by 1.

Notes and downloads

  • Worksheet

    pH Worksheet

    9 questions on the pH scale and pH calculations for strong acids and bases. Answer key included.

    IntermediateFree

References

  1. Brown, T. L.; LeMay, H. E., Jr.; Bursten, B. E.; Murphy, C. J.; Woodward, P. M.; Stoltzfus, M. W. Chemistry: The Central Science, 15th ed.; Pearson, 2022.

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