Logarithmic Nature of the pH Scale
The pH scale is an inverse logarithmic measure of the aqueous hydrogen ion concentration \([\text{H}^+]\). A change of 1 pH unit represents a 10-fold change in \([\text{H}^+]\).
For example, a solution with \(\text{pH} = 3\) has \(100 \times\) higher \([\text{H}^+]\) than a solution with \(\text{pH} = 5\).
What is pH?
pH stands for "power of hydrogen" and provides a convenient way to express the acidity or basicity of a solution on a scale typically ranging from 0 to 14 (at 25°C).
pH and pOH Calculations
The pH Scale
The Logarithmic Relationship
Because pH uses a log10 scale, each unit change represents a 10-fold change in [H+]:
| pH | [H+] / mol dm-3 | Classification |
|---|---|---|
| 1 | 0.1 (10-1) | Strongly acidic |
| 3 | 0.001 (10-3) | Acidic |
| 7 | 10-7 | Neutral (at 25°C) |
| 11 | 10-11 | Basic |
| 14 | 10-14 | Strongly basic |
Calculating pH from Hydronium Concentration
Problem: Calculate the pH of a solution with \([\text{H}_3\text{O}^+] = 2.5 \times 10^{-3}\text{ mol dm}^{-3}\).
\[\text{pH} = -\log_{10}(2.5 \times 10^{-3}) = 2.60\]Sig Fig Rule: Since \(2.5\) has 2 significant figures, the pH must have 2 decimal places (\(2.60\)).
The Ionic Product of Water (Kw)
Pure water undergoes autoionisation:
H2O(l) ⇌ H+(aq) + OH-(aq)
At 25°C, Kw = [H+][OH-] = 1.0 x 10-14. Since [H+] = [OH-] in pure water, both equal 10-7, giving a neutral pH of 7.
Significant Figures in pH Values
Crucial IB Rule: The digits before the decimal point in a pH value indicate only the power of 10. Only the digits after the decimal point count as significant figures!
If \([\text{H}^+] = 3.45 \times 10^{-4}\text{ M}\) (3 s.f.), write \(\text{pH} = 3.462\) (3 decimal places).
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