📘 IB Understanding
The pH and pOH scales are logarithmic, inverse measures of [H⁺] and [OH⁻]. At 25 °C, pH + pOH = 14.
Key Equations
\[\text{pH} = -\log[H^+] \qquad [H^+] = 10^{-\text{pH}}\]
\[\text{pOH} = -\log[OH^-] \qquad [OH^-] = 10^{-\text{pOH}}\]
\[K_w = [H^+][OH^-] = 1.00 \times 10^{-14} \text{ at } 25^\circ\text{C}\]
\[\text{pH} + \text{pOH} = pK_w = 14.00 \text{ at } 25^\circ\text{C}\]
Worked Examples
1. Strong acid: Calculate the pH of 0.10 M HCl.
HCl ionises 100%, so [H⁺] = 0.10 M
\(\text{pH} = -\log(0.10) = \textbf{1.00}\)
2. Strong base: Calculate the pH of 0.0044 M Ca(OH)₂.
Ca(OH)₂ gives 2 OH⁻ ions: [OH⁻] = 2 × 0.0044 = 0.0088 M
\(\text{pOH} = -\log(0.0088) = 2.06\)
\(\text{pH} = 14.00 - 2.06 = \textbf{11.94}\)
📋 Exam Tips
- For polybasic bases like Ca(OH)₂, multiply molarity by 2 for [OH⁻]
- Kw = 10⁻¹⁴ and neutral pH = 7 are only valid at 25 °C
- Autoionisation of water is endothermic, so Kw increases at higher temperatures
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