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Kw increases with temperature because the autoionisation of water is endothermic, so equilibrium shifts right. Free AQA notes and 15 questions answered.
Kw Calculations and Temperature Dependence is part of Acids and bases (A-level only) in A Level AQA Chemistry.
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Kw increases with temperature because the autoionisation of water is endothermic, so equilibrium shifts right. Free AQA notes and 15 questions answered.
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Use this lesson to stay inside Acids and bases (A-level only) while connecting the detail back to the wider Physical chemistry topic.
Read the core explanations from Kw Calculations and Temperature Dependence before testing yourself from memory.
You already know how to find the pH of a strong acid: take the concentration, apply pH = -log10[H+], done. Strong bases look harder because you are given [OH-], not [H+]. The bridge between them is Kw — the ionic product of water.
Water autoionises according to the equilibrium $H_2O(l) \rightleftharpoons H^+(aq) + OH^-(aq)$. Because this is an equilibrium, we can write an expression for its equilibrium constant. Since the concentration of pure water is effectively constant, it is absorbed into the constant, giving $K_w = [H^+][OH^-]$.
The power of this expression is that it links [H+] and [OH-] in every aqueous solution. If you know one, you can always find the other. For a strong base, you know [OH-] directly from its concentration, so finding [H+] — and therefore pH — is a two-line calculation.
A strong base dissociates completely in water. Sodium hydroxide, NaOH, is the classic example: $NaOH(aq) \rightarrow Na^+(aq) + OH^-(aq)$. A 0.10 mol dm-3 solution of NaOH gives [OH-] = 0.10 mol dm-3 directly. From there, the route to pH has three clear steps.
Worked example: Calculating the pH of 0.10 mol dm⁻³ NaOH at 298 K
Calculate the pH of a 0.10 mol dm⁻³ solution of sodium hydroxide at 298 K. (Kw = 1.00 × 10⁻¹⁴ mol² dm⁻⁶)
Answer: pH = 13.00 at 298 K
Notice the logic: you never need to memorise a separate formula for bases. The single relationship $K_w = [H^+][OH^-]$ does all the work. The only thing that changes between different problems is the value of Kw — and that depends on temperature.
Here is where the concept deepens. Kw is an equilibrium constant, and you know from your study of equilibria that K only changes when temperature changes. The autoionisation of water is endothermic — energy must be absorbed to break O–H bonds and form the ions.
By Le Chatelier's principle, increasing temperature shifts the equilibrium to the right, producing more H+ and OH- ions. This means Kw increases as temperature rises. The table below shows how dramatically Kw changes across a realistic temperature range.
| Temperature / °C | Kw / mol² dm⁻⁶ | pH of pure water | Nature of pure water |
|---|---|---|---|
| 0 | 1.14 × 10⁻¹⁵ | 7.47 | Neutral |
| 25 (298 K) | 1.00 × 10⁻¹⁴ | 7.00 | Neutral |
| 37 (body temperature) | 2.51 × 10⁻¹⁴ | 6.80 | Neutral |
| 60 | 9.55 × 10⁻¹⁴ | 6.51 | Neutral |
| 100 | 5.13 × 10⁻¹³ | 6.14 | Neutral |
Every entry in that table describes pure water, yet the pH values range from 7.47 down to 6.14. This is one of the most important conceptual points in this topic: neutral does not always mean pH 7. Neutrality means [H+] = [OH-], and the pH at which that occurs depends on the temperature.
Now that you can see Kw varies with temperature, you need to be able to calculate the neutral pH at any temperature where Kw is given. The logic is clean: in a neutral solution, [H+] = [OH-], so $K_w = [H^+]^2$, which gives $[H^+] = \sqrt{K_w}$.
Worked example: Finding the neutral pH at 37°C (body temperature)
At 37°C, Kw = 2.51 × 10⁻¹⁴ mol² dm⁻⁶. Calculate the pH of pure water at this temperature.
Answer: pH of pure water at 37°C = 6.80 (neutral, not acidic)
This result has real biological relevance. Blood plasma at body temperature has a pH of approximately 7.4, which is above the neutral pH of 6.80 at 37°C — meaning blood is genuinely basic at body temperature, not neutral. The reference point for neutrality shifts with temperature.
Exam questions frequently give you a Kw value at a temperature other than 298 K and ask you to calculate the pH of a strong base. The method is identical to what you practised in Section 2 — the only change is the number you substitute for Kw. This is where students lose marks by defaulting to 1.00 × 10-14 out of habit.
Worked example: pH of NaOH at a non-standard temperature
Calculate the pH of a 0.050 mol dm⁻³ solution of NaOH at 60°C, where Kw = 9.55 × 10⁻¹⁴ mol² dm⁻⁶.
Answer: pH = 11.72 at 60°C
You have seen the pattern — Kw increases with temperature. Now let us pin down why, using the language the examiner expects. The autoionisation of water is endothermic: $\Delta H > 0$. By Le Chatelier's principle, raising the temperature shifts the position of equilibrium to the right, favouring the products (H+ and OH-).
Because Kw is an equilibrium constant, and equilibrium constants respond to temperature changes, Kw increases as temperature rises. Crucially, changing concentration or pressure does not change Kw — only temperature does. This is the same principle you apply to Kc and Kp in other equilibrium contexts.
This connects directly back to the equilibrium constant principles from earlier in your course. Kw behaves exactly like Kc: temperature is the only variable that changes its value. The position of equilibrium can shift without Kw changing — for example, adding acid shifts the equilibrium left, but Kw stays constant at that temperature.
The calculations in this topic are short, but the marks are easy to drop through predictable errors. The following guidance targets the specific traps that appear most frequently in AQA mark schemes.
To consolidate everything: Kw is the single tool that connects [H+] and [OH-] in any aqueous solution. Use it to find pH from a strong base concentration, and remember that its value — and therefore the neutral pH — shifts with temperature because the autoionisation of water is endothermic. These two spec points are tightly linked, and exam questions frequently test both in a single calculation.
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Move to the related lessons or back to the topic page when you need the wider sequence before exam-style practice.
Kw increases with temperature because the autoionisation of water is endothermic. By Le Chatelier's principle, raising the temperature shifts the equilibrium H₂O ⇌ H⁺ + OH⁻ to the right, producing more H⁺ and OH⁻ ions, so Kw rises from 1.00 × 10⁻¹⁴ at 25 °C to 5.13 × 10⁻¹³ at 100 °C.
The value of Kw, the ionic product of water, is 1.00 × 10⁻¹⁴ mol² dm⁻⁶ at 298 K. It is not a fixed number for all conditions: Kw increases with temperature, to 5.13 × 10⁻¹³ mol² dm⁻⁶ at 100 °C.
To calculate the pH of a strong base, take [OH⁻] from its concentration, find [H⁺] = Kw ÷ [OH⁻], then use pH = −log₁₀[H⁺]. For 0.10 mol dm⁻³ NaOH at 298 K, [H⁺] = 1.00 × 10⁻¹⁴ ÷ 0.10 = 1.00 × 10⁻¹³ mol dm⁻³, so pH = 13.00.
Kw changes with temperature, and temperature is the only thing that changes it. Like Kc, Kw is an equilibrium constant, so changing concentration or pressure does not change it; adding acid shifts the equilibrium left, but Kw stays constant at that temperature.
Kw at any temperature is the product [H⁺][OH⁻]; in pure water [H⁺] = [OH⁻], so Kw = [H⁺]². For example, at 37 °C pure water has [H⁺] = 1.58 × 10⁻⁷ mol dm⁻³, giving Kw = 2.51 × 10⁻¹⁴ mol² dm⁻⁶. In calculations, the Kw value given for that temperature must be used.
Kw values for water rise with temperature: 1.14 × 10⁻¹⁵ mol² dm⁻⁶ at 0 °C (pH 7.47), 1.00 × 10⁻¹⁴ at 25 °C (pH 7.00), 2.51 × 10⁻¹⁴ at 37 °C (pH 6.80), 9.55 × 10⁻¹⁴ at 60 °C (pH 6.51) and 5.13 × 10⁻¹³ at 100 °C (pH 6.14).
Pure water is always neutral, even though its pH falls as temperature rises, to 6.80 at 37 °C and 6.14 at 100 °C. Neutral means [H⁺] = [OH⁻], and both concentrations increase equally, so pH 7 is only the neutral point at 298 K.
To find the neutral pH at a given temperature, use [H⁺] = √Kw, because [H⁺] = [OH⁻] in a neutral solution. At 37 °C, Kw = 2.51 × 10⁻¹⁴ mol² dm⁻⁶, so [H⁺] = 1.584 × 10⁻⁷ mol dm⁻³ and pH = 6.80.
At 298 K, pH + pOH = pKw = 14, where pOH = −log₁₀[OH⁻]. For 0.10 mol dm⁻³ NaOH, pOH = 1.00, so pH = 14.00 − 1.00 = 13.00, which is a reliable cross-check on a Kw calculation.
Kw increases as temperature rises. It is 1.14 × 10⁻¹⁵ mol² dm⁻⁶ at 0 °C, 1.00 × 10⁻¹⁴ at 25 °C, 2.51 × 10⁻¹⁴ at 37 °C, 9.55 × 10⁻¹⁴ at 60 °C and 5.13 × 10⁻¹³ at 100 °C, because the autoionisation of water is endothermic.
Kw increases with temperature. The autoionisation of water, H₂O ⇌ H⁺ + OH⁻, is endothermic with ΔH > 0, so by Le Chatelier's principle raising the temperature shifts the equilibrium to the right, producing more H⁺ and OH⁻ ions and a larger Kw.
When temperature increases, Kw increases and the pH of pure water falls, from 7.00 at 25 °C to 6.14 at 100 °C. The water is still neutral, because [H⁺] still equals [OH⁻]; both concentrations have increased equally, so neutral does not always mean pH 7.
Kw at room temperature, 298 K or 25 °C, is 1.00 × 10⁻¹⁴ mol² dm⁻⁶. At this temperature pure water has [H⁺] = [OH⁻] = 1.00 × 10⁻⁷ mol dm⁻³, so its pH is 7.00.
The pH of 0.050 mol dm⁻³ NaOH at 60 °C, where Kw = 9.55 × 10⁻¹⁴ mol² dm⁻⁶, is 11.72. [H⁺] = Kw ÷ [OH⁻] = 9.55 × 10⁻¹⁴ ÷ 0.050 = 1.91 × 10⁻¹² mol dm⁻³. Using 1.00 × 10⁻¹⁴ here would be wrong, as that value only applies at 298 K.
Blood is basic at body temperature. Blood plasma at 37 °C has a pH of approximately 7.4, which is higher than the neutral pH of 6.80 at 37 °C, where Kw = 2.51 × 10⁻¹⁴ mol² dm⁻⁶. The reference point for neutrality shifts with temperature.