General Chemistry · Acid–Base Equilibria · ION-PRODUCT OF WATER
Ion-Product of Water Kw and pH
Water ionizes by itself (autoionization, 2H₂O ⇌ H₃O⁺ + OH⁻). If you add an acid or a base and change [H⁺],
what happens to [OH⁻]? If you heat pure water, what is its pH? Every value is calculated by solving exactly the charge balance and
Kw = [H⁺][OH⁻] (no approximation).
Estimated time 15 min · Prerequisites: equilibrium-constant expressions, Brønsted–Lowry acids and bases
Learning objectives After this activity you can …
use Kw = [H⁺][OH⁻] to calculate [H⁺] from [OH⁻] and the other way round.
explain that [OH⁻] gets smaller when [H⁺] gets larger, and that OH⁻ is present even in an acidic solution.
judge the change of neutral pH with temperature and the definition of neutral.
1) In every aqueous solution, [H⁺][OH⁻] = Kw (1.0×10⁻¹⁴ at 25 °C). 2) If the concentration of one ion goes up, predict what happens to the other.If one goes up 10 times, the other goes down to 1/10 — neither ever becomes 0.
3) Neutral is defined as [H⁺] = [OH⁻], not as pH = 7. Does neutral pH change when the temperature changes?When the temperature rises, Kw becomes larger, so neutral pH = ½pKw becomes smaller than 7.
[H⁺]–[OH⁻] seesaw (log bars)
Focus the graph. Up or right arrow raises the temperature by 1 °C; down or left arrow lowers it. The result is read aloud in the live region.
[H⁺]—
[OH⁻]—
[H⁺][OH⁻] = Kw—
Temperature and neutral pH (½pKw)
Current pH · acidic/neutral/basic—
Kw(T) · neutral pH—
Entry check Before you start — prerequisites and key terms
What do we call an aqueous solution in which [H⁺] > [OH⁻]?
AcidicNeutralBasic
Key terms
Autoionization (self-ionization) of water: water molecules pass a proton between them, forming H₃O⁺ and OH⁻. ·
Ion-product constant Kw: Kw = [H⁺][OH⁻], 1.0×10⁻¹⁴ at 25 °C. ·
Neutral: [H⁺] = [OH⁻]. Acidic means [H⁺] > [OH⁻]; basic means [OH⁻] > [H⁺]. ·
pH = −log[H⁺] (common, base-10 logarithm).
Predict Think first, before you observe
Pure water at body temperature (37 °C) has a pH of about 6.8. What is this water?
pH < 7, so it is acidicIt is pure water, so it is still neutralHeating makes more OH⁻, so it is basic
ConfidenceMedium
pH = —
Change the solute and the temperature and observe [H⁺] and [OH⁻].
The explanation opens after you lock in a prediction
Kw is an equilibrium constant, so it is constant at a given temperature. If HCl raises [H⁺] 10 times, the equilibrium shifts to the left and
[OH⁻] becomes 1/10. Even in 0.010 M HCl, OH⁻ is present at 1.0×10⁻¹² M — it is not zero. Soil and irrigation-water pH are measured on this same scale.
Kw = [H⁺][OH⁻] = 1.0×10⁻¹⁴ (25 °C)
Temperature: the neutral point moves
Autoionization is an endothermic reaction, so Kw increases with temperature (Le Chatelier). In pure water it is always true that
[H⁺] = [OH⁻] = √Kw, so neutral pH = ½pKw. At 37 °C this is about 6.8, but the water is still neutral.
Neutral: [H⁺] = [OH⁻] = √Kw, pH = ½ pKw
Explanation cards
The explanation cards "the product is constant" and "the neutral point" and the full key summary open after you lock in a prediction.
Limits of the model — Ideal behavior of dilute solutions is assumed (activity coefficient = 1). Near 0.1 M the real activities differ somewhat because of ionic-strength effects.
Kw(T) is calculated from a literature interpolation formula (Harned–Robinson) for 0–60 °C. HCl and NaOH are treated as fully dissociated.
Check Formative check — pass all items to complete
Q1Which statement about 0.010 M HCl at 25 °C is correct?
It is acidic, so there is no OH⁻ at allOH⁻ is present at 1.0×10⁻¹² MOH⁻ is 1.0×10⁻⁷ M, the same as in pure water
Hint
Set the solute to HCl and the concentration to 0.010 M (log = −2), then read [OH⁻].
Q2 · Hands-on taskWith pure water, move the temperature slider to reach —, then press [Check]. Also check that [H⁺] and [OH⁻] are equal.
Now: —
Q3 · Calculation—
Hint
—
Q4 · Fill in the blankFill in the blank: At any temperature, a solution with [H⁺] = [OH⁻] is a [_____] solution.
Hint
It is neither acidic nor basic. It is defined by comparing the two ion concentrations, not by a pH number.
Q5 · Apply (higher-order, not required for completion)At 20 °C the ion product of heavy water (D₂O) is Kw = 8.9×10⁻¹⁶. What is [D⁺] in neutral D₂O, in M?
Hint
If it is neutral, [D⁺] = [OD⁻] = x, and x² = Kw.
Reflect Reflect — metacognition · completion
My prediction: Not predicted yet
In one sentence, explain why pure water at 37 °C is not acidic even though its pH is 6.8:
Apply Use the idea in a new context (not required for completion)
Human blood is kept at about pH 7.4 at 37 °C. Compare this with the neutral pH at 37 °C (read it in the simulation).
Is blood acidic, neutral or basic? Is the difference larger or smaller than when you judge it against the 25 °C reference (pH 7)? Explain in one or two sentences.
Next up Next up
The pH scale (pH, pOH and pKw) → Ka of weak acids and percent ionization → acid–base titration curves.
COMPLETE · Completed — all checks passed.
Worksheet — Ion-product of water Kw and pH
Name ________ Class ________ Date ________
Write >, = or < in each bracket. For all three bottles at 25 °C, [H⁺][OH⁻] = [_______].
1. Predict — Is pure water at 37 °C (pH about 6.8) acidic, neutral or basic? Why?
2. Observe — 0.010 M HCl: [OH⁻] = ________ M · pure water at 37 °C: Kw = ________, neutral pH = ______
3. Calculate — At 25 °C, a solution has [OH⁻] = 1.8×10⁻⁹ M. [H⁺] = ________ M; acidic, neutral or basic: ______
4. Fill in the blank — At any temperature, a solution with [H⁺] = [OH⁻] is a [_____] solution.
5. Conclusion — Why does neutral pH become smaller than 7 when the temperature rises?
Self-check answers (mark your own work after solving) 1.____ 2.____ 3.____ 4.____ 5.____
[Answer key — teacher] bottles: >, =, < · product 1.0×10⁻¹⁴ · 1 neutral ([H⁺]=[OH⁻]) · 2 1.0×10⁻¹² M; Kw≈2.4×10⁻¹⁴ (literature), neutral pH≈6.81 · 3 5.6×10⁻⁶ M, acidic · 4 neutral · 5 autoionization is endothermic, so Kw increases and √Kw increases
Teacher notes — open the lesson plan
Lesson plan · 5E phase and time
Explore · Explain stage, 15 min. Works right after autoionization of water, before or after the pH scale is introduced.
Demo in 3 steps
(1) Water at 25 °C → HCl 0.010 M: [OH⁻]=1.0×10⁻¹² M (not zero).
(2) Raise the HCl concentration 10 times at each step and watch [OH⁻] fall to 1/10 each time (seesaw; the product does not change).
(3) Go back to pure water and change the temperature 0→60 °C: neutral pH 7.47→6.51, yet [H⁺]=[OH⁻].
3 key questions
"Is there no OH⁻ at all in an acidic solution?"
"If [H⁺] goes up 100 times, what happens to [OH⁻]?"
"Can we call water with pH 6.8 acidic? What was the definition of neutral?"
Common misconceptions
MC-kw-01: "An acidic solution has no OH⁻" → Kw is constant, so [OH⁻]=Kw/[H⁺] > 0.
MC-kw-02: "Water at 37 °C has pH 6.8, so it is acidic" → neutral is defined as [H⁺]=[OH⁻]; neutral pH = ½pKw(T).
Answer key
Prediction: neutral · Q1: b · Q2: target by level (pure water, change the temperature) · Q3: Basic 1.0×10⁻¹² / Standard 5.6×10⁻⁶ / Advanced 1.4×10⁻⁷ M · Q4: neutral · Q5: 3.0×10⁻⁸ M.
Sources of values · cautions (check by PI)
Reference values: Kw = 1.0×10⁻¹⁴ (25 °C), Kw = 2.1×10⁻¹⁴ at 37 °C (a value often given in exercises), D₂O 8.9×10⁻¹⁶.
Two values for Kw at 37 °C: 2.1×10⁻¹⁴ and 2.4×10⁻¹⁴ are both found in teaching materials. The literature value (Harned–Robinson, CRC) is 2.4×10⁻¹⁴ (pKw 13.62), and the Kw(T) curve in this simulation also gives 2.40×10⁻¹⁴. Advanced Q3 uses 2.1×10⁻¹⁴ as given data — point out in class why the two values differ.
Kw(T) curve: Harned & Robinson (1940) interpolation log Kw = −4470.99/T + 6.0875 − 0.01706T (T in K, 0–60 °C). 25 °C 1.01×10⁻¹⁴ (shown as 1.0×10⁻¹⁴, 2 significant figures), 37 °C 2.40×10⁻¹⁴, 60 °C 9.6×10⁻¹⁴. Agrees with the CRC Handbook ion-product table.
Difference: 2.1×10⁻¹⁴ at 37 °C (neutral pH 6.84) is smaller than the literature 2.4×10⁻¹⁴ (6.81). Both give "about 6.8", so the learning conclusion is the same. Advanced Q3 gives the reference value as problem data.
Prerequisites
Equilibrium-constant expressions (pure liquids omitted), Le Chatelier's principle, calculations with powers of ten and logarithms.
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