Ionic product of water Kw = 10⁻¹⁴ at 25 °C
The autoionization equilibrium
Why does this happen? Water is polar. The δ⁺ hydrogen of one molecule is attracted to the δ⁻ oxygen of another. Occasionally, thermal energy causes a complete proton transfer. It's rare—only about 2 out of every 10⁹ water molecules are ionized at any moment—but it's always happening.
Deriving Kw from first principles
Step 1: Write the equilibrium expression
For any equilibrium, we write:
For water autoionization:
Why this form? Each concentration term gets an exponent equal to its stoichiometric coefficient. Water appears twice on the left (as reactant), so it's squared in the denominator.
Step 2: Recognize that [H₂O] is essentially constant
Pure water has a molarity of:
Why can we treat this as constant? When only10⁻⁷ M of water ionizes, we go from 55.5 M to 55.4999 M—a negligible change. The concentration of liquid water doesn't meaningfully change during ionization.
Step 3: Absorb the constant into a new equilibrium constant
Since [H₂O] is constant:
Define Kw (the ionic product of water):
where
Step 4: Determine Kw experimentally at 25 °C
Conductivity measurements show that pure water at 25 °C has:
- M
- M
Therefore:
Critical insight: This relationship holds for ANY aqueous solution, not just pure water. If you add acid and raise [H⁺], the [OH⁻] must decrease to keep the product at 10⁻¹⁴. If you add base and raise [OH⁻], the [H⁺] must decrease proportionally.
Why Kw depends on temperature
By Le Chatelier's principle: Increasing temperature shifts equilibrium toward products (more ions). Therefore, Kw increases with temperature.
| Temperature | Kw value |
|---|---|
| 0 °C | 1.14 × 10⁻¹⁵ |
| 25 °C | 1.00 × 10⁻¹⁴ |
| 50 °C | 5.47 × 10⁻¹⁴ |
| 100 °C | 5.13 × 10⁻¹³ |
Key point: At 50 °C, neutral water has [H⁺] = 2.34 × 10⁻⁷ M (pH = 6.63), but it's still neutral because [H⁺] = [OH⁻]. Neutral doesn't always mean pH = 7!
Worked examples
Solution: Use
Why this step? We rearrange the Kw expression algebraically. The product must stay constant, so if [H⁺] is large (acidic), [OH⁻] must be proportionally small.
Check: ✓
Solution:
Why this step? In basic solutions, [OH⁻] is large, so [H⁺] must be small to maintain the 10⁻¹⁴ product. The solution is basic (pH = 11), but H⁺ ions still exist—they're just very dilute.
Solution: In pure water, . Let this value be .
Why this step? The autoionization equation shows one H⁺ and one OH⁻ form together, so their concentrations must be equal in pure water.
pH calculation:
Is this acidic? No! It's neutral at 50 °C because [H⁺] = [OH⁻]. The pH of neutrality shifts with temperature.
Solution: HCl is a strong acid:
The added H⁺ shifts the water equilibrium:
This consumes OH⁻ ions. The new [OH⁻] is:
Verification:
> K_w = (0.01)(10^{-12}) = 10^{-14} > $$-\log K_w = -\log[\ce{H+}] - \log[\ce{OH-}]$$ $$\text{p}K_w = \text{pH} + \text{pOH}$$At 25 °C: \text{p}K_w = 14, so:$$\boxed{\text{pH} + \text{pOH} = 14}$$ **Why this is useful:** You can instantly convert between pH and pOH. If pH = 3, then pOH = 11. If you know [OH⁻], calculate pOH, then subtract from 14 to get pH. > [!recall]- Explain it to a 12-year-old > Imagine a crowded room where people are constantly shaking hands and letting go. Water molecules are like that—they're always bumping into each other, and occasionally one grabs a tiny positive piece (a proton) from another. When this happens, you get one molecule with an extra positive charge (H⁺) and one with an extra negative charge (OH⁻). They don't stay apart for long—they usually find each other and recombine into normal water. But at any moment, a few pairs are always separated. The number 10⁻¹⁴ tells us how many of these separated pairs exist. It's like saying "in a crowd of 10million handshakes, only 1 pair is separated at any moment." That's how rare it is! Here's the magic: if you add lemon juice (acid), you're dumping tons of H⁺ into the room. Now there are so many H⁺ ions that they quickly grab all the OH⁻ ions and combine. The number of free OH⁻ ions drops. But the rule stays the same—the number of H⁺ times the number of OH⁻ always equals 10⁻¹⁴. It's like a seesaw: when one side goes up, the other *must* go down to keep the balance. > [!mnemonic] Remember Kw = 10⁻¹⁴ > **"K-water is won (1) over ten thousand trillion (10¹⁴)"** Or picture: **K**w at **25**°C = **1**0⁻**14** → "Quarter-century (25) gives you1 with 14 zeros below" For pH + pOH = 14: "**P**ositive **H** plus **P**ositive **OH** equals **P**erfect **14**" ## Connections - [[Le Chatelier's principle]] — explains why Kw increases with temperature - [[pH and pOH scale]] — both derived from Kw - [[Strong acids and bases]] — ionize completely, shifting water equilibrium - [[Buffer solutions]] — use Kw to calculate conjugate base concentrations - [[Common ion effect]] — adding ions suppresses water ionization - [[Solubility product Ksp]] — similar logic for ionic solid equilibria - [[Arrhenius theory]] — defines acids/bases by their effect on [H⁺] and [OH⁻] - [[Weak acids Ka]] — use Kw to find Kb from Ka: $K_w = K_a \times K_b$ --- #flashcards/chemistry What is the ionic product of water Kw at 25 °C? :: Kw = 1.0 × 10⁻¹⁴ = [H⁺][OH⁻] Write the equation for autoionization of water :: H₂O(l) ⇌ H⁺(aq) + OH⁻(aq) OR2H₂O(l) ⇌ H₃O⁺(aq) + OH⁻(aq) If [H⁺] = 10⁻³ M at 25 °C, what is [OH⁻]? ::: [OH⁻] = Kw/[H⁺] = 10⁻¹⁴/10⁻³ = 10⁻¹ M Why is Kw treated as a constant even though water concentration decreases during ionization? ::: Because [H₂O] ≈ 55.5 M and only ~10⁻⁷ M ionizes, the change is negligible (55.5 vs 55.4999999 M). We absorb the essentially constant [H₂O]² term into Kw. How does temperature affect Kw and why? ::: Kw increases with temperature because autoionization is endothermic (ΔH° > 0). By Le Chatelier's principle, heat shifts equilibrium toward products (more H⁺ and OH⁻). At 25 °C, what is the relationship between pH and pOH? :: pH + pOH = 14 (because pKw = 14 at this temperature) In pure water at 50 °C, Kw = 5.47 × 10⁻¹⁴. Find [H⁺] :: [H⁺] = [OH⁻] = √Kw = √(5.47 × 10⁻¹⁴) = 2.34 × 10⁻⁷ M (pH = 6.63, still neutral!) True or false: Adding HCl to water increases the value of Kw :: False. Kw only depends on temperature. Adding HCl increases [H⁺] but decreases [OH⁻] so that [H⁺][OH⁻] remains constant at 10⁻¹⁴. Why is pH 7 not always neutral? ::: Neutral means [H⁺] = [OH⁻], which occurs when [H⁺] = √Kw. Since Kw changes with temperature, the neutral pH changes. At 25 °C, neutral is pH 7, but at 50 °C, neutral is pH 6.63. If [OH⁻] = 1.0 × 10⁻⁴ M, calculate [H⁺] and identify if the solution is acidic or basic ::: [H⁺] = 10⁻¹⁴/10⁻⁴ = 10⁻¹⁰ M. Since [OH⁻] > [H⁺], the solution is basic (pH = 10, pOH = 4). What is the molarity of pure water and why can it be treated as constant? ::: [H₂O] = 1000 g/L ÷ 18 g/mol = 55.5 M. It's essentially constant because the tiny amount that ionizes (~10⁻⁷ M) is negligible compared to 55.5 M. Express Kw in terms of Ka and Kb for conjugate acid-base pair ::: Kw = Ka × Kb (at a given temperature) ## 🖼️ Concept Map ```mermaid flowchart TD W[Water is polar] -->|enables proton transfer| A[Autoionization equilibrium] A -->|H2O gives H plus and OH minus| KC[Equilibrium expression Kc] KC -->|H2O conc 55.5 M constant| ABS[Absorb H2O into constant] ABS -->|defines| KW[Kw = H plus times OH minus] KW -->|measured at 25 C| VAL[Kw = 1.0e-14] VAL -->|from| CONC[H plus = OH minus = 1.0e-7 M] KW -->|holds for| AQ[Any aqueous solution] AQ -->|add acid raises H plus| INV[OH minus decreases inversely] KW -->|controls| PH[pH scale 0 to 14] ENDO[Endothermic +56 kJ/mol] -->|Le Chatelier| TEMP[Kw rises with temperature] TEMP -->|changes| VAL ``` ## 🔊 Hinglish (regional understanding) > [!intuition]- Hinglish mein samjho > Pani ka ionic product (Kw) ek bahut important concept hai equilibrium mein. Dekhiye, pani ke molecules itne simple nahi hain jitna dikhte hain. Actually, har second mein kuch pani ke molecules apne ap se toot jate hain aur H⁺ aur OH⁻ ions ban jaate hain. Ye process autoionization kehlata hai. Imagine karo jaise ek bheed mein log hath milate hain aur chhod dete hain continuously—waisa hi pani ke molecules mein hota hai. > > Ab 25°C temperature par, ye tote hue ions ki sankhya itni kam hai kiagar hum unka product nikalte hain ([H⁺] × [OH⁻]), to woh exactly 1.0 × 10⁻¹⁴ ata hai. Iskoum Kw bolte hain. Ye value sirf temperature par depend karti hai. Agar tum pani mein acid add karo to [H⁺] badh jayega, lekin automatically [OH⁻] kam ho jayega taki product 10⁻¹⁴ hi rahe. Ye seesaw jaisa hai—ek side upar, dosri neeche. > > Interesting baat ye hai ki jab temperature badhta hai (jaise 50°C ya 100°C), to Kw bhi badh jata hai kyunki pani ka ionization endothermic process hai (heat absorb hota hai). Isliye hot pani mein zyada ions milenge. Aur ek common mistake jo students karte hain woh ye hai ki woh sochte hain pH 7 hamesha neutral hota hai. Actually, neutral ka matlab hai [H⁺] = [OH⁻], jo25°C par pH 7 deta hai, lekin higher temperatures par neutral pH kam ho jata hai (jaise 50°C par neutral pH 6.63 hai). Ye chemistry mein bahut critical concept hai kyunki isse pora pH scale, acid-base reactions, aur buffer solutions samajhne mein help milti hai. ![[audio/2.6.09-Ionic-product-of-water-Kw-=-10−14-at-25-°C.mp3]]