Salt hydrolysis — pH of salt solutions (4 cases - SA - SB, SA - WB, WA - SB, WA - WB)

2.6.16 · Chemistry › Equilibrium

The Four Cases

Case 1: Strong Acid + Strong Base → Neutral salt

Example: NaCl, KNO₃, Na₂SO₄

Neutral kyun hai?

Na⁺ NaOH (strong base) se aaya hai → completely dissociated, Na⁺ ka koi tendency nahi ki woh OH⁻ wapas pakde
Cl⁻ HCl (strong acid) se aaya hai → completely dissociated, Cl⁻ ka koi tendency nahi ki woh H⁺ pakde
Water autoionize karta hai: H₂O ⇌ H⁺ + OH⁻, lekin equilibrium mein koi shift nahi
Result: [H⁺] = [OH⁻] = 10⁻⁷ M → pH = 7

Case 2: Strong Acid + Weak Base → Acidic salt

Example: NH₄Cl, NHNO₃, [NH₄]₂SO₄

Acidic kyun hai?

NH₄⁺ NH₃ (weak base, Kb = 1.8×10⁻⁵) ka conjugate acid hai
Cl⁻ HCl (strong) se hai → inert, koi hydrolysis nahi
NH₄⁺ dobara NH₃ banna chahta hai (apna weak parent):

$NH_{4}^{+} + H_{2} O ⇌ NH_{3} + H_{3} O^{+}$

Yeh reaction H₃O⁺ produce karta hai → [H⁺] badhta hai → pH < 7

Case 3: Weak Acid + Strong Base → Basic salt

Example: CH₃CONa, NaCN, KF

Basic kyun hai?

CH₃COO⁻ CH₃COOH (weak acid, Ka = 1.8×10⁻⁵) ka conjugate base hai
Na⁺ NaOH (strong) se hai → inert, koi hydrolysis nahi
CH₃COO⁻ dobara CH₃COOH banna chahta hai:

$C H_{3} C O O^{-} + H_{2} O ⇌ C H_{3} C O O H + O H^{-}$

Yeh OH⁻ produce karta hai → [OH⁻] badhta hai → pH > 7

Figure — Salt hydrolysis — pH of salt solutions (4 cases - SA - SB, SA - WB, WA - SB, WA - WB)

Case 4: Weak Acid + Weak Base → pH depends on Ka vs Kb

Example: CH₃COONH₄, NH₄CN

Complex kyun hai?

Cation (NH₄⁺) H⁺ produce karta hai: $NH_{4}^{+} + H_{2} O ⇌ NH_{3} + H_{3} O^{+}$
Anion (CH₃COO⁻) OH⁻ produce karta hai: $C H_{3} C O O^{-} + H_{2} O ⇌ C H_{3} C O O H + O H^{-}$
Competition: kaun sa reaction dominate karega?

Teen sub-cases:

Ka > Kb → acidic (H⁺ production jeet jaata hai)
Ka < Kb → basic (OH⁻ production jeet jaata hai)
Ka ≈ Kb → almost neutral

Formula WA/WB salt ka pH

$pH = \frac{1}{2} (pK_{w} + pK_{a} - pK_{b})$

First principles se derivation:

Dono hydrolysis reactions hoti hain: $N H_{4}^{+} + H_{2} O ⇋ N H_{3} + H_{3} O^{+} K_{h 1} = \frac{K _{w}}{K _{b}}$ $C H_{3} C O O^{-} + H_{2} O ⇌ C H_{3} C O O H + O H^{-} K_{h 2} = \frac{K _{w}}{K _{a}}$

Equilibrium par, dono H⁺ produce/consume karte hain:

Cation se: $[H^{+}]_{1}$ produce hota hai
Anion se: $[OH^{-}]$ produce hota hai, jo H⁺ consume karta hai Net [H⁺] dono ko balance karke aata hai: $[H^{+}] = \frac{K _{w} \cdot K _{a}}{K _{b}}$

Kyun? System equilibrium par pahunchta hai jahan dono hydrolysis reactions simultaneously satisfy hoti hain. Exact derivation mein coupled equilibria solve karne padte hain, lekin result yeh hai: $[H^{+}]^{2} = K_{w} \cdot \frac{K _{a}}{K _{b}}$

-log lein: $2 pH = - lo g K_{w} - lo g K_{a} + lo g K_{b}$ $2 pH = pK_{w} + pK_{a} - pK_{b}$ $pH = \frac{1}{2} (pK_{w} + pK_{a} - pK_{b})$

Note: Yeh formula concentration se independent hai — WA/WB salts ki ek unique feature!

Worked example Worked example — Ammonium acetate

Given: Ka(CH₃COOH) = 1.8×10⁻⁵, Kb(NH₃) = 1.8×10⁻⁵

Step 1: Ka vs Kb check karein Ka = Kb → pH ≈ 7 expect karein Yeh step kyun? Calculation se pehle pH ki direction predict karna.

Step 2: Formula se calculate karein $pH = \frac{1}{2} (14 + 4.74 - 4.74) = \frac{14}{2} = 7.0$ Yeh step kyun? Jab Ka = Kb hota hai, toh pKa aur pKb terms cancel ho jaate hain.

Result: Neutral solution, even though dono ions hydrolyze karte hain!

Example 2: NH₄CN (Ka of HCN = 6.2×10⁻¹⁰, Kb of NH₃ = 1.8×10⁻⁵) Step 1: Strengths compare karein pKa(HCN) = 9.21, pKb(NH₃) = 4.74 Ka < Kb → CN⁻ (base) NH₄⁺ (acid) se zyada strong hai → basic expect karein Yeh step kyun? CN⁻ NH₄⁺ se zyada OH⁻ produce karega. Step 2: Calculate karein $pH = \frac{1}{2} (14 + 9.21 - 4.74) = \frac{18.47}{2} = 9.24$ Yeh step kyun? Basic nature ko quantify karta hai.

Result: Basic solution (pH > 7) ✓

Summary Table

Salt Type	Example	Hydrolysis	pH	Formula
SA + SB	NaCl	Koi nahi	7	pH = 7
SA + WB	NH₄Cl	Cation	< 7	pH = ½(pKw - pKb - log C)
WA + SB	CH₃COONa	Anion	> 7	pH = ½(pKw + pKa + log C)
WA + WB	CH₃COONH₄	Dono	Depend karta hai	pH = ½(pKw + pKa - pKb)

Common mistake "Saare salts neutral hote hain kyunki acids aur bases cancel ho jaate hain"

Sahi kyun lagta hai: Neutralization reaction mein, H⁺ + OH⁻ → H₂O, toh lagta hai sab cancel ho gaya.

Steel-man argument: Yeh formation reaction ke liye sach hai (strong acid + strong base → salt + water), jahan reaction completion tak jaati hai.

Galat kyun hai: Formation ke baad, salt paani mein dissolve hota hai. Ab ions free agents hain. Agar woh weak parents se aaye hain, toh woh reactive hain — woh paani ki autoionization se H⁺ ya OH⁻ pakad sakte hain. Strong parent ke ions inert hain — woh already fully satisfied hain.

Fix: Neutralization (formation) aur hydrolysis (dissolution) ko alag samjho. Solution mein, ions ka paani ke saath apna equilibrium hota hai.

Memory hook: "Neutralization salt banata hai. Hydrolysis check karta hai ki woh neutral rehta hai ya nahi."

Recall Feynman: 12-saal ke bachche ko explain karo

Socho tumhare paas building blocks ka ek box hai (salt). Kuch blocks do strong pieces ko jodhkar banaye gaye the (strong acid + strong base). Agar tum unhe paani mein daalo, toh woh bas wahan baithe rehte hain — woh alag pieces ke roop mein khush hain aur paani se react nahi karte. pH 7 rehta hai (neutral).

Lekin kuch blocks banaye gaye the

The Four Cases

Case 1: Strong Acid + Strong Base → Neutral salt

Case 2: Strong Acid + Weak Base → Acidic salt

Case 3: Weak Acid + Strong Base → Basic salt

Case 4: Weak Acid + Weak Base → pH depends on Ka vs Kb

Summary Table

Concept Map