CHEMCA
EXAM MASTER FORMULA SHEET
Chemical & Ionic Equilibrium
High-Yield Content for JEE Main, Advanced & NEET
1. Chemical Equilibrium
Law of Mass Action:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
\(K_p\) and \(K_c\) Relation:
\[ K_p = K_c(RT)^{\Delta n_g} \]
\(\Delta n_g = \text{moles of gaseous prod. - react.}\)
Thermodynamic Relation:
\[ \Delta G = \Delta G^\circ + RT \ln Q \]
At Equilibrium (\(\Delta G = 0\)): \[ \Delta G^\circ = -2.303 RT \log K_{eq} \]
2. pH Scale & Ostwald's Law
Ionic Product of Water (\(K_w\))
\(10^{-14} \text{ (at 25°C)}\)
pH Definition
\(-\log [H^+]\)
Relation
\(pH + pOH = 14\)
Ostwald Dilution Law (Weak Electrolytes):
\[ \alpha = \sqrt{\frac{K_a}{C}} \quad (\text{if } \alpha < 0.05) \]
\[ [H^+] = C\alpha = \sqrt{K_a \cdot C} \implies pH = \frac{1}{2}[pK_a - \log C] \]
3. Buffer Solutions
Acidic Buffer:
(Weak Acid + Salt with Strong Base)
\[ pH = pK_a + \log \frac{[\text{Salt}]}{[\text{Acid}]} \]
Basic Buffer:
(Weak Base + Salt with Strong Acid)
\[ pOH = pK_b + \log \frac{[\text{Salt}]}{[\text{Base}]} \]4. Salt Hydrolysis Summary
| Type of Salt | Hydrolysis Const. (\(K_h\)) | pH Formula |
|---|---|---|
| SA + WB (\(NH_4Cl\)) | \(K_w/K_b\) | \(7 - \frac{1}{2}(pK_b + \log C)\) |
| WA + SB (\(CH_3COONa\)) | \(K_w/K_a\) | \(7 + \frac{1}{2}(pK_a + \log C)\) |
| WA + WB (\(CH_3COONH_4\)) | \(K_w/(K_a \cdot K_b)\) | \(7 + \frac{1}{2}(pK_a - pK_b)\) |
5. Solubility Product (\(K_{sp}\))
For salt \(A_xB_y \rightleftharpoons xA^{y+} + yB^{x-}\):
\[ K_{sp} = (xs)^x (ys)^y = x^x y^y s^{(x+y)} \]
AB Type (\(AgCl\))
\(K_{sp} = s^2\)
AB\(_2\) Type (\(PbCl_2\))
\(K_{sp} = 4s^3\)
A\(_2\)B\(_3\) Type (\(As_2S_3\))
\(K_{sp} = 108s^5\)
Precipitation Condition:
If \(\text{Ionic Product } (Q_{sp}) > K_{sp}\) \(\implies\) Precipitation occurs.
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