Chemca Formula Sheet - Equilibrium

CHEMCA

EXAM MASTER FORMULA SHEET

Chemical & Ionic Equilibrium

Ultimate Revision for JEE Main, Advanced & NEET

1. Chemical Equilibrium & Thermodynamics

Law of Mass Action:

For $aA + bB \rightleftharpoons cC + dD$

\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]

Pure solids and pure liquids are taken as unity (1).

$K_p$ and $K_c$ Relation:

\[ K_p = K_c(RT)^{\Delta n_g} \]

$\Delta n_g = (\text{moles of gaseous prod.}) - (\text{moles of gaseous react.})$

Thermodynamic Relation:

\[ \Delta G = \Delta G^\circ + RT \ln Q \]

At Eq ($Q = K, \Delta G = 0$):

\[ \Delta G^\circ = -2.303 RT \log K_{eq} \]

Van 't Hoff Equation:

Temperature dependence of Equilibrium Constant

\[ \log\left(\frac{K_2}{K_1}\right) = \frac{\Delta H^\circ}{2.303 R} \left[ \frac{T_2 - T_1}{T_1 T_2} \right] \]

Endothermic ($\Delta H>0$): $T \uparrow \implies K \uparrow$
Exothermic ($\Delta H<0$): $T \uparrow \implies K \downarrow$

Le Chatelier's Principle (Shift to undo change)

• Pressure Increase: Shifts equilibrium towards fewer moles of gas ($\Delta n_g$).
• Volume Increase: Pressure drops, shifts towards more moles of gas.
• Inert Gas added at Constant Volume: No shift (partial pressures remain same).
• Inert Gas added at Constant Pressure: Volume increases, shifts towards more gaseous moles.
• Catalyst: Reaches equilibrium faster, but NO effect on the value of $K_{eq}$ or final yield.

2. Acids, Bases & Ionic Equilibrium

Ionic Product of Water ($K_w$) $10^{-14}$ (at 25°C / 298K)

pH & pOH $-\log [H^+]$ & $-\log [OH^-]$

Universal Relation $pH + pOH = pK_w$ (= 14 at 25°C)

Conjugate Acid-Base Pair $K_a \times K_b = K_w$

Temperature Effect on $K_w$: Auto-ionization of water is Endothermic. As $T \uparrow$, $K_w \uparrow$.
At $90^\circ C$, $K_w \approx 10^{-12}$. Therefore, at $90^\circ C$, neutral $pH = 6$. (pH 7 is BASIC at 90°C!).

Ostwald's Dilution Law (For Weak Electrolytes):

Degree of Dissociation ($\alpha$):

\[ \alpha = \sqrt{\frac{K_a}{C}} \quad (\text{Valid if } \alpha < 0.05) \]

Concentration & pH:

\[ [H^+] = C\alpha = \sqrt{K_a \cdot C} \] \[ pH = \frac{1}{2}[pK_a - \log C] \]

3. Buffer Solutions

Solutions which resist change in pH upon addition of small amounts of strong acid or strong base.

Acidic Buffer (WA + Salt of WA w/ SB)

E.g., $CH_3COOH + CH_3COONa$

\[ pH = pK_a + \log \frac{[\text{Salt}]}{[\text{Acid}]} \]

Basic Buffer (WB + Salt of WB w/ SA)

E.g., $NH_4OH + NH_4Cl$

\[ pOH = pK_b + \log \frac{[\text{Salt}]}{[\text{Base}]} \]

Buffer Capacity ($\beta$ or $\phi$):

\[ \beta = \frac{dC}{dpH} \]

Moles of strong acid/base added per liter to change pH by 1 unit. Maximum when $[Salt] = [Acid]$.

Effective Buffer Range:

\[ pH = pK_a \pm 1 \]

Buffer works best when ratio of Salt to Acid is between 1/10 and 10.

4. Salt Hydrolysis Summary

Reaction of cation or anion (or both) of a salt with water to produce acidity or basicity.

Type of Salt & Nature	Hydrolysis Const. ($K_h$)	Degree of Hyd. ($h$)	pH Formula (at 25°C)
Strong Acid + Strong BaseNeutral ($NaCl, KNO_3$)	No Hydrolysis		$pH = 7$
Strong Acid + Weak BaseAcidic ($NH_4Cl$)	$\frac{K_w}{K_b}$	$\sqrt{\frac{K_w}{K_b \cdot C}}$	$7 - \frac{1}{2}(pK_b + \log C)$
Weak Acid + Strong BaseBasic ($CH_3COONa$)	$\frac{K_w}{K_a}$	$\sqrt{\frac{K_w}{K_a \cdot C}}$	$7 + \frac{1}{2}(pK_a + \log C)$
Weak Acid + Weak BaseDepends on Ka/Kb ($CH_3COONH_4$)	$\frac{K_w}{K_a \cdot K_b}$	$\sqrt{\frac{K_w}{K_a \cdot K_b}}$	$7 + \frac{1}{2}(pK_a - pK_b)$ (Independent of Concentration C)

5. Solubility Product ($K_{sp}$) & Precipitation

For sparingly soluble salt $A_xB_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)$:

\[ K_{sp} = [A^{y+}]^x [B^{x-}]^y = (xs)^x (ys)^y = x^x y^y s^{(x+y)} \]

Where $s$ is the solubility in mol/L.

AB Type ($AgCl$)

$K_{sp} = s^2$

$s = \sqrt{K_{sp}}$

AB$_2$ / A$_2$B ($PbCl_2$)

$K_{sp} = 4s^3$

$s = (K_{sp}/4)^{1/3}$

AB$_3$ / A$_3$B ($Al(OH)_3$)

$K_{sp} = 27s^4$

$s = (K_{sp}/27)^{1/4}$

A$_2$B$_3$ ($As_2S_3$)

$K_{sp} = 108s^5$

$s = (K_{sp}/108)^{1/5}$

Precipitation Condition:

• $Q_{sp} < K_{sp}$: Unsaturated, no precipitate.
• $Q_{sp} = K_{sp}$: Saturated, at equilibrium.
• $Q_{sp} > K_{sp}$: Supersaturated, Precipitation occurs!

Common Ion Effect:

Addition of a common ion suppresses the dissociation of a weak electrolyte or solubility of a sparingly soluble salt.

Solubility of $AgCl$ in $0.1M\ NaCl$ is $s' = \frac{K_{sp}}{0.1}$

© 2026 CHEMCA Academy. All Rights Reserved.

Quiz Revision Notes Downloads Class Notes Video Lectures

🎯 Complete Chemistry Revision Toolkit

Score higher by combining Formula Sheets, Flashcards and the Mistake Bank. These three resources help you revise faster, remember longer and avoid common exam mistakes for JEE Main, JEE Advanced, NEET and CBSE Board.

📄 Formula Sheets

Quick chapter-wise formulas, equations, constants and revision charts for last-minute preparation.

🧠 Chemistry Flashcards

Revise using active recall with interactive flashcards covering important concepts, reactions and exceptions.

❌ Mistake Bank

Identify common mistakes, eliminate weak areas and improve your accuracy in competitive examinations.

💡 Best Revision Strategy: Start with Formula Sheets for quick revision, reinforce concepts using Flashcards, and finish with the Mistake Bank to avoid repeating errors in the examination.