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