Equilibrium formulas for JEE Main & Advanced

17 formula entries for Equilibrium, in the order the chapter builds them. Each shows the formula, when to use it and the first trap to avoid.

Law of Mass Action

For

a A + b B ⇌ c C + d D

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

When to use. To write equilibrium constant expressions for homogeneous reactions.

Trap. Active mass is molar concentration (mol/L), not total moles.

Equilibrium Constant $K_{c}$ and $K_{p}$

K_{p} = K_{c} (R T)^{Δ n_{g}}

where

Δ n_{g} = (c + d) - (a + b)

for gaseous species.

When to use. When converting between concentration-based and pressure-based equilibrium constants.

Trap. Use R = 0.0821 L atm mol⁻¹ K⁻¹ when pressure in atm.

Reaction Quotient $Q$

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

(using initial concentrations)

When to use. To determine the direction a reaction will shift to reach equilibrium.

Trap. Do not confuse $Q$ with $K$ ; $Q$ changes as reaction proceeds.

Effect of Temperature on $K$

\ln \frac{K_{2}}{K_{1}} = - \frac{Δ H}{R} (\frac{1}{T_{2}} - \frac{1}{T_{1}})

(van't Hoff equation)

When to use. To calculate $K$ at different temperatures or analyze temperature effect.

Trap. Temperature change always changes $K$ , unlike concentration/pressure.

Bronsted-Lowry Acid and Base

Acid

⇌

Conjugate base + H⁺

When to use. For proton transfer reactions in any solvent.

Trap. Water can act as both acid and base (amphoteric).

Ionization of Water and pH

K_{w} = [H^{+}] [O H^{-}] = 10^{- 14}

at 25°C,

p H = - \log [H^{+}]

p O H = - \log [O H^{-}]

p H + p O H = 14

When to use. To calculate pH, pOH, or [H⁺]/[OH⁻] in aqueous solutions.

Trap. $K_{w}$ is temperature dependent; at 100°C, $K_{w} \approx 5.5 \times 10^{- 13}$ (neutral pH ≈ 6.1; $10^{- 12}$ is only a rounded value).

Ionization Constants $K_{a}$ and $K_{b}$

For weak acid HA:

K_{a} = \frac{[H^{+}] [A^{-}]}{[H A]}

; For weak base B:

K_{b} = \frac{[B H^{+}] [O H^{-}]}{[B]}

;

K_{a} \times K_{b} = K_{w}

When to use. To quantify strength of weak acids/bases and calculate pH of their solutions.

Trap. Strong acids have very large $K_{a}$ (complete ionization).

pH of Weak Acid/Base (Approximation)

[H^{+}] = \sqrt{K_{a} C}

(if

C / K_{a} ≳ 400

[O H^{-}] = \sqrt{K_{b} C}

for weak base

When to use. To calculate pH of weak acid or base solutions quickly.

Trap. Always check the 5% rule: if $[H^{+}] / C < 0.05$ , approximation is valid.

Henderson-Hasselbalch Equation

p H = p K_{a} + \log \frac{[A^{-}]}{[H A]}

When to use. To calculate pH of buffer solutions or find ratio of conjugate pair for desired pH.

Trap. Use concentrations at equilibrium, not initial (but often initial used if no reaction).

Solubility Product $K_{s p}$

K_{s p} = [A^{y +}]^{x} [B^{x -}]^{y}

When to use. To determine solubility of salts or predict precipitation in ionic solutions.

Trap. $K_{s p}$ is temperature dependent.

Relationship Between Solubility (s) and $K_{s p}$

For

A_{x} B_{y} (s) ⇌ x A^{y +} + y B^{x -}

K_{s p} = (x s)^{x} (y s)^{y} = x^{x} y^{y} s^{x + y}

When to use. To calculate solubility from $K_{s p}$ or vice versa.

Trap. For AgCl (1:1), $K_{s p} = s^{2}$ .

Degree of Ionization ( $α$ )

α = \frac{number of molecules ionized}{initial number}

; For weak acid:

α = \sqrt{\frac{K_{a}}{C}}

When to use. To find extent of ionization of weak electrolytes.

Trap. $α$ decreases with increasing concentration (dilution increases ionization).

Hydrolysis of Salts

For salt of weak acid (A⁻) and strong base:

A^{-} + H_{2} O ⇌ H A + O H^{-}

K_{h} = K_{w} / K_{a}

When to use. To predict pH of salt solutions.

Trap. Salt of strong acid + strong base gives neutral solution (no hydrolysis).

pH of Salt Solutions

Weak acid/strong base:

p H = \frac{1}{2} p K_{w} + \frac{1}{2} p K_{a} + \frac{1}{2} \log C

; Weak base/strong acid:

p H = \frac{1}{2} p K_{w} - \frac{1}{2} p K_{b} - \frac{1}{2} \log C

When to use. To calculate pH of salt solutions quickly.

Trap. These formulas assume $C$ is not too low and hydrolysis is small.

Titration Curves and Indicators

Equivalence point: moles acid = moles base; pH at half-equivalence = pK_a (for weak acid)

When to use. To choose appropriate indicator or analyze titration data.

Trap. For weak acid titration, buffer region exists before equivalence.

Relation Between $K_{p}$ and $K_{c}$ for Gaseous Reactions

K_{p} = K_{c} (R T)^{Δ n_{g}}

When to use. To convert between $K_{p}$ and $K_{c}$ for gas-phase equilibria.

Trap. Use R = 0.0821 L atm mol⁻¹ K⁻¹ when $K_{p}$ in atm.

ICE Table Method

Example: For

N_{2} + 3 H_{2} ⇌ 2 N H_{3}

, initial [N₂]=a, [H₂]=b, [NH₃]=0, change: -x, -3x, +2x, equilibrium: a-x, b-3x, 2x

When to use. To calculate equilibrium concentrations from initial conditions and $K$ .

Trap. Ensure changes are consistent with stoichiometric coefficients.

Values to remember

$R = 0.0821 {L atm mol}^{- 1} K^{- 1}$ Equilibrium Constant $K_{c}$ and $K_{p}$
$R = 8.314 {J mol}^{- 1} K^{- 1}$ Equilibrium Constant $K_{c}$ and $K_{p}$
$K_{w} = 1.0 \times 10^{- 14} at 25^{\circ} C$ Ionization of Water and pH

Read the full chapter: Equilibrium for JEE, with what JEE asks and the common traps.