Equilibrium

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Equilibrium — Key Facts for CUET Law of Mass Action: rate $\propto [A]^a[B]^b$; equilibrium constant $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ for $aA + bB \rightleftharpoons cC + dD$ $K_p = K_c(RT)^{\Delta n}$; $\Delta n =$ moles of gaseous products − reactants Le Chatelier’s principle: system shifts to oppose change; temperature, pressure, concentration, catalyst Weak acids: $\alpha = \sqrt{\frac{K_a}{c}}$; weak bases: $\alpha = \sqrt{\frac{K_b}{c}}$; $K_w = K_a \times K_b = 10^{-14}$ at 298 K pH: $pH = -\log[H^+]$; pOH = 14 - pH; buffer: $pH = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]}$ ⚡ Exam tip: Adding inert gas at constant volume doesn’t affect equilibrium position; at constant pressure, it shifts toward more moles of gas

---

🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding of chemical and ionic equilibrium.

Equilibrium — CUET Chemistry Study Guide

Chemical equilibrium occurs when the forward and reverse reaction rates become equal, so that concentrations of reactants and products remain constant (though not necessarily equal) over time. This is a dynamic equilibrium — reactions don’t stop; they occur at equal rates in both directions.

Law of Mass Action and Equilibrium Constants: For a general reaction $aA + bB \rightleftharpoons cC + dD$:

• $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ (in terms of molar concentrations)
• $K_p = \frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$ (in terms of partial pressures)
• Relationship: $K_p = K_c(RT)^{\Delta n}$, where $\Delta n = (c+d) - (a+b)$

The magnitude of $K$ indicates extent of reaction: $K >> 1$ → products favoured; $K << 1$ → reactants favoured. $K$ changes only with temperature.

Le Chatelier’s Principle: When a system at equilibrium is disturbed, it shifts in the direction that partially counteracts the disturbance.

Change	Effect on Equilibrium
Increase [reactant]	Shifts right (toward products)
Decrease [reactant]	Shifts left (toward reactants)
Increase pressure	Shifts toward fewer moles of gas
Decrease pressure	Shifts toward more moles of gas
Increase temperature (exothermic)	Shifts left
Increase temperature (endothermic)	Shifts right
Catalyst	No shift (increases both rates equally)

Ionic Equilibrium: Strong acids (HCl, HBr, HI, HNO₃, HClO₄) completely dissociate. Weak acids (acetic acid, formic acid) partially dissociate: $K_a = \frac{[H^+][A^-]}{[HA]}$. For weak base: $K_b = \frac{[OH^-][BH^+]}{[B]}$.

pH Calculations:

• Strong acid (pH < 7): $[H^+] = C_{\text{acid}}$ (fully dissociated)
• Weak acid: $[H^+] = \sqrt{K_a \times c}$ (for $c >> K_a$)
• Buffer: $pH = pK_a + \log\frac{[\text{salt}]}{[\text{acid}]}$ (Henderson-Hasselbalch equation)

Solubility Product: For $AB_{(s)} \rightleftharpoons A^+{(aq)} + B^-{(aq)}$, $K_{sp} = [A^+][B^-]$. For $A_2B_3$, $K_{sp} = [A^+]^2[B^{3-}]^3$. Precipitation occurs when ionic product > $K_{sp}$.

Example: Find pH of 0.01 M acetic acid ($K_a = 1.8 \times 10^{-5}$). $[H^+] = \sqrt{K_a \times c} = \sqrt{1.8 \times 10^{-5} \times 0.01} = \sqrt{1.8 \times 10^{-7}} = 4.24 \times 10^{-4}$ M. $pH = -\log(4.24 \times 10^{-4}) = 3.37$.

---

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Equilibrium — Complete CUET Chemistry Notes

Degree of Dissociation: $\alpha = \frac{\text{moles dissociated}}{\text{moles initially present}}$. For weak electrolytes: $\alpha = \sqrt{\frac{K}{c}}$ (from $K = \frac{c\alpha^2}{1-\alpha} \approx c\alpha^2$ when $\alpha << 1$). For polyprotic acids (H₂SO₄, H₃PO₄), each dissociation has its own $K_a$: $K_{a1} >> K_{a2} >> K_{a3}$.

Salt Hydrolysis: When a salt of weak acid and strong base (e.g., Na₂CO₃) is dissolved in water, the conjugate base hydrolyses: CO₃²⁻ + H₂O → HCO₃⁻ + OH⁻, making solution basic. For salt of weak base and strong acid (e.g., NH₄Cl), solution is acidic. For salt of weak acid and weak base, $pH \approx \frac{1}{2}(pK_a + pK_b)$.

Common Ion Effect: The suppression of dissociation of a weak electrolyte by adding a strong electrolyte with a common ion. Example: Adding NaCl to AgCl equilibrium decreases AgCl solubility because of increased [Cl⁻]. This is applied in qualitative analysis — adding HCl to precipitate Ag⁺, Pb²⁺, Hg₂²⁺ as chlorides.

Buffer Solutions: Resist pH change upon addition of small amounts of acid or base. Capacity depends on concentration of acid/salt pair. Blood is a buffer system (carbonic acid/bicarbonate, $pH \approx 7.4$). Buffer range = $pK_a \pm 1$. Inside this range, the buffer is effective.

Thermodynamic View of Equilibrium: $\Delta G = \Delta G° + RT\ln Q$. At equilibrium, $\Delta G = 0$ and $Q = K$, so $\Delta G° = -RT\ln K$. This links free energy to equilibrium constant. Since $\Delta G° = \Delta H° - T\Delta S°$, temperature dependence: $\ln K = -\frac{\Delta H°}{RT} + \frac{\Delta S°}{R}$.

Heterogeneous Equilibrium: When reactants and products are in different phases. Example: CaCO₃(s) ⇌ CaO(s) + CO₂(g). $K_p = P_{CO₂}$ (solids omitted). The equilibrium pressure of CO₂ (dissociation pressure) depends only on temperature.

Ostwald’s Dilution Law: $\alpha = \sqrt{\frac{K}{c}}$. As dilution increases ($c$ decreases), degree of dissociation increases. This holds for weak electrolytes only — strong electrolytes are fully dissociated at all concentrations (though activity coefficients change).

CUET Exam Patterns (2022–2024):

• pH calculations (weak acids, buffers) are most frequent (1–2 marks)
• Le Chatelier’s principle questions appear every year
• $K_c$ and $K_p$ relationship ($\Delta n$) is commonly tested
• Solubility product and precipitation questions appeared in 2023
• Common mistakes: forgetting that solids and liquids are omitted from $K$ expressions; using wrong units in $K_c$; confusing $\alpha$ (degree) with $K_a$

⚡ Key insight: When solving equilibrium problems, always check whether the reaction has proceeded significantly before establishing the equilibrium table. If $K$ is very small ($< 10^{-3}$), you can assume $x$ is negligible compared to initial concentrations. If $K$ is large ($> 10^3$), the reaction goes nearly to completion. For intermediate $K$, solve the quadratic exactly.

---

Content adapted based on your selected roadmap duration. Switch tiers using the pill selector above.