Equilibrium
📐 Formula & Cheat Sheet (English)
Class 11 Chemistry: Chapter 6 - Equilibrium (साम्यावस्था)
Quick Revision Notes & Formula Sheet
Part 1: Chemical Equilibrium (रासायनिक साम्यावस्था)
1. Key Definitions & Concepts
- Reversible Reaction (उत्क्रमणीय अभिक्रिया): A reaction that proceeds in both forward and backward directions simultaneously.
- Chemical Equilibrium (रासायनिक साम्यावस्था): A dynamic state in a reversible reaction where the rate of forward reaction ($R_f$) equals the rate of backward reaction ($R_b$). At this state, concentrations of reactants and products remain constant over time.
- Law of Mass Action (द्रव्यमान अनुपाती क्रिया का नियम): Given by Guldberg and Waage. At a constant temperature, the rate of a chemical reaction is directly proportional to the product of the active masses (molar concentrations) of the reacting substances.
2. Equilibrium Constant Formulas
For a general reversible reaction:
aA + bB ⇌ cC + dD
Equilibrium Constant in terms of Concentration ($K_c$):
$$K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$ (Note: Active mass of pure solids and pure liquids is taken as 1)
Equilibrium Constant in terms of Partial Pressure ($K_p$):
$$K_p = \frac{(P_C)^c \cdot (P_D)^d}{(P_A)^a \cdot (P_B)^b}$$
Relationship between $K_p$ and $K_c$:
$$K_p = K_c (RT)^{\Delta n_g}$$
- $R$ = Gas constant ($0.0821 \text{ L atm K}^{-1} \text{mol}^{-1}$ or $8.314 \text{ J K}^{-1} \text{mol}^{-1}$)
- $T$ = Temperature in Kelvin
- $\Delta n_g$ = (Moles of gaseous products) - (Moles of gaseous reactants) $= (c + d) - (a + b)$
Cases of $\Delta n_g$:
- If $\Delta n_g = 0 \implies K_p = K_c$ (e.g., $H_2 + I_2 \rightleftharpoons 2HI$)
- If $\Delta n_g > 0 \implies K_p > K_c$ (e.g., $PCl_5 \rightleftharpoons PCl_3 + Cl_2$)
- If $\Delta n_g < 0 \implies K_p < K_c$ (e.g., $N_2 + 3H_2 \rightleftharpoons 2NH_3$)
3. Characteristics of Equilibrium Constant ($K$)
- Reversing a Reaction: If $A \rightleftharpoons B$ has constant $K$, then $B \rightleftharpoons A$ has $K' = \frac{1}{K}$.
- Multiplying Coefficients: If reaction is multiplied by a factor $n$, new constant $K'' = K^n$.
- Adding Reactions: If Reaction 3 = Reaction 1 + Reaction 2, then $K_3 = K_1 \times K_2$.
4. Reaction Quotient ($Q$) & Predicting Reaction Direction
For aA + bB ⇌ cC + dD at any state (not necessarily equilibrium):
$$Q_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$$
| Condition | Direction of Reaction |
|---|---|
| $Q_c < K_c$ | Reaction moves in Forward direction (उत्तरोत्तर / आगे) |
| $Q_c = K_c$ | Reaction is at Equilibrium (साम्यावस्था) |
| $Q_c > K_c$ | Reaction moves in Backward direction (पश्चात / पीछे) |
5. Thermodynamics of Equilibrium
- Standard Free Energy Change ($\Delta G^\circ$): $$\Delta G^\circ = -2.303 R T \log_{10} K$$
- Free Energy Change ($\Delta G$): $$\Delta G = \Delta G^\circ + 2.303 R T \log_{10} Q$$ (At equilibrium, $\Delta G = 0$)
6. Le Chatelier's Principle (ला-शातेलिए का नियम)
"If a system at equilibrium is subjected to a change in concentration, temperature, or pressure, the system shifts in a direction that tends to counteract the effect of the change."
| Factor / Factor Shift | Change Applied | Effect on Equilibrium Shift |
|---|---|---|
| Concentration | Increase Reactant conc. | Shifts Forward |
| Increase Product conc. | Shifts Backward | |
| Pressure | Pressure Increase | Shifts towards fewer gaseous moles ($\Delta n_g$) |
| Pressure Decrease | Shifts towards more gaseous moles | |
| Volume | Volume Increase | Shifts towards more gaseous moles |
| Temperature | Temp Increase | Favors Endothermic reaction ($\Delta H > 0$) |
| Temp Decrease | Favors Exothermic reaction ($\Delta H < 0$) | |
| Catalyst | Addition of Catalyst | No shift (Only speeds up rates equally) |
| Inert Gas | Added at Constant Volume | No effect |
| Added at Constant Pressure | Shifts towards more gaseous moles |
Part 2: Ionic Equilibrium (आयनिक साम्यावस्था)
1. Acid-Base Theories
- Arrhenius Theory:
- Acid: Gives $H^+$ ions in water.
- Base: Gives $OH^-$ ions in water.
- Brönsted-Lowry Theory:
- Acid: Proton ($H^+$) donor.
- Base: Proton ($H^+$) acceptor.
- Conjugate Acid-Base Pair: Differ by a single proton ($H^+$). $$\text{Acid} \rightleftharpoons \text{Conjugate Base} + H^+$$
- Lewis Theory:
- Acid: Electron pair acceptor (e.g., $BF_3, AlCl_3, H^+$).
- Base: Electron pair donor (e.g., $NH_3, H_2O, F^-$).
2. Ostwald's Dilution Law (for Weak Electrolytes)
For a weak acid $HA \rightleftharpoons H^+ + A^-$: $$K_a = \frac{C \alpha^2}{1 - \alpha}$$
If degree of dissociation $\alpha \ll 1$ (i.e., $\alpha < 5%$): $$\alpha = \sqrt{\frac{K_a}{C}} = \sqrt{K_a \cdot V}$$ $$[H^+] = C \cdot \alpha = \sqrt{K_a \cdot C}$$
- $\alpha$ = Degree of dissociation (वियोजन की मात्रा)
- $C$ = Concentration in $\text{mol/L}$
- $V$ = Dilution (Volume containing 1 mole of electrolyte)
3. Ionic Product of Water ($K_w$) & pH Concept
- Ionic Product of Water ($K_w$): $$K_w = [H^+][OH^-] = 1.0 \times 10^{-14} \quad \text{at } 298 \text{ K } (25^\circ\text{C})$$
- pH Scale Formulation: $$pH = -\log_{10}[H^+] \implies [H^+] = 10^{-pH}$$ $$pOH = -\log_{10}[OH^-] \implies [OH^-] = 10^{-pOH}$$ $$pK_w = pH + pOH = 14 \quad (\text{at } 25^\circ\text{C})$$
Nature of Solutions at $25^\circ\text{C}$:
- Neutral: $[H^+] = 10^{-7}\text{ M} \implies pH = 7$
- Acidic: $[H^+] > 10^{-7}\text{ M} \implies pH < 7$
- Basic: $[H^+] < 10^{-7}\text{ M} \implies pH > 7$
4. Common Ion Effect (सम-आयन प्रभाव)
The suppression of dissociation of a weak electrolyte by the addition of a strong electrolyte containing a common ion.
Example: Dissociation of weak acid $CH_3COOH$ decreases upon adding $CH_3COONa$ (common ion: $CH_3COO^-$).
5. Buffer Solutions (बफर विलयन)
Solutions that resist changes in pH upon addition of small amounts of acid or base.
Types & Henderson-Hasselbalch Equations:
-
Acidic Buffer (अम्लीय बफर): Weak Acid + Salt of Weak Acid with Strong Base (e.g., $CH_3COOH + CH_3COONa$) $$pH = pK_a + \log_{10}\left( \frac{[\text{Salt}]}{[\text{Acid}]} \right)$$ where $pK_a = -\log_{10} K_a$
-
Basic Buffer (क्षारीय बफर): Weak Base + Salt of Weak Base with Strong Acid (e.g., $NH_4OH + NH_4Cl$) $$pOH = pK_b + \log_{10}\left( \frac{[\text{Salt}]}{[\text{Base}]} \right)$$ $$pH = 14 - pOH$$ where $pK_b = -\log_{10} K_b$
6. Solubility Product ($K_{sp}$) (विलेयता गुणनफल)
For a sparingly soluble salt $A_x B_y \rightleftharpoons x A^{y+} + y B^{x-}$: $$K_{sp} = [A^{y+}]^x [B^{x-}]^y$$
If $S$ is the solubility in $\text{mol/L}$: $$K_{sp} = (x^x \cdot y^y) \cdot S^{(x+y)}$$
Examples:
- 1:1 Salt (e.g., $AgCl$): $K_{sp} = S^2 \implies S = \sqrt{K_{sp}}$
- 1:2 or 2:1 Salt (e.g., $CaCl_2, Ag_2CrO_4$): $K_{sp} = 4S^3 \implies S = \left(\frac{K_{sp}}{4}\right)^{1/3}$
- 1:3 Salt (e.g., $AlCl_3$): $K_{sp} = 27S^4$
Criteria for Precipitation (अवक्षेपण की शर्त):
- $Q_{sp} < K_{sp}$: Unsaturated solution (No precipitation)
- $Q_{sp} = K_{sp}$: Saturated solution (Equilibrium state)
- $Q_{sp} > K_{sp}$: Supersaturated solution (Precipitation occurs / अवक्षेप बनेगा)
Key Exam Tips for MP Board
- Units of $K_c$ and $K_p$:
- Unit of $K_c = (\text{mol L}^{-1})^{\Delta n_g}$
- Unit of $K_p = (\text{atm})^{\Delta n_g}$ or $(\text{bar})^{\Delta n_g}$
- Conjugate Pair Questions: Remember that a Strong Acid has a Weak Conjugate Base, and a Weak Acid has a Strong Conjugate Base.
- Le Chatelier Applications: Be ready for direct conceptual questions on Haber's Process ($N_2 + 3H_2 \rightleftharpoons 2NH_3, \Delta H < 0$) and Contact Process ($2SO_2 + O_2 \rightleftharpoons 2SO_3, \Delta H < 0$).