Equilibrium — Revision Notes

⚡ 30-Second Revision

Dynamic Equilibrium: — Rate of forward reaction = Rate of reverse reaction.
Equilibrium Constant: — $K_c = \frac{[Products]}{[Reactants]}$, $K_p = \frac{(P_{Products})}{(P_{Reactants})}$.
Relationship: — $K_p = K_c(RT)^{\Delta n_g}$, where $\Delta n_g = n_{g,products} - n_{g,reactants}$.
Le Chatelier's Principle: — System shifts to counteract stress (conc., pressure, temp.).
Temperature Effect: — Only factor changing $K$. Endothermic: $T \uparrow, K \uparrow$. Exothermic: $T \uparrow, K \downarrow$.
Catalyst: — Speeds up equilibrium attainment; no effect on $K$ or equilibrium position.
pH: — $pH = -log[H^+]$, $pOH = -log[OH^-]$, $pH + pOH = 14$ (at $25^circ C$).
Weak Acid/Base: — $K_a = \frac{[H^+][A^-]}{[HA]}$, $K_b = \frac{[B^+][OH^-]}{[BOH]}$.
Buffer pH (Acidic): — $pH = pK_a + log\frac{[Salt]}{[Acid]}$.
Buffer pOH (Basic): — $pOH = pK_b + log\frac{[Salt]}{[Base]}$.
Solubility Product: — $K_{sp} = [Cation]^x[Anion]^y$. For $MX(s)$, $K_{sp} = s^2$. For $MX_2(s)$, $K_{sp} = 4s^3$.

2-Minute Revision

Equilibrium is a dynamic state where forward and reverse reaction rates are equal, leading to constant macroscopic properties. The equilibrium constant ($K_c$ for concentrations, $K_p$ for partial pressures) quantifies the extent of a reaction, with $K_p = K_c(RT)^{\Delta n_g}$ linking them.

Le Chatelier's Principle is crucial: increasing reactant concentration shifts equilibrium to products, increasing pressure shifts to fewer moles of gas, and increasing temperature shifts to absorb heat (endothermic forward, exothermic reverse).

Remember, only temperature changes $K$, and catalysts merely speed up equilibrium attainment. Ionic equilibrium covers acid-base concepts: pH ($pH = -log[H^+]$), weak acid/base dissociation ($K_a$, $K_b$), and buffer solutions (weak acid/base + conjugate salt) which resist pH changes, calculated using the Henderson-Hasselbalch equation.

The common ion effect suppresses dissociation. Finally, solubility product ($K_{sp}$) describes the equilibrium of sparingly soluble salts, where $K_{sp} = s^2$ for 1:1 salts, and $Q_{sp}$ compared to $K_{sp}$ predicts precipitation.

5-Minute Revision

Chemical equilibrium is a dynamic state in reversible reactions where the rates of forward and reverse processes are equal, resulting in constant concentrations of reactants and products. The **equilibrium constant ($K$)** is a temperature-dependent value that indicates the relative amounts of products and reactants at equilibrium.

For concentrations, it's $K_c = \frac{[Products]^{coeff}}{[Reactants]^{coeff}}$, and for gases, $K_p = \frac{(P_{Products})^{coeff}}{(P_{Reactants})^{coeff}}$. The relationship between them is $K_p = K_c(RT)^{\Delta n_g}$, where $\Delta n_g$ is the change in moles of gaseous species.

Pure solids and liquids are excluded from $K$ expressions.

Le Chatelier's Principle is vital for predicting shifts:

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Concentration: — Adding a reactant shifts to products; removing a product shifts to products.
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Pressure (for gases): — Increasing pressure shifts to the side with fewer moles of gas; decreasing pressure shifts to more moles of gas. (No effect if $\Delta n_g = 0$ or inert gas added at constant volume).
3
Temperature: — For endothermic reactions ($\Delta H > 0$), increasing temperature shifts to products (increases $K$). For exothermic reactions ($\Delta H < 0$), increasing temperature shifts to reactants (decreases $K$).
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Catalyst: — Speeds up attainment of equilibrium but does not change $K$ or equilibrium position.

Ionic Equilibrium focuses on solutions:

pH Scale: — $pH = -log[H^+]$, $pOH = -log[OH^-]$, $pH + pOH = 14$ at $25^circ C$.
Weak Acids/Bases: — Partially dissociate, characterized by $K_a$ or $K_b$. For $HA \rightleftharpoons H^+ + A^-$, $K_a = \frac{[H^+][A^-]}{[HA]}$.
Common Ion Effect: — Addition of a common ion suppresses the dissociation of a weak electrolyte.
Buffer Solutions: — Resist pH changes. Composed of a weak acid/base and its conjugate salt. pH is calculated using the Henderson-Hasselbalch equation: $pH = pK_a + log\frac{[Salt]}{[Acid]}$ (for acidic buffers) or $pOH = pK_b + log\frac{[Salt]}{[Base]}$ (for basic buffers).
Solubility Product ($K_{sp}$): — For sparingly soluble salts, $K_{sp}$ is the product of ion concentrations in a saturated solution. For $M_x A_y(s) \rightleftharpoons xM^{y+}(aq) + yA^{x-}(aq)$, $K_{sp} = [M^{y+}]^x[A^{x-}]^y$. If $Q_{sp} < K_{sp}$, no precipitation; if $Q_{sp} > K_{sp}$, precipitation occurs. For a 1:1 salt, $K_{sp} = s^2$, where 's' is molar solubility. For $MX_2$, $K_{sp} = 4s^3$.

Prelims Revision Notes

1
Equilibrium Definition: — Dynamic state where forward rate ($R_f$) equals reverse rate ($R_r$). Macroscopic properties are constant.
2
Law of Mass Action: — $K_c = \frac{[Products]^{coeff}}{[Reactants]^{coeff}}$. For gases, $K_p = \frac{(P_{Products})^{coeff}}{(P_{Reactants})^{coeff}}$.
3
Relationship $K_p$ and $K_c$: — $K_p = K_c(RT)^{\Delta n_g}$, where $\Delta n_g = (n_{g,products} - n_{g,reactants})$. Remember $R = 0.0821,L,atm,mol^{-1},K^{-1}$ for $K_p$ and $R = 8.314,J,mol^{-1},K^{-1}$ for energy calculations.
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Units of K: — $K_c$ has units of $(mol/L)^{\Delta n}$, $K_p$ has units of $(atm)^{\Delta n_g}$.
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Le Chatelier's Principle:

* Concentration: Add reactant $\rightarrow$ shift right. Remove product $\rightarrow$ shift right. * Pressure (gases only): Increase P $\rightarrow$ shift to fewer moles of gas. Decrease P $\rightarrow$ shift to more moles of gas.

* Temperature: Endothermic ($\Delta H > 0$, heat is reactant): $T \uparrow \rightarrow$ shift right, $K \uparrow$. Exothermic ($\Delta H < 0$, heat is product): $T \uparrow \rightarrow$ shift left, $K \downarrow$.

* Inert Gas: Constant V $\rightarrow$ no effect. Constant P $\rightarrow$ shift to more moles of gas. * Catalyst: No effect on equilibrium position or $K$, only speeds up attainment.

1
Ionic Equilibrium:

* pH: $pH = -log[H^+]$. $pOH = -log[OH^-]$. $pH + pOH = 14$ at $25^circ C$. * Strong Acids/Bases: Complete dissociation. $[H^+]$ or $[OH^-]$ directly from concentration. * Weak Acids/Bases: Partial dissociation.

Use $K_a = \frac{[H^+][A^-]}{[HA]}$ or $K_b = \frac{[B^+][OH^-]}{[BOH]}$. Often use ICE table and approximation $[HA]_{eq} \approx [HA]_{initial}$ if dissociation is small. * Common Ion Effect: Reduces dissociation of weak electrolyte by adding common ion.

* Buffer Solutions: Weak acid + conjugate base (e.g., $CH_3COOH/CH_3COO^-$) or weak base + conjugate acid (e.g., $NH_4OH/NH_4^+$). * Henderson-Hasselbalch: $pH = pK_a + log\frac{[Salt]}{[Acid]}$ (acidic buffer).

$pOH = pK_b + log\frac{[Salt]}{[Base]}$ (basic buffer). * **Solubility Product ($K_{sp}$):** For $M_x A_y(s) \rightleftharpoons xM^{y+}(aq) + yA^{x-}(aq)$, $K_{sp} = [M^{y+}]^x[A^{x-}]^y$. * Molar Solubility (s): For $MX(s)$, $K_{sp} = s^2$.

For $MX_2(s)$, $K_{sp} = 4s^3$. For $M_2X_3(s)$, $K_{sp} = 108s^5$. * Precipitation: $Q_{sp} < K_{sp}$ (unsaturated, no ppt). $Q_{sp} = K_{sp}$ (saturated, equilibrium). $Q_{sp} > K_{sp}$ (supersaturated, ppt forms).

Vyyuha Quick Recall

LE CHATELIER'S PRINCIPLE: Look for Equilibrium Changes, How And To Each Load It Effects Reaction Shifts. (Focus on the 'stress' and the 'shift' to counteract it.)

For pH and pOH: Power Hydrogen, Power Oxide Hydrogen. Remember $pH+pOH=14$ and $K_w = [H^+][OH^-]$.

For Buffer: Buffers Undergo Few Fluctuations, Employing Resistance. (Weak Acid/Base + Conjugate Salt).