Chemical Equilibrium and Acid-Base Systems Study Guide

Equilibrium reactions exhibit several defining characteristics that distinguish them from irreversible reactions: - Closed Systems: Equilibrium can only be established in closed systems where no matter is exchanged with the surroundings. - Dynamic Nature: Equilibrium is a dynamic process; while macroscopic properties (like color or pressure) remain constant, the forward and reverse reactions continue at equal rates. - Reversibility: Reactions are reversible ( $\rightleftharpoons$ ), meaning products can react to reform reactants. - Constant Temperature: For a system to remain at equilibrium, the temperature must be kept constant. - Phase States: Equilibrium is not restricted to the gas phase; it can occur in aqueous or heterogeneous systems.
Conditions for established equilibrium: - The forward reaction rate ( $r_f$ ) is exactly equal to the reverse reaction rate ( $r_r$ ). - There is a compromise or balance between the tendency toward maximum disorder (entropy) and the tendency toward minimum energy (enthalpy). - Measurable and observable properties (concentration, pressure, density, color) become constant over time.

Equilibrium Constant ( $K_c$ ): Calculated using molar concentrations of products over reactants, each raised to the power of their stoichiometric coefficients. - In a general reaction $X(g) + Y(g) \rightleftharpoons Z(g) + Q(g)$ , if $K_c = 1$ , the following equality always holds regardless of initial concentrations: $[X] \times [Y] = [Z] \times [Q]$ .
Relation between $K_p$ and $K_c$ : - The relationship is defined by the formula: $K_p = K_c(RT)^{\Delta n}$ . - For the reaction $X(k) + Y_2(g) \rightleftharpoons XY_2(g)$ , $\Delta n = 1 - 1 = 0$ (solid $X$ is excluded). Therefore, $K_p = K_c$ .
Equilibrium Calculation Example: - Reaction: $XY_2(g) \rightleftharpoons X(g) + 2Y(g)$ . - Initial conditions: $1\,mol$ of $XY_2$ in a $2\,L$ container. - Process: $20\%$ of $XY_2$ reacts ( $0.2\,mol$ ). - Equilibrium amounts: $XY_2 = 0.8\,mol$ , $X = 0.2\,mol$ , $Y = 0.4\,mol$ . - Concentrations: $[XY_2] = 0.4\,M$ , $[X] = 0.1\,M$ , $[Y] = 0.2\,M$ . - $K_c = \frac{[X][Y]^2}{[XY_2]} = \frac{0.1 \times (0.2)^2}{0.4} = 0.01$ .
Le Chatelier's Principle: - If a system at equilibrium is disturbed (e.g., adding more product), the system shifts to counteract the change. - For $H_2(g) + I_2(g) \rightleftharpoons 2HI(g)$ , adding $HI$ gas will increase the total moles of $HI$ but will also cause the reaction to shift toward the reactants, eventually establishing a new equilibrium where the concentration of all species is adjusted.

Strong Bases: For a $0.05\,M$ solution of $KOH$ (a strong base): - $[OH^-] = 5 \times 10^{-2}\,M$ . - $pOH = -\log(5 \times 10^{-2}) = 2 - \log(5) = 2 - 0.7 = 1.3$ . - $pH = 14 - 1.3 = 12.7$ .
Weak Acids ( $K_a$ ): - For a $0.4\,M$ solution of $HA$ where $K_a = 2.5 \times 10^{-6}$ : - Using the approximation $K_a = \frac{[H^+]^2}{[HA]_{initial}}$ : $2.5 \times 10^{-6} = \frac{[H^+]^2}{0.4}$ . - $[H^+]^2 = 1.0 \times 10^{-6} \rightarrow [H^+] = 10^{-3}$ . - $pH = 3$ .
Weak Bases and Ionization Percentage: - For $0.2\,M$ solution of $XOH$ ionizing at $0.05\%$ - $[OH^-] = 0.2 \times \frac{0.05}{100} = 1 \times 10^{-4}\,M$ . - $pOH = 4 \rightarrow pH = 10$ .
Acidic, Basic, and Neutral Oxides: - $N_2O$ : Neutral oxide ( $pH = 7$ ). - $MgO$ : Basic oxide ( $pH > 7$ ). - $Na_2O$ : Basic oxide ( $pH > 7$ ). - $NO_2$ : Acidic oxide ( $pH < 7$ ).

Hydrolysis: - Occurs when the salt of a weak acid or weak base reacts with water. - In the reaction $F^-(aq) + H_2O(l) \rightleftharpoons OH^-(aq) + HF(aq)$ , the fluoride ion ( $F^-$ ) undergoes hydrolysis, making the solution basic. - $(NH_4)^+$ reacts with water: $(NH_4)^+(aq) + H_2O(l) \rightleftharpoons NH_3(aq) + H_3O^+(aq)$ , making the solution acidic.
Buffer Solutions: - Consist of a weak acid and its conjugate base (e.g., $HF$ and $NaF$ ) or a weak base and its conjugate acid. - They are resistant to pH changes upon the addition of small amounts of strong acid or base. - Biological systems, such as human blood, rely on buffer systems to maintain a constant pH. - Diluting a buffer with pure water generally does not significantly change its pH, though it may change its buffering capacity.

Solubility Product ( $K_{sp}$ ): The equilibrium constant for a solid substance dissolving in an aqueous solution. - For $CuCl(s) \rightleftharpoons Cu^+(aq) + Cl^-(aq)$ , $K_{sp} = [Cu^+][Cl^-] = 1 \times 10^{-6}$ . - Saturated concentration ( $s$ ): $s^2 = 10^{-6} \rightarrow s = 10^{-3}\,M$ . - Moles in $500\,mL$ : $n = M \times V = 10^{-3} \times 0.5 = 5 \times 10^{-4}\,mol$ .
Common Ion Effect: - Adding a common ion (e.g., adding $NaCl$ to an $AgCl$ solution) shifts the equilibrium to the left, decreasing the solubility of the salt. - The $K_{sp}$ value remains constant (it only changes with temperature).
Le Chatelier and Solubility: - If a solubility process is endothermic ( $PbCl_2(s) + heat \rightleftharpoons Pb^{2+}(aq) + 2Cl^-(aq)$ ), decreasing the temperature will decrease solubility and the concentration of ions. - Adding water to a container with undissolved solid will cause more solid to dissolve to maintain the same molar concentration of ions, provided solid remains.

Equivalence Point: The point in a titration where the number of moles of $H^+$ equals the number of moles of $OH^-$ . - For strong acid-strong base titrations, the pH at the equivalence point is exactly 7 at $25\,^\circ C$ . - Indicators are used to visually detect the "endpoint," which should ideally coincide with the equivalence point.
Titration Calculations: - To fully neutralize $400\,mL$ of $0.1\,M\,HCl$ ( $0.04\,mol\,H^+$ ) with $0.2\,M\,Mg(OH)_2$ : - $Mg(OH)_2$ provides $2\,OH^-$ per formula unit. - Required moles of $Mg(OH)_2 = 0.02\,mol$ . - Volume required: $V = \frac{n}{M} = \frac{0.02}{0.2} = 0.1\,L = 100\,mL$ .

Question regarding Equilibrium Trends: In which reaction is the maximum disorder trend toward the products? - Response: Reactions where the product side has more gas moles or substances in more disordered states. For example, $PCl_5(g) \rightleftharpoons PCl_3(g) + Cl_2(g)$ (1 gas mole to 2 gas moles).
Question on Salt Hydrolysis: Which salt's cation undergoes hydrolysis? - Response: The cation of a salt derived from a weak base and a strong acid, such as $NH_4Cl$ . The $NH_4^+$ ion reacts with water to produce $H_3O^+$ .
Question on Graphing Neutralization: When adding $0.1\,M\,HCl$ dropwise into pure water: - Response: The initial pH is 7. As acid is added, the $[H^+]$ concentration increases, and the pH decreases toward 1. The $pOH$ would increase from 7 toward 13.
Question onto Solubility Factors: How does adding $Mg(NO_3)_2$ affect a saturated $Mg(OH)_2$ solution? - Response: It introduces a common ion ( $Mg^{2+}$ ). According to Le Chatelier, the equilibrium shifts to the left, decreasing the solubility of $Mg(OH)_2$ and decreasing the concentration of $OH^-$ ions.