Chemistry Textbook

• At equilibrium, the rate of forward reaction equals the rate of reverse reaction. 

• The concentration of reactants and products does not change at equilibrium. This does not mean the reaction has stopped. It only means the reaction has reached a dynamic equilibrium.

• The equilibrium constant, K, is the ratio of product concentrations raised to their coefficients to reactant concentrations raised to their equilibrium. For a general reaction,
  $$m\text{A}+n\text{B}\rightleftharpoons x\text{C}+y\text{D},$$
  The equilibrium constant, K_c is given by:
  $$K_c=\frac{{[\text{C}]}^x[\text{D}{]}^y}{{[\text{A}]}^m[\text{B}{]}^n},$$
• Pure solids and liquids do not appear in the equilibrium expression because their relative concentration values are equal to 1.

• When the reactants and products are in gas phase, the equilibrium constant can be expressed with respect to concentration of products and reactants (notated K_c) or with respect to partial pressure of products and reactants (notated K_P). For the reaction,

  $$m\text{A}+n\text{B}\rightleftharpoons x\text{C}+y\text{D},$$

  The relationship between K_c and K_P is:
   
  $$K_P=K_c{\left(RT\right)}^{\text{Δ}n}$$
  where Δn is (x+y)-(m+n)

• Le Châtelier’s Principle: When the equilibrium is disturbed by either changing concentration of reactants/products or changing the temperature or pressure, the reaction equilibrium shifts in a direction that opposes the change.

Acid- base concepts:

• According to the Bronsted-Lowry definition, an acid is a proton (H⁺ donor and a base is a proton (H⁺ acceptor. Substances that act as both Bronsted acids and bases are said to be amphoteric. 

• The extent of the water autoionization process is reflected in the value of its equilibrium constant, the ion-product constant for water, K_w:

   

  $${\text{H}}_2\text{O}(l)+{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq)K_{\text{w}}=[{\text{H}}_3{\text{O}}^{\text{+}}][{\text{OH}}^{\text{−}}]$$
• Concentrations of hydronium and hydroxide ions in aqueous media are often represented as logarithmic pH and pOH values, respectively. At 25 °C, the autoprotolysis equilibrium for water requires the sum of pH and pOH to equal 14 for any aqueous solution. The relative concentrations of hydronium and hydroxide ion in a solution define its status as acidic ([H₃O⁺] > [OH⁻]), basic ([H₃O⁺] < [OH⁻]), or neutral ([H₃O⁺] = [OH⁻]). At 25 °C, a pH < 7 indicates an acidic solution, a pH > 7 a basic solution, and a pH = 7 a neutral solution.

  pH = −log[H⁺]

  pOH = −log[OH⁻]

  [H₃O⁺] = 10^−pH

  [OH⁻] = 10^−pOH

  pH + pOH = pK_w = 14.00 at 25 °C

• The equilibrium constant for an acid is called the acid-ionization constant (K_a), . For the reaction of an acid HA:
  $$\text{HA}(aq)+{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{H}}_3{\text{O}}^{\text{+}}(aq)+{\text{A}}^{\text{−}}(aq),$$

  the acid ionization constant is written

  $$K_{\text{a}}=\frac{[{\text{H}}_3{\text{O}}^{\text{+}}][{\text{A}}^{\text{−}}]}{\text{[HA]}}$$

• Just as for acids, the relative strength of a base is reflected in the magnitude of its base-ionization constant (K_b) in aqueous solutions. For the reaction of a base, B:

   

  $$\text{B}(aq)+{\text{H}}_2\text{O}(l)\rightleftharpoons {\text{HB}}^{\text{+}}(aq)+{\text{OH}}^{\text{−}}(aq),$$

  the ionization constant is written as

  $$K_{\text{b}}=\frac{[{\text{HB}}^{\text{+}}]\left[{\text{OH}}^{\text{−}}\right]}{\left[\text{B}\right]}$$

• A buffer solution resists pH changes when a small amount of strong acid/base are to it. A buffer solution contains a weak acid and a salt of it's conjugate base, or, a weak base and a salt of it's conjugate acid.

• The Henderson-Hasselbalch equation to the calculate the pH of a buffer is:
  $\text{pH}=\text{p}{K}_{\text{a}}+\text{log}\frac{\left[{\text{A}}^{\text{−}}\right]}{\left[\text{HA}\right]}$

Solubility Equilibria

• The equilibrium constant for an equilibrium involving the precipitation or dissolution of a slightly soluble ionic solid is called the solubility product, K_sp, of the solid. For a heterogeneous equilibrium involving the slightly soluble solid M_pX_q and its ions M^m+ and X^n–:

  $${\text{M}}_p{\text{X}}_q(s)\rightleftharpoons p{\text{M}}^{\text{m+}}(aq)+q{\text{X}}^{\text{n−}}(aq)$$

  the solubility product expression is:

  $$K_{\text{sp}}={{\text{[M}}^{\text{m+}}]}^p{{\text{[X}}^{\text{n−}}]}^q$$

  The solubility product of a slightly soluble electrolyte can be calculated from its solubility; conversely, its solubility can be calculated from its K_sp, provided the only significant reaction that occurs when the solid dissolves is the formation of its ions.

  A slightly soluble electrolyte begins to precipitate when the magnitude of the reaction quotient for the dissolution reaction exceeds the magnitude of the solubility product. Precipitation continues until the reaction quotient equals the solubility product.