Lecture Notes:

Equilibrium Part II

• The Equilibrium Constant
  • Reversible reactions reach an equilibrium where macroscopic change ceases and the concentration of both the products and the reactants ceases to change
  • This idea can be expressed mathematically as an equilibrium constant according to the Law of Mass Action:
  • “For a reversible reaction at equilibrium and a constant temperature, a certain ratio of reactant and product concentrations has a constant value, K (the equilibrium constant)”
  • The general form of an equilibrium constant expression is:
    aA + bB ↔ cC + dD
    

          [C]c[D]d
    Keq = ————————
          [A]a[B]b
    

  • A, B, C, and D represent the formulas of reactants and products. The small letters are the coefficients in the balanced chemical equation
  • The square brackets around each formula mean that the number used in calculations is a concentration in mol/L (M)
  • It is important to note that the concentrations of pure solids and liquids (such as H₂O) are not included in the equilibrium expression because they are considered to be constant relative to the much smaller concentrations of other reactants/products
  • The units of K_eq are not important; just remember that the concentrations of the reactants/products are not constants: they can have different values depending on the initial conditions
  • K_eq is sometimes written K_c; the ‘c’ stands for concentration in mol/L
  • The specific value of the constant depends both temperature and on the balanced equation that is used
  • Take the following reaction: which can just as easily be written:
    (1) N₂O₄ ↔ 2NO₂ (2) 2NO₂ ↔ N₂O₄
    K_{eq 1} = [NO₂]²/[N₂O₄] K_{eq 2} = [N₂O₄]/[NO₂]²
    And K_{eq 1} = 1/K_{eq 2} if both are considered at the same temperature
  • If K_eq is equal to 1.00 at a given temperature then no reaction will occur at that temperature; the concentrations of the reactants and products will stay as they are initially
  • If K_eq is greater than 1.00 at a given temperature then products are favored in the reaction as written; the concentrations of products will increase and the concentrations of reactants will decrease
  • If K_eq is less than 1.00 at a given temperature then reactants are favored in the reaction as written; the concentrations of reactants will increase and the concentrations of products will decrease
• The Reaction Quotient This section will not print out, you are not responsible for these notes
  • The equilibrium constant K_eq is determined using the equilibrium concentrations of the reactants/products; the reaction quotient (Q) is calculated using the equilibrium constant expression and the initial concentrations (rather than the equilibrium concentrations)
  • If the reaction quotient is greater than the value of K_eq (Q > K_eq) then the initial concentration of products is too large and to reach equilibrium products must be converted to reactants
  • If the reaction quotient is equal to the value of K_eq (Q = K_eq) then the system is already at equilibrium
  • If the reaction quotient is smaller than the value of K_eq (Q < K_eq) then the initial concentration of reactants is too large and to reach equilibrium reactants must be converted to products
  • These rules follow logically from the form of the equilibrium expression
• The Solubility Product
  • The solubility product (K_sp) is essentially the same thing as the equilibrium constant but is used exclusively for reactions of the form:
    aA(s) ↔ bB(aq) + cC(aq)
  • In other words, the solubility product is used to describe the solubility of substances that are only slightly soluble
  • The concentration of the solid salt is not included in the solubility product expression because it is essentially constant; hence the name
  • The expression for K_sp for the above reaction is
    

    Ksp = [B]b[C]c
    

  • The solubility product can be used to find the concentration of the dissociated ions in a solution of a slightly soluble salt; it can also be used to find the solubility of the salt at a given temperature in mol/L
  • To find the solubility of the salt, simply use the solubility product expression and the value of K_sp to find the concentration of the dissolved ions; since there is a 1:1 relationship between the solid salt and the ion’s concentration, then this is the molar solubility