Chemical Equilibrium Notes

Chemical Reactions and Equilibrium

Reaction Direction

• Some reactions favor the formation of products, while others favor the presence of reactants.
• Many chemical reactions are reversible under ordinary conditions of temperature and concentration.
• These reactions will reach a state of equilibrium unless a substance is removed from the reaction system.
• In some cases, the forward reaction is predominant, converting almost all reactants into products.
• When products are favored, the equilibrium is said to "lie to the right," indicating a higher concentration of products at equilibrium.
  • Example: $2SO<em>2(g) + O</em>2(g) \rightleftharpoons 2SO_3(g)$
  • The longer arrow indicates the favored direction.
• If the reverse reaction rate equals the forward reaction rate early on, equilibrium is established with high reactant and low product amounts.
  • In this case, the equilibrium "lies to the left," with reactants being the predominant species.
  • Example: $H<em>2CO</em>3(aq) + H<em>2O(l) \rightleftharpoons H</em>3O^+(aq) + HCO_3^-(aq)$
• In other cases, forward and reverse reactions occur to nearly the same extent, resulting in considerable concentrations of both reactants and products at equilibrium.
  • Example: $H<em>2SO</em>3(aq) + H<em>2O(l) \rightleftharpoons H</em>3O^+(aq) + HSO_3^-(aq)$
• Chemists aim to convert as much of available reactants into desirable products as possible.
• The extent of this conversion is indicated by the numerical value of the equilibrium constant.

Equilibrium

• At equilibrium, the concentrations of reactants and products remain constant.
• Consider a reversible reaction: $nA + mB \rightleftharpoons xC + yD$
• Initially, concentrations of C and D are zero, while A and B are at their maximum.
• Over time, the forward reaction rate decreases as A and B are consumed, and the reverse reaction rate increases as C and D are formed.
• Equilibrium is established when the forward and reverse reaction rates become equal.
• At equilibrium, the concentrations of A, B, C, and D remain constant under constant conditions.
• The ratio of product concentrations to reactant concentrations remains constant.
• The equilibrium constant (K) is the ratio of the mathematical product of product concentrations to the mathematical product of reactant concentrations, each raised to the power of their coefficients in the balanced equation.

Equilibrium Constant

• The equilibrium constant $K$ is defined as: $K = \frac{[C]^x[D]^y}{[A]^n[B]^m}$
  • ([A], [B], [C], [D]) represent the concentrations of substances A, B, C, and D in mol/L.
  • (n, m, x, y) are the coefficients from the balanced chemical equation.
• Substances on the right side of the chemical equation (products) appear in the numerator, while substances on the left side (reactants) appear in the denominator.
• The constant K is independent of initial concentrations but dependent on the temperature of the system.
• To determine the numerical value of K, chemists analyze the equilibrium mixture experimentally to find the concentrations of all substances.
• The value of K indicates the extent to which reactants are converted into products.
  • A small K indicates that the forward reaction occurs only slightly before equilibrium is established, favoring reactants.
  • A large K indicates that the original reactants are largely converted to products.
• Only the concentrations of substances that can change are included in K; pure solids and liquids are omitted because their concentrations cannot change.

H2, I2, HI Equilibrium System

• The reaction between $H<em>2$ and $I</em>2$ vapor in a sealed flask at an elevated temperature is an example of an equilibrium system.
  $H<em>2(g) + I</em>2(g) \rightleftharpoons 2HI(g)$
• The rate of the reaction can be observed by noting how quickly the violet color of the iodine vapor diminishes.
• The color fades to a constant intensity but does not disappear completely, because the reaction is reversible.
• Hydrogen iodide decomposes to re-form hydrogen and iodine.
• As the concentrations of hydrogen and iodine decrease, the rate of the forward reaction decreases.
• As the concentration of hydrogen iodide increases, the rate of the reverse reaction increases.
• Equilibrium is established when the rates of the opposing reactions become equal.
• At equilibrium: $K = \frac{[HI]^2}{[H<em>2][I</em>2]}$
  • The concentration of HI is raised to the power of 2 because the coefficient of HI in the balanced chemical equation is 2.
• Chemists have measured the concentrations of $H<em>2$, $I</em>2$, and HI in equilibrium mixtures at various temperatures.
• The equilibrium constant for this reaction system at $425°C$ has an average value of 54.34.

Using the Equilibrium Constant

• Once the value of the equilibrium constant is known, the equilibrium constant expression can be used to calculate concentrations of reactants or products at equilibrium.
• Given the equilibrium constant:
  $K = \frac{[HI]^2}{[H<em>2][I</em>2]}$
• We can rearrange the chemical equilibrium expression as:
  $[HI] = \sqrt{K[H<em>2][I</em>2]}$
• If $[H<em>2] = 0.015 mol/L$, $[I</em>2] = 0.015 mol/L$, and $K = 54.34$, then:
  $[HI] = \sqrt{0.015 \times 0.015 \times 54.34} = 0.11 mol/L$
• When calculating concentrations at equilibrium, note the temperature at which the reaction is taking place because values for K change with changing temperature.