Chemical Equilibrium Notes

Chemical Equilibrium

The Equilibrium State and Equilibrium Constant

Agenda

• The Equilibrium State
• The Equilibrium Constant

Reaction Dynamics

• When a reaction starts, reactants are consumed, and products are formed.
• Forward reaction: reactants → products
• Eventually, the products can react to re-form some of the reactants.
• Reverse reaction: products → reactants
• Processes that proceed in both the forward and reverse directions are said to be reversible.
  • Reactants ⇋ products

Reaction Dynamics Example: H2(g) + I2(g) ⇋ 2 HI(g)

• Equilibrium is established when the rate of the forward reaction equals the rate of the reverse reaction.
• Equilibrium does not mean that the concentrations of reactants and products are equal.

Reaction Dynamics Graph

• A graph illustrating the change in reaction rate over time, showing forward and reverse rates converging at equilibrium.

Reaching Equilibrium on Macroscopic and Molecular Levels: N2O4(g) ⇋ 2 NO2(g)

• A: Initially, the reaction mixture consists mostly of colorless N2O4.
• B: As N2O4 decomposes to NO2, the mixture becomes pale brown.
• C: The color deepens as more N2O4 decomposes and more NO2 is produced until the color reaches a maximum at equilibrium.
• At equilibrium, the reaction continues in both directions at equal rates, so the concentrations of NO2 and N2O4, and therefore the color, no longer change.

A Fundamental Idea of Chemical Equilibrium: N2O4(g) colorless ⇋ 2 NO2(g) brown, $\Delta$H = 58 kJ/mole

• Graphs showing concentration (M) vs. time (ns) for N2O4 and NO2, illustrating the change in concentrations until equilibrium is reached.

Derivation of K (Equilibrium Constant) From k (Rate Constant): N2O4(g) ⇋ 2 NO2(g)

• For a simple one-step mechanism reversible reaction:
• At equilibrium, ratefwd = raterev, therefore: $k<em>{fwd} [N</em>2O<em>4]</em>{eq} = k<em>{rev} [NO</em>2]^2_{eq}$
• Then, $\frac{k<em>{fwd}}{k</em>{rev}} = \frac{[NO<em>2]^2</em>{eq}}{[N<em>2O</em>4]_{eq}}$
• The ratio of constants gives a new constant, the equilibrium constant: $K = \frac{k<em>{fwd}}{k</em>{rev}} = \frac{[NO<em>2]^2</em>{eq}}{[N<em>2O</em>4]_{eq}}$

Equilibrium Constant Expression: a A(g) + b B(g) ⇋ c C(g) + d D(g)

• We can define a constant:
  • Kc is the equilibrium constant, defined for a reversible reaction at a given temperature.
  • K is a measure of reaction extent.
  • This expression is valid for all reactions.
• $K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b}$

The Magnitude of the Equilibrium Constant, K

Example 1: N2 + 3H2 ⇋ 2NH3, Kc = 3.6 × 10^8 @ 25°C

• If Kc >> 1 → product-favored reaction, so Kc = large product # / (small reactant # × small reactant#)
• The concentration of products is greater than the concentration of reactants at equilibrium.

Example 2: N2 + O2 ⇋ 2 NO, Kc = 1 × 10^-30 @ 25°C

• If Kc << 1 → reactant-favored reaction, so Kc = small product # / (large reactant # × large reactant#)
• The concentration of reactants is greater than the concentration of products at equilibrium.

General Rules for Kc

• Kc < 1: reactant-favored
• Kc > 1: product-favored
• Kc ≈ 1: similar concentrations of reactants and products

Properties of Equilibrium Constant

• Equilibrium constants are unitless.
• Activities are directly related to molarity.
• For any balanced chemical equation, the value of Kc is:
  • Constant at a given T
  • Changed if the T changes
  • Does not depend on the initial concentrations
• No matter what combinations of reactant and product concentrations we start with, the resulting equilibrium concentration at a certain T for the reversible reaction would always give the same value of Kc.

Heterogenous Equilibria

• Pure solids and pure liquids are not included in the equilibrium constant expression.
• For the reaction aA(s) + bB(aq) ⇋ cC(l) + dD(aq), the equilibrium constant expression is:
  • $K_c = \frac{[D]^d}{[B]^b}$

Relationships Between K and Chemical Equations

• The form of K depends on the direction in which the balanced equation is written.
• When the reaction is written backward, the equilibrium constant is inverted:
  • $K<em>{backward} = \frac{1}{K</em>{forward}}$
• When the coefficients of an equation are multiplied by a factor, the equilibrium constant is raised to that factor.
• When you add equations to get a new equation, the equilibrium constant of the new equation is the product of the equilibrium constants of the old equations:
  • $K<em>{new} = K</em>1 \times K_2$

Conclusion

• Overview of the equilibrium state
• Introduction to the equilibrium constant

Up Next:

• Further exploration of the equilibrium constant
• Introduction to the reaction quotient
• Application of the reaction quotient in determining the direction of reactions

Reference

• Silberberg, M. S. & Amateis, P. G. (2024). Chemistry: The molecular nature of matter and change (10th ed.). McGraw-Hill. (101