Chemical Equilibrium Notes

Equilibrium
- Reversible vs. irreversible reactions
- Chemical equilibrium
- Equilibrium constant expression (definition, understanding, calculation)
- Determining the sign of $\,\Delta G$ and reaction direction using $K_{eq}$
Gas Phase
- Equilibrium constant for gas phase equilibrium in terms of partial pressures
Le Chatelier’s Principle
- Using Le Chatelier’s principle to determine the effects of changing conditions (temperature, pressure, concentration) on a reaction at equilibrium
Kinetic and Thermodynamic Control
- Identifying conditions favoring kinetic or thermodynamic products
- Distinguishing between kinetic and thermodynamic pathways on a reaction coordinate diagram

Kinetics: Study of reaction rates (speed of reaction).
- Factors affecting rate: concentrations of reactants, temperature, catalyst presence.
Equilibrium: Concerned with the state where concentrations of reactants and products are constant.
- Forward and reverse reactions proceed at the same rate.
Kinetics describes how fast a reaction occurs; equilibrium describes how much of reactants transform into products when complete.

Irreversible Reactions: Proceed in one direction until completion.
- Products do not readily convert back to reactants.
- Example: Combustion of gasoline.
Reversible Reactions: Do not proceed to completion; products can regenerate reactants.
- Forward and reverse reactions occur.

State where the rate of the forward reaction equals the rate of the reverse reaction.
Concentrations of reactants and products remain constant.
Reactions continue in both directions at equal rates (dynamic equilibrium).

Quantitative analysis of chemical equilibrium.
For a generic reaction: $aA + bB \rightleftharpoons cC + dD$
- a, b, c, d are stoichiometric coefficients.
Equilibrium constant expression: $K = \frac{[C]^c [D]^d}{[A]^a [B]^b}$
- [C] and [D] are product concentrations.
- [A] and [B] are reactant concentrations.
- Concentrations raised to the power of their stoichiometric coefficients.

At equilibrium, the rate of the forward reaction equals the rate of the reverse reaction.
Rate expressions are written in terms of concentrations raised to the power of their stoichiometric coefficients.
Bridges kinetics and equilibrium. Predicts reaction direction when concentration, pressure, or temperature changes.
For the generic reaction: $aA + bB \rightleftharpoons cC + dD$

$K_{eq}$ : General equilibrium constant.
$K_c$ : Equilibrium constant in terms of molar concentrations (for reactions in solution).
$K_p$ : Equilibrium constant in terms of partial pressures (for gaseous reactions).
$K<em>{sp}$ , $K</em>a$ , and $K_b$ introduced in later chapters.

Using the ICE (Initial, Change, Equilibrium) table.
ICE Table:
- Initial (I): Initial concentrations of reactants and products.
- Change (C): Changes in concentration as the system reaches equilibrium (represented by x).
- Equilibrium (E): Equilibrium concentrations (I ± C).

Simplification: Assume that the change in concentration (x) is negligible compared to the initial concentration.
If x is less than 5% of the initial concentration, the assumption is generally valid.
Valid when K is very small or very large, or when the initial concentration is significantly high.
If K is comparable to initial concentrations, solve the problem without this assumption.

Example Problem: A 250 mL flask with 1.4 mol $O_2$ and 1.9 mol NO.
- Reaction: $N<em>2(g) + O</em>2(g) \rightleftharpoons 2NO(g)$
- $K = 2.91$
- Goal: Calculate the equilibrium molarity of $O_2$
Steps:
1. Write the equilibrium constant expression.
2. Set up the ICE table.
3. Convert moles to molarity for initial concentrations.
4. Represent changes with x.
5. Determine the direction of the initial shift.
6. Express equilibrium concentrations in terms of x.
7. Substitute into the equilibrium expression.
8. Solve for x using the quadratic formula if necessary.
9. Check the validity of the solutions (discard any negative values).
10. Calculate the final equilibrium molarities.

Measures the relative amount of products and reactants present in a reaction at any given time.
$Q = \frac{[C]^c [D]^d}{[A]^a [B]^b}$
K is calculated only at equilibrium, Q at any time.
Q is a snapshot; Keq describes the end state.

Predicts the direction the reaction will proceed to reach equilibrium.
- $Q < K$ : Forward reaction has not reached equilibrium; reaction proceeds forward ( $\Delta G < 0$ ).
- $Q = K$ : Reaction is at dynamic equilibrium ( $\Delta G = 0$ ).
- $Q > K$ : Forward reaction has exceeded equilibrium; reaction proceeds in reverse ( $\Delta G > 0$ ).

Relationship between Q, K, and $\,\Delta G$ :
- $Q < K$ : $\,\Delta G < 0$ , forward reaction is spontaneous.
- $Q = K$ : $\,\Delta G = 0$ , dynamic equilibrium.
- $Q > K$ : $\,\Delta G > 0$ , forward reaction is non-spontaneous.

If a stress is applied to a system in equilibrium, the system will adjust to counteract the stress and re-establish equilibrium.
- Stresses include changes in concentration, pressure, and temperature.

Addition of Reactants or Removal of Products: System shifts forward to produce more products.
Removal of Reactants or Addition of Products: System shifts in reverse to produce more reactants.

Affect gaseous equilibria.
Increase in Pressure (Decrease in Volume): Shift to produce fewer moles of gas.
Decrease in Pressure (Increase in Volume): Shift to produce more moles of gas.
Applicable only to reactions involving gases (solids and liquids are incompressible).

Definition: Forms the fastest; favored when the reaction cannot reach equilibrium.
Conditions: Lower temperatures and shorter reaction times.
Forms via a pathway with a lower activation energy (Ea).

Definition: Most stable product; favored when the reaction reaches equilibrium.
Conditions: Higher temperatures and longer reaction times.
Reactants overcome a higher activation energy barrier to form the more stable product.

Kinetic and thermodynamic control regulate biochemical reactions.
Example: ATP breakdown controlled kinetically by enzymes.
Enzyme Activity: Temperature and solvents alter the balance between kinetics and thermodynamics.