Chapter 15: Chemical Equilibrium – Study Notes

Chapter 15: Chemical Equilibrium

15.1 The Concept of Equilibrium

Chemical equilibrium occurs when the rates of the forward and reverse reactions in a chemical system are equal, resulting in no net change in the concentrations of reactants and products. This dynamic state is fundamental to many chemical processes.

• Definition: Chemical equilibrium is the state in which the concentrations of all reactants and products remain constant with time.

• Dynamic Equilibrium: Both forward and reverse reactions continue to occur, but at equal rates.

• Example: For the reaction $A(g) \rightleftharpoons B(g)$, at equilibrium, the rate of $A \to B$ equals the rate of $B \to A$.

15.2 The Equilibrium Constant

The equilibrium constant quantifies the ratio of product and reactant concentrations at equilibrium. It is a central concept for predicting the direction and extent of chemical reactions.

• General Form: For a reaction $aA + bB \rightleftharpoons cC + dD$:

$K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Equilibrium Constant in Terms of Pressure: For gases, the equilibrium constant can also be expressed as $K_p$ using partial pressures:

$K_p = \frac{(P_C)^c (P_D)^d}{(P_A)^a (P_B)^b}$

• Relationship between $K_p$ and $K_c$:

$K_p = K_c(RT)^{\Delta n}$ where $\Delta n = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants})$

• Units: $K_c$ and $K_p$ may have different units depending on the reaction stoichiometry.

• Equilibrium Constant Expressions: Only include species in the gas or aqueous phase; pure solids and liquids are omitted.

15.3 Interpreting and Working with Equilibrium Constants

Understanding the magnitude and meaning of the equilibrium constant allows chemists to predict the position of equilibrium and the relative amounts of reactants and products.

• Magnitude of $K$:

  • If $K \gg 1$, products are favored at equilibrium (reaction proceeds nearly to completion).

  • If $K \ll 1$, reactants are favored at equilibrium (very little product forms).

  • If $K \approx 1$, significant amounts of both reactants and products are present.

• Comparing $Q$ and $K$: The reaction quotient $Q$ is calculated using initial concentrations or pressures. Comparing $Q$ to $K$ predicts the direction of reaction:

  • If $Q < K$, the reaction proceeds forward (toward products).

  • If $Q > K$, the reaction proceeds in reverse (toward reactants).

  • If $Q = K$, the system is at equilibrium.

• Example Table:

  K Value	Proportion of Reactants	Proportion of Products
  Very large ($K \gg 1$)	Mostly converted	Mostly products
  ~1	Significant	Significant
  Very small ($K \ll 1$)	Mostly reactants	Very little product

15.4 Heterogeneous Equilibria

Heterogeneous equilibria involve reactions with more than one phase (solid, liquid, gas). The equilibrium constant expression omits pure solids and liquids, as their concentrations are constant.

• Example: For $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$:

$K = [CO_2]$

• Only the concentration (or pressure) of $CO_2$ appears in the equilibrium expression.

15.5 Calculating Equilibrium Constants

Equilibrium constants can be calculated from experimental data by substituting equilibrium concentrations or pressures into the appropriate expression.

• Steps:

  1. Write the balanced chemical equation.

  2. Write the equilibrium constant expression.

  3. Substitute measured equilibrium values and solve for $K$.

• ICE Tables: (Initial, Change, Equilibrium) tables are often used to organize data and solve for unknowns.

• Example: Given initial and equilibrium concentrations, use the ICE table to find $K_c$.

15.6 Some Applications of Equilibrium Constants

Equilibrium constants are used to predict the direction of reaction, calculate equilibrium concentrations, and determine the effect of changes in conditions.

• Predicting Direction: Use $Q$ and $K$ to determine which way a reaction will proceed to reach equilibrium.

• Le Châtelier’s Principle: If a system at equilibrium is disturbed, it will shift to counteract the disturbance and re-establish equilibrium.

• Example Application: If a product is removed from a system at equilibrium, the reaction will shift to produce more product.

Key Equations and Concepts

• General Equilibrium Constant:

  $K_c = \frac{[\text{products}]}{[\text{reactants}]}$ (each raised to the power of their coefficients)

• Relationship between $K_p$ and $K_c$:

  $K_p = K_c(RT)^{\Delta n}$

• Reaction Quotient:

  $Q = \frac{[\text{products}]_{\text{initial}}}{[\text{reactants}]_{\text{initial}}}$

• ICE Table Example:

  	Initial	Change	Equilibrium
  [A]	1.0 M	-x	1.0 - x
  [B]	0 M	+x	x

Additional info: These notes are based on lecture slides and follow the structure of a typical General Chemistry textbook chapter on chemical equilibrium. Some details, such as the ICE table and example calculations, are inferred for completeness and clarity.