Chemical Equilibrium: Principles, Constants, and Applications

Intro to Equilibrium

Overview of Chemical Equilibrium

Chemical equilibrium is a fundamental concept in chemistry describing the state in which the rate of the forward reaction equals the rate of the reverse reaction. At equilibrium, the system is in dynamic equilibrium, meaning that reactions continue to occur, but the concentrations of reactants and products remain constant over time.

• Dynamic Equilibrium: Reactants are continuously converted to products and vice versa, but at equal rates.

• Constant Concentrations: The amounts of reactants and products do not change once equilibrium is reached (though they are not necessarily equal).

• Possible Outcomes: At equilibrium, a reaction may have mostly reactants, mostly products, or a mixture of both.

13.2 Equilibrium Constant

Defining the Equilibrium Constant (K)

The equilibrium constant (K) quantitatively describes the ratio of product concentrations to reactant concentrations at equilibrium for a given chemical reaction at a specific temperature.

• General Form: For a reaction $aA + bB \rightarrow cC + dD$, the equilibrium constant is: $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Phase Considerations: Only substances in the aqueous (aq) or gaseous (g) phase are included in the K expression. Solids and liquids are omitted.

• Example: For $O_2 + NO \rightarrow NO_3$, $K = \frac{[NO_3]}{[O_2][NO]}$

• Uniqueness: The value of K is unique for every reaction and depends on temperature.

Rules for Writing K Expressions

• Coefficients become exponents: For $2NO_2 (g) \rightarrow N_2 (g) + 2O_2 (g)$, $K = \frac{[N_2][O_2]^2}{[NO_2]^2}$

• Exclude solids and liquids: For $HBr (l) \rightarrow H_2 (g) + Br_2 (g)$, $K = [H_2][Br_2]$

Examples of K Expressions

• For $5NO_2 (g) \rightarrow 2N_2 (g) + 5O_2 (g)$: $K = \frac{[N_2]^2[O_2]^5}{[NO_2]^5}$

• For $Ni(NO_3)_2 (aq) \rightarrow Ni^{2+} (aq) + 2NO_3^- (aq)$: $K = \frac{[Ni^{2+}][NO_3^-]^2}{[Ni(NO_3)_2]}$

• For $S_8 (s) + 12Br_2 (l)$: No K expression, as both are solids/liquids (excluded).

Interpreting the Value of K

The magnitude of K indicates the relative amounts of products and reactants at equilibrium.

Value of K	Example	Description
K >> 1	K ≈ 1000	Almost all products; very little reactants
K ≈ 1	K ≈ 1	Almost equal products to reactants
K << 1	K ≈ 0.001	Almost all reactants; very little products

13.2 Manipulating Equilibrium Equations

How Changes Affect K

When a chemical equation is manipulated (e.g., multiplied, reversed), the equilibrium constant K changes accordingly.

• Multiplying the equation by n: $K_{new} = K_{original}^n$

• Reversing the equation: $K_{new} = \frac{1}{K_{original}}$

• Adding equations: $K_{overall} = K_1 \times K_2$

• Example: If $K = 0.20$ for $FO_2 (aq)$, then for $2FO_2 (aq)$, $K = 0.20^2 = 0.040$

13.2 Kc and Kp

Concentration vs. Pressure Equilibrium Constants

Equilibrium can be described using concentrations (Kc) or partial pressures (Kp).

• Kc: Uses molarity (M) for concentrations.

• Kp: Uses partial pressures (atm).

• Relationship: $K_p = K_c(RT)^{\Delta n}$, where R = 0.08206 L·atm/(mol·K), T = temperature in Kelvin, and $\Delta n$ = moles of gaseous products minus moles of gaseous reactants.

• Example: For $3H_2 (g) + N_2 (g) \rightarrow 2NH_3 (g)$ at T = 325 K, $\Delta n = 2 - (3+1) = -2$

13.1 Reaction Quotient (Q)

Comparing Q and K

The reaction quotient (Q) is calculated using the same expression as K, but with initial concentrations or pressures. Comparing Q to K predicts the direction the reaction will shift to reach equilibrium.

• If Q < K: Reaction shifts right (toward products).

• If Q > K: Reaction shifts left (toward reactants).

• If Q = K: System is at equilibrium.

• Example: For $FO_2 (aq)$, if Q = 568.18 and K = 0.20, Q > K, so the reaction shifts left.

13.3 Le Chatelier’s Principle

Response to Disturbance

Le Chatelier’s Principle states that if a system at equilibrium is disturbed, the system will adjust to minimize the disturbance and re-establish equilibrium.

• Add Reactant: Q decreases; shifts right (toward products).

• Add Product: Q increases; shifts left (toward reactants).

• Remove Reactant: Q increases; shifts left.

• Remove Product: Q decreases; shifts right.

Disturbance	Effect on Q	Shift Direction
Add Reactant	Decrease in Q	Right
Add Product	Increase in Q	Left
Remove Reactant	Increase in Q	Left
Remove Product	Decrease in Q	Right

Practice Examples

• Adding HCl to $Mg (s) + 2HCl (aq) \rightarrow MgCl_2 (aq) + H_2 (g)$: Shifts right.

• Removing HCl: Shifts left.

• Adding CO2 to $CaO (s) + CO_2 (g) \rightarrow CaCO_3 (s)$: Shifts right.

Summary Table: Q vs K

Condition	Direction of Shift
Q < K	Right (toward products)
Q > K	Left (toward reactants)
Q = K	No shift; equilibrium

Key Concepts and Definitions

• Dynamic Equilibrium: State where forward and reverse reactions occur at equal rates.

• Equilibrium Constant (K): Ratio of product to reactant concentrations at equilibrium.

• Reaction Quotient (Q): Ratio calculated from initial conditions; predicts direction of shift.

• Le Chatelier’s Principle: System responds to disturbances to restore equilibrium.

• Kc vs. Kp: Kc uses concentrations; Kp uses partial pressures.

Example Application: Predicting the effect of adding or removing reactants/products, or changing pressure, on the position of equilibrium in a chemical system.

Additional info: These notes expand on the original slides by providing full definitions, equations, and context for equilibrium concepts, including the mathematical relationships and practical implications for chemical reactions.