Chemical Equilibrium, ICE Tables, and Le Chatelier's Principle Study Guide

The equilibrium constant for a reaction involving gases can be expressed in terms of partial pressures ( $K_p$ ) or molar concentrations ( $K_c$ ).
The mathematical relationship between these two constants is defined by the formula: $K_p = K_c(RT)^{\Delta n}$
In this equation, $\Delta n$ represents the change in the number of moles of gaseous components: $\Delta n = \text{moles of gas products} - \text{moles of gas reactants}$
$K_p$ values are used exclusively for gaseous equilibrium systems.

The reaction quotient ( $Q$ ) is calculated using the same expression as the equilibrium constant but utilizes initial concentrations rather than equilibrium concentrations.
By comparing the magnitude of the equilibrium constant ( $K$ ) to the reaction quotient ( $Q$ ), the direction of the shift toward equilibrium can be predicted: * Case 1: K > Q * The ratio of products to reactants is currently too small. * The system will shift to the right (toward the products) to reach equilibrium. * Case 2: K < Q * The ratio of products to reactants is currently too large. * The system will shift to the left (toward the reactants) to reach equilibrium. * Case 3: $K = Q$ * The concentrations are equal to their equilibrium values. * No net shift occurs.

The ICE method is utilized to calculate equilibrium concentrations from initial conditions.
I (Initial): Represents the initial concentrations provided in the problem description.
C (Change): Represents the change in concentration required to reach equilibrium. * Symbols like $+x$ or $-x$ are used based on the direction of the reaction. * If the reaction proceeds to the right, reactants are represented by $-x$ (or the appropriate coefficient, e.g., $-x$ ) and products by a positive value (e.g., $+2x$ depending on the stoichiometry).
E (Equilibrium): The final concentration value. * The equilibrium expression is set up as the product of the concentrations of products raised to their stoichiometric coefficients divided by the product of the concentrations of reactants raised to their stoichiometric coefficients. * The calculated value is substituted back for $x$ to solve for individual species concentrations.
Heuristic for Direction: To determine shifts, one should set up the comparison alphabetically (place $K$ then $Q$ ) and follow the direction indicated by the resulting "arrow" or inequality.

The magnitude of the equilibrium constant ( $K_c$ ) indicates the position of equilibrium at a specific temperature: * K_c > 100: Products are heavily favored. According to the transcript, the equilibrium lies to the left. * K_c < 0.01: Reactants are favored. According to the transcript, the equilibrium lies to the right. * $0.01 \leq K_c \leq 100$ : Neither products nor reactants are significantly favored.
Exclusions: Only aqueous solutions ( $aq$ ) and gases ( $g$ ) are included in equilibrium expressions. Pure solids ( $s$ ) and pure liquids ( $l$ ) are omitted.

Reversed Reactions: When a reversible reaction is reversed ( $aA + bB \rightleftharpoons cC + dD$ becomes $cC + dD \rightleftharpoons aA + bB$ ), the new equilibrium constant is the inverse of the original: $K_{\text{new}} = \frac{1}{K_{\text{old}}} = \frac{\text{Reactants}}{\text{Products}}$
Multiplied by a Constant: If the coefficients of a balanced chemical equation are multiplied by a constant ( $n$ ), the new equilibrium constant is the original value raised to the power of that constant: $K_{\text{new}} = (K_c)^{n}$

Le Chatelier’s Principle states that a system at equilibrium will shift to counteract any applied stress.
Changes in Concentration: * If the concentration of a substance is increased, the system shifts to consume that substance. * If the concentration of a substance is decreased, the system shifts to produce more of that substance.
Changes in Volume and Pressure: * Reducing volume of a gas increases pressure, causing the system to shift toward the side with fewer moles of gas to reduce pressure. * Increasing volume causes a decrease in pressure, shifting the system toward the side that produces more moles of gas.

Thermal Effects on Equilibrium: Heat behaves similarly to concentration shifts depending on whether the reaction is exothermic or endothermic. * Exothermic Reactions (\Delta H < 0): Heat is treated as a product. Adding heat shifts the equilibrium to the reactant side. * Endothermic Reactions (\Delta H > 0): Heat is treated as a reactant. Adding heat shifts the equilibrium toward the product side.
The Role of Catalysts: * A catalyst increases the speed of both the forward and reverse reactions to an equal degree. * Consequently, a catalyst does not change the numerical value of the equilibrium constant ( $K$ ). * A catalyst does not shift the position of the equilibrium.