Chemical Equilibrium Practice Flashcards

Introduction to Chemical Equilibrium

• Stoichiometry vs. Reality: In standard stoichiometry, it is often assumed that reactions proceed to completion, meaning they continue until at least one reactant is entirely consumed. While many reactions do this, many others stop far short of completion.
• The Dimerization of Nitrogen Dioxide:     * Reaction: $2NO_2(g) \rightleftharpoons N_2O_4(g)$     * $NO_2$ is a reddish-brown gas; $N_2O_4$ is a colorless gas.     * In a sealed, evacuated vessel at $25\,^{\circ}\text{C}$, the dark brown color of $NO_2$ decreases as it converts to $N_2O_4$, but the color never disappears entirely. Instead, it reaches a constant intensity, indicating that the concentration of $NO_2$ is no longer changing.
• Chemical Equilibrium: The state in which the concentrations of all reactants and products remain constant with time. Any chemical reaction carried out in a closed vessel will eventually reach equilibrium.
• Equilibrium Position:     * Right-leaning: If the equilibrium highly favors the products, the reaction appears to have gone to completion. For example, forming water vapor from hydrogen and oxygen.     * Left-leaning: If the reaction occurs only to a slight extent, the equilibrium position lies far to the left. For example, the decomposition of solid $CaO$ into solid $Ca$ and gaseous $O_2$ at $25\,^{\circ}\text{C}$ is virtually undetectable.

6.1 The Equilibrium Condition

• Dynamic Nature: On the molecular level, equilibrium is not static but a highly dynamic situation characterized by "frenetic activity."
• The Bridge Analogy: Chemical equilibrium is analogous to two island cities connected by a bridge. If the traffic flow is equal in both directions, the number of cars in each city remains constant even though motion (frequent crossing) is occurring. There is no net change in population.
• Reaction Profile (Steam and Carbon Monoxide):     * Equation: $H_2O(g) + CO(g) \rightleftharpoons H_2(g) + CO_2(g)$     * If equal moles of $CO$ and $H_2O$ are mixed, they react at a $1:1$ ratio. Initially, concentrations of reactants decrease while those of products ($H_2$ and $CO_2$) increase from zero.     * Beyond a specific time (the equilibrium point), concentrations stop changing. Reactants never reach zero concentration.
• Causes of Equilibrium:     * Reactions occur via molecular collisions that break bonds and allow rearrangement.     * Forward Reaction: As reactants collide and form products, their concentrations decrease, causing the forward rate to slow down.     * Reverse Reaction: Initially, there are no products, so the reverse reaction cannot occur. As product concentrations build, the reverse reaction rate increases.     * Equilibrium Achievement: Equilibrium is reached when the rate of the forward reaction equals the rate of the reverse reaction.     * The Equilibrium Condition Defined: The concentrations of reactants and products remain constant at equilibrium because the forward and reverse reaction rates are equal.

6.2 The Equilibrium Constant

• Law of Mass Action: Proposed in 1864 by Norwegian chemists Cato Maximilian Guldberg (1836–1902) and Peter Waage (1833–1900).
• General Expression: For a reaction $jA + kB \rightleftharpoons lC + mD$, the equilibrium expression is:     $K = \frac{[C]^l [D]^m}{[A]^j [B]^k}$     * Square brackets indicate molar concentrations ($mol/L$) at equilibrium.     * $K$ is the equilibrium constant (specifically $K_{obs}$ when units are present; thermodynamic $K$ is unitless).
• The Haber Process: Synthesis of ammonia: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$.     * Developed by Fritz Haber (1868–1934) initially for fertilizers, later used for explosives in WWI.     * At $127\,^{\circ}\text{C}$, if $[NH_3] = 3.1 \times 10^{-2}\,M$, $[N_2] = 8.5 \times 10^{-1}\,M$, and $[H_2] = 3.1 \times 10^{-3}\,M$:     $K = \frac{(3.1 \times 10^{-2})^2}{(8.5 \times 10^{-1})(3.1 \times 10^{-3})^3} = 3.8 \times 10^4\,L^2/mol^2$
• Manipulating Equilibrium Expressions:     1. Reversing the Equation: The new constant ($K_r$) is the reciprocal of the original: $K_r = \frac{1}{K}$.     2. Multiplying by a Factor ($n$): The new constant ($K_s$) is the original constant raised to the power of $n$: $K_{new} = (K_{original})^n$.
• Equilibrium Constant vs. Equilibrium Position:     * Equilibrium Constant: There is only one value for $K$ for a system at a specific temperature.     * Equilibrium Position: There are an infinite number of positions (specific sets of concentrations) that depend on initial concentrations. However, all positions must satisfy the value of $K$.

6.3 Equilibrium Expressions Involving Pressures

• Relationship to Concentration: Using the ideal gas law $PV = nRT$, concentration ($C$) is $n/V = P/RT$.
• Pressure-based Constant ($K_p$): Uses partial pressures ($P$).     * Example for Haber process: $K_p = \frac{P_{NH_3}^2}{(P_{N_2})(P_{H_2}^3)}$
• General Relationship Between $K$ and $K_p$:     $K_p = K(RT)^{\Delta n}$     * $\Delta n$ is the sum of the coefficients of the gaseous products minus the sum of the coefficients of the gaseous reactants.     * Example: For $H_2(g) + F_2(g) \rightleftharpoons 2HF(g)$, $\Delta n = 2 - (1 + 1) = 0$, so $K = K_p$.
• Units: If the sum of powers in the numerator equals the denominator, $K$ and $K_p$ are unitless and equal. Otherwise, they have "apparent units."

6.4 The Concept of Activity

• Definition: Activity ($a_i$) is the ratio of the equilibrium pressure (or concentration) of a substance to a reference pressure (or concentration).
• Reference States:     * For gases: $P_{reference} = 1\,atm$ (or $1\,bar$ per IUPAC 1982 convention).     * For solutions: $C_{reference} = 1\,mol/L$.
• Thermodynamic $K$: Because activities are ratios, they are unitless, making the thermodynamic equilibrium constant unitless. This text adopts the convention of omitting units for $K$.

6.5 Heterogeneous Equilibria

• Definition: Equilibria involving more than one phase (e.g., solids and gases).
• Pure Solids and Liquids: The activity of a pure solid or liquid is always $1$.
• Application to Expressions: Concentrations or pressures of pure solids and pure liquids are not included in the equilibrium expression.
• Example: Decomposition of Calcium Carbonate:     $CaCO_3(s) \rightleftharpoons CaO(s) + CO_2(g)$     * $K = [CO_2]$     * $K_p = P_{CO_2}$     * The equilibrium position does not depend on the amount of $CaCO_3(s)$ or $CaO(s)$ present, so long as some of each is there.

6.6 Applications of the Equilibrium Constant

• Extent of Reaction:     * $K \gg 1$: Reaction consists mostly of products; equilibrium lies to the right (essentially goes to completion).     * $K \ll 1$: Reaction consists mostly of reactants; equilibrium lies to the left (does not occur significantly).     * Note: The size of $K$ does not indicate the speed of the reaction (kinetics); only the tendency to occur.
• Reaction Quotient ($Q$): Calculated by applying the Law of Mass Action to initial concentrations.     * $Q = K$: System is at equilibrium.     * $Q > K$: Ratio of products to reactants is too large. System shifts left (consuming products, forming reactants).     * $Q < K$: Ratio of products to reactants is too small. System shifts right (forming products).

6.7 Solving Equilibrium Problems

• Procedure (ICE Table):     1. Write the balanced equation.     2. Write the equilibrium expression.     3. List initial concentrations.     4. Calculate $Q$ to determine direction of shift.     5. Define the change needed ($x$) and the final equilibrium concentrations in terms of initial concentrations and $x$.     6. Substitute into the equilibrium expression and solve for $x$.     7. Check the calculated concentrations by plugging back into the expression for $K$.
• Quadratic Formula: Used when expressions are of the form $ax^2 + bx + c = 0$.     $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
• Small Equilibrium Constants Approximation: If $K$ is very small, the shift ($x$) is likely very small. In such cases, terms like $0.50 - 2x$ can be approximated as $0.50$.     * The 5% Rule (Guideline): A discrepancy of about $4-6\%$ is usually acceptable relative to the precision of the experimental $K$ value.

6.8 Le Châtelier’s Principle

• Definition: If a change in conditions (stress) is imposed on a system at equilibrium, the position will shift in a direction that tends to reduce that change.
• Change in Concentration:     * Add a component: System shifts away from the added component.     * Remove a component: System shifts toward the removed component.
• Change in Pressure:     1. Add/Remove gaseous reactant/product: Shifts as per concentration change.     2. Add inert gas (at constant volume): No effect on concentration or partial pressures; no shift occurs.     3. Change volume:         * Reduce Volume: System shifts toward the side with fewer gaseous molecules to reduce volume.         * Increase Volume: System shifts toward the side with more gaseous molecules.
• Change in Temperature: Changes the value of K.     * Exothermic Reaction ($Reaction \rightleftharpoons Products + Energy$): Adding heat (increasing temperature) shifts the reaction to the left; $K$ decreases.     * Endothermic Reaction ($Energy + Reaction \rightleftharpoons Products$): Adding heat shifts the reaction to the right; $K$ increases.

6.9 Equilibria Involving Real Gases

• Non-ideal Behavior: At high pressures (above $1\,atm$), the observed pressure ($P_{obs}$) deviates from ideal pressure ($P_{ideal}$).
• Observed $K_p$ ($K_{p\,obs}$): For the Haber process at $723\,K$, $K_{p\,obs}$ increases significantly with total pressure (from $4.4 \times 10^{-5}$ at $10\,atm$ to $5.3 \times 10^{-4}$ at $1000\,atm$).
• Activity Coefficients ($\gamma_i$): Used to correct observed pressures to ideal values: $a_i = \gamma_i \frac{P_{i\,obs}}{P_{ref}}$.
• General Rule: Values calculated from observed pressures are usually within $1\%$ of the true value if equilibrium pressures are $1\,atm$ or less.