5.3 Calculating equilibrium constants

Equilibrium constants are crucial for understanding chemical reactions. They tell us how much product forms compared to reactants at equilibrium. By calculating these constants, we can predict if a reaction will favor products or reactants.

Knowing how to calculate equilibrium constants helps us figure out reaction direction and extent. We can use this info to optimize reactions in labs and industry. It's a key skill for controlling chemical processes and maximizing product yield.

Equilibrium Constants

Calculating Equilibrium Constants

• Calculate equilibrium constants (Kc and Kp) from equilibrium concentrations or partial pressures
• The equilibrium constant (Kc) represents the ratio of the product of the equilibrium concentrations of the products raised to their stoichiometric coefficients divided by the product of the equilibrium concentrations of the reactants raised to their stoichiometric coefficients
• The equilibrium constant (Kp) represents the ratio of the product of the equilibrium partial pressures of the products raised to their stoichiometric coefficients divided by the product of the equilibrium partial pressures of the reactants raised to their stoichiometric coefficients
• For example, for the reaction $aA + bB \rightleftharpoons cC + dD$, the equilibrium constant Kc would be expressed as $K_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

Relationship between Kc and Kp

• Kc and Kp are related by the ideal gas constant (R) and the temperature (T) in Kelvin, with the equation $K_p = K_c(RT)^{\Delta n}$, where $\Delta n$ represents the change in the number of moles of gas in the reaction
• Equilibrium constants are dimensionless, as the units of concentration or partial pressure cancel out when the equilibrium expression is written
• The value of the equilibrium constant remains independent of the initial concentrations or partial pressures of the reactants and products, and depends only on the temperature

Predicting Reaction Direction

Comparing Reaction Quotient and Equilibrium Constant

• Use equilibrium constants to determine the direction in which a reaction will proceed to reach equilibrium
• If the reaction quotient (Q) is less than the equilibrium constant (K), the reaction will proceed in the forward direction to reach equilibrium
• If the reaction quotient (Q) is greater than the equilibrium constant (K), the reaction will proceed in the reverse direction to reach equilibrium
• If the reaction quotient (Q) equals the equilibrium constant (K), the reaction is at equilibrium and no net change will occur

Calculating Reaction Quotient

• The reaction quotient (Q) is calculated using the same expression as the equilibrium constant, but with the instantaneous concentrations or partial pressures of the reactants and products at any point during the reaction
• For example, for the reaction $aA + bB \rightleftharpoons cC + dD$, the reaction quotient Q would be expressed as $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$ using the instantaneous concentrations at a given point in the reaction

Equilibrium Constant Magnitude

Interpreting Equilibrium Constant Values

• Relate the magnitude of the equilibrium constant to the extent of a reaction and the relative concentrations of reactants and products at equilibrium
• A large equilibrium constant (K >> 1) indicates that the reaction favors the formation of products at equilibrium, with higher concentrations of products relative to reactants (water dissociation, $K_w = 1.0 \times 10^{-14}$)
• A small equilibrium constant (K << 1) indicates that the reaction favors the formation of reactants at equilibrium, with higher concentrations of reactants relative to products (dinitrogen tetroxide dissociation, $K_c = 4.6 \times 10^{-3}$)
• An equilibrium constant close to 1 (K ≈ 1) indicates that the reaction has similar concentrations of reactants and products at equilibrium

Relating Equilibrium Constant to Reaction Extent

• The magnitude of the equilibrium constant can be used to determine the extent of the reaction, with a larger K value indicating a more complete reaction and a smaller K value indicating a less complete reaction
• For example, the formation of ammonia from nitrogen and hydrogen ($N_2 + 3H_2 \rightleftharpoons 2NH_3$) has a relatively small equilibrium constant ($K_c = 5.8 \times 10^{-3}$ at 500 K), indicating that the reaction is not very complete and favors the reactants at equilibrium

Equilibrium Calculations

Degree of Dissociation

• Solve problems involving equilibrium constants, concentrations, partial pressures, and degrees of dissociation
• The degree of dissociation (α) represents the fraction of a reactant that dissociates into products at equilibrium, and can be calculated using the equilibrium concentrations or partial pressures
• The equilibrium concentrations or partial pressures of the reactants and products can be calculated using the initial concentrations or partial pressures, the stoichiometric coefficients, and the degree of dissociation

Calculating Equilibrium Concentrations and Partial Pressures

• The equilibrium constant can be calculated using the equilibrium concentrations or partial pressures, and the stoichiometric coefficients of the reactants and products
• The initial concentrations or partial pressures of the reactants and products can be calculated using the equilibrium constant, the equilibrium concentrations or partial pressures, and the stoichiometric coefficients
• The ICE (Initial, Change, Equilibrium) table method can be used to solve equilibrium problems by setting up a table with the initial concentrations, the changes in concentrations, and the equilibrium concentrations of the reactants and products
• For example, consider the reaction $2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)$ with $K_c = 280$ at a certain temperature. If the initial concentrations are $[SO_2] = 0.500 M$, $[O_2] = 0.250 M$, and $[SO_3] = 0 M$, an ICE table can be used to calculate the equilibrium concentrations