Premed · Premed · General Chemistry 2
Lecture 3: Chemical Equilibrium: Principles
General Chemistry II
Learning Objectives
By the end of this lecture, students will be able to:
- Define dynamic equilibrium and explain its characteristics
- Write equilibrium constant expressions (Kc and Kp) for a given reaction
- Relate Kc and Kp using the ideal gas law
- Interpret the magnitude of K in terms of the extent of reaction
- Manipulate equilibrium expressions when reactions are reversed, multiplied, or combined
- Calculate the reaction quotient Q and predict the direction of reaction
Lecture Content
I. The Nature of Chemical Equilibrium
Chemical equilibrium is a dynamic state in which the rate of the forward reaction equals the rate of the reverse reaction. At equilibrium, the concentrations of reactants and products remain constant over time, but they are not necessarily equal to one another. Equilibrium can be approached from either direction, whether starting with pure reactants or pure products, and the same equilibrium state will be reached at a given temperature.
Several characteristics define the equilibrium state. The system must be closed, meaning there is no exchange of matter with the surroundings. Macroscopic properties such as concentrations, pressure, and color remain constant. At the molecular level, however, both the forward and reverse reactions continue to occur; the system is dynamic, not static. Equilibrium can be established at any temperature, but the position of equilibrium, meaning the relative amounts of reactants and products, depends on the temperature.
<image>A graph showing concentration vs. time for a generic reversible reaction A <=> B approaching equilibrium. Two curves are plotted: [A] starts high and decreases, leveling off at [A]_eq; [B] starts at zero and increases, leveling off at [B]_eq. A vertical dashed line marks the point where equilibrium is established. To the right of the line, both concentrations remain constant. A second smaller graph below shows the forward rate decreasing and the reverse rate increasing until they become equal at the equilibrium point.</image>
II. The Equilibrium Constant Expression (Kc)
For a general reaction aA + bB <=> cC + dD, the equilibrium constant in terms of molar concentrations is written as Kc = [C]^c[D]^d / ([A]^a[B]^b). By convention, product concentrations appear in the numerator and reactant concentrations in the denominator, with each concentration raised to the power of its stoichiometric coefficient.
Several important rules govern how to write Kc expressions. Pure solids and pure liquids are not included because their activities are defined as 1. Only aqueous species and gases appear in the expression. For example, the decomposition of calcium carbonate, CaCO3(s) <=> CaO(s) + CO2(g), yields simply Kc = [CO2]. While Kc is technically dimensionless when expressed in terms of thermodynamic activities, in practice general chemistry courses often work with numerical values that carry implied units.
III. The Equilibrium Constant in Terms of Pressure (Kp)
For reactions involving gases, equilibrium can also be expressed using partial pressures instead of molar concentrations. The expression takes the form Kp = (P_C)^c (P_D)^d / ((P_A)^a (P_B)^b). The relationship between Kc and Kp is given by Kp = Kc(RT)^(Delta n), where Delta n equals the total moles of gaseous products minus the total moles of gaseous reactants, R = 0.08206 Latm/(molK), and T is the temperature in Kelvin. When Delta n = 0, meaning equal moles of gas on both sides, Kp and Kc are numerically equal.
IV. Magnitude of K and the Extent of Reaction
The numerical value of K conveys essential information about the position of equilibrium. When K is much greater than 1 (for example, 10^3 or larger), the equilibrium lies far to the right and products are strongly favored. When K is much less than 1 (for example, 10^-3 or smaller), the equilibrium lies far to the left and reactants are strongly favored. When K is near 1, significant amounts of both reactants and products coexist at equilibrium.
It is important to recognize that K says nothing about how fast equilibrium is reached; that is the domain of kinetics. Furthermore, K depends only on temperature, not on the initial concentrations of reactants or products.
<image>A horizontal number line showing the magnitude of K on a logarithmic scale from 10^-10 to 10^10. The left side (K << 1) is labeled "Reactants favored" with an arrow pointing left. The right side (K >> 1) is labeled "Products favored" with an arrow pointing right. The center (K approximately 1) is labeled "Comparable amounts." Above the line, three example beakers illustrate the equilibrium composition: left beaker mostly filled with reactant color, center beaker with a mix, right beaker mostly filled with product color.</image>
V. Manipulating Equilibrium Expressions
When chemical equations are manipulated algebraically, the equilibrium constant changes in predictable ways. Reversing a reaction inverts the equilibrium constant: K_reverse = 1/K_forward. So if A <=> B has K = 100, then B <=> A has K = 0.01. Multiplying a reaction by a factor n raises the equilibrium constant to that power: K_new = (K_original)^n. For instance, doubling the reaction 2A <=> 2B gives K = (100)^2 = 10,000. When reactions are added together, analogous to Hess's Law for enthalpies, the corresponding equilibrium constants are multiplied: K_overall = K1 K2 K3 and so on. These rules are essential when you need to combine known equilibrium expressions to find K for a desired overall reaction.
VI. The Reaction Quotient (Q)
The reaction quotient Q has exactly the same mathematical form as K, but it uses current (non-equilibrium) concentrations rather than equilibrium concentrations. For a reaction aA + bB <=> cC + dD, Qc = [C]^c[D]^d / ([A]^a[B]^b) evaluated at any point during the reaction.
Comparing Q to K reveals the direction in which the reaction must proceed to reach equilibrium. If Q < K, there is a relative excess of reactants and the reaction proceeds to the right, forming more products. If Q > K, there is a relative excess of products and the reaction proceeds to the left, regenerating reactants. If Q = K, the system is already at equilibrium. The reaction quotient is a powerful predictive tool that can determine whether a precipitate will form, whether a reaction will proceed spontaneously, or in which direction a system will shift.
<image>A diagram showing three scenarios for the reaction quotient Q compared to K. Three horizontal bars represent the "equilibrium scale." Left bar: Q < K, with an arrow pointing right labeled "Net forward reaction, system shifts toward products." Middle bar: Q = K, labeled "System at equilibrium, no net change." Right bar: Q > K, with an arrow pointing left labeled "Net reverse reaction, system shifts toward reactants." Each bar shows a schematic representation of relative reactant and product concentrations.</image>
VII. Equilibrium and Thermodynamics (Preview)
The equilibrium constant is intimately connected to thermodynamics through the standard Gibbs free energy change: Delta G^0 = -RT ln(K). A large negative Delta G^0 corresponds to a large K, indicating that products are strongly favored at equilibrium. Conversely, a large positive Delta G^0 corresponds to a small K, meaning reactants are favored. This deep connection between thermodynamics and equilibrium will be explored in greater detail in later lectures.
