Chemical equilibrium is the dynamic state achieved in a reversible reaction when the rate of product formation equals the rate at which products revert back to reactants. This balance means concentrations remain constant over time, though not necessarily equal. To quantify the position of this balance, chemists use the Equilibrium Constant, symbolized by \(K\). This numerical value describes the ratio of product to reactant concentrations once equilibrium has been established. Writing the mathematical expression for \(K\) is the foundational step in analyzing any reversible chemical system.
Establishing the Basic Structure
The fundamental step in defining the equilibrium expression involves setting up a ratio comparing the amounts of products to the amounts of reactants. This structure applies specifically to homogeneous reactions, where all substances are in the same physical state (e.g., all gases or all aqueous). The numerator is dedicated to the products, while the denominator contains the reactants.
Every substance’s concentration is represented in the expression, and each is raised to a power corresponding to its stoichiometric coefficient from the balanced chemical equation. For a generic reaction, \(aA + bB \rightleftharpoons cC + dD\), the mathematical framework is established directly from the coefficients \(a, b, c,\) and \(d\).
Applying this rule, the expression for the generic reaction becomes \(K = \frac{[C]^c [D]^d}{[A]^a [B]^b}\), where the square brackets denote the concentration. The exponents are derived directly from the coefficients, making the initial balancing step necessary before writing the expression. This structure is often referred to as the law of mass action.
Consider the homogeneous reaction: \(\text{N}_2(g) + 3\text{H}_2(g) \rightleftharpoons 2\text{NH}_3(g)\). The ammonia product is placed in the numerator, and the reactants, nitrogen and hydrogen, are placed in the denominator.
The balanced equation shows coefficients of 2 for \(\text{NH}_3\), 1 for \(\text{N}_2\), and 3 for \(\text{H}_2\). Therefore, the product concentration is squared, and the hydrogen concentration is cubed. The resulting expression is \(K = \frac{[\text{NH}_3]^2}{[\text{N}_2][\text{H}_2]^3}\).
Adjusting for Different Physical States
A modification is necessary when the chemical system involves heterogeneous equilibrium, which includes substances in more than one physical state. This requires the exclusion of pure solids and pure liquids from the final equilibrium expression.
The reason for this exclusion is that the “concentration” of a pure solid or liquid is essentially its density, which remains constant throughout the reaction. Because their values do not change, they are mathematically incorporated into the constant \(K\) itself, simplifying the final written expression.
Chemists define the thermodynamic activity of a pure solid or liquid as equal to one. This simplification focuses the expression only on the components whose concentrations can actually vary, typically gases and dissolved species (aqueous). Ignoring these constant components is standard practice.
A common example is the thermal decomposition of calcium carbonate: \(\text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g)\). Since both calcium carbonate and calcium oxide are pure solids, they must be excluded. The only component remaining that can change its concentration is the gaseous carbon dioxide.
The resulting simplified expression becomes \(K = [\text{CO}_2]\). The equilibrium position for this reaction is therefore solely dependent on the concentration of the carbon dioxide gas produced.
Concentration vs. Pressure Expressions
After establishing the structure and phase adjustments, the appropriate notation must be selected based on the units used. The two primary forms of the equilibrium constant are \(K_c\) and \(K_p\), which are distinct yet related expressions for the same chemical system. The choice depends on the physical states and how concentrations are reported.
The equilibrium constant based on molar concentrations, \(K_c\), uses molarity (moles per liter) for all variable components. This concentration is symbolized using square brackets, such as \([\text{A}]\). \(K_c\) is most frequently employed for reactions in liquid solutions, but it can also be used for gaseous reactions.
Conversely, the equilibrium constant based on partial pressures, \(K_p\), is used exclusively for systems involving gases. \(K_p\) utilizes the partial pressure of each gas, denoted by \(P\) followed by the chemical formula (e.g., \(P_{\text{A}}\)). Pressure measurement is often more convenient for high-temperature gas-phase reactions.
While both \(K_c\) and \(K_p\) describe the same point of equilibrium, their numerical values are not always the same. The relationship between them is governed by the ideal gas law, linking concentration to pressure. The difference is accounted for by a term involving the change in the number of moles of gas (\(\Delta n_{\text{gas}}\)). For reactions where the total moles of gaseous products equals the total moles of gaseous reactants, \(\Delta n_{\text{gas}}\) is zero, and the two constants are numerically equivalent.
Interpreting the Equilibrium Constant
The final step after writing the equilibrium expression is understanding what the resulting numerical value of \(K\) signifies about the chemical reaction. The magnitude of the equilibrium constant provides direct insight into the extent to which a reversible reaction proceeds toward product formation. This numerical value is a powerful tool for predicting the composition of the mixture at equilibrium.
If the calculated value of \(K\) is significantly greater than one, it indicates that the numerator (products) is much larger than the denominator (reactants). A large \(K\) value means that the concentration of products is favored at equilibrium, and the reaction proceeds far to the right, almost to completion. For example, a \(K\) value of \(10^5\) suggests a strong preference for product formation.
Conversely, a \(K\) value that is much less than one suggests that the reactants are favored at equilibrium. In this scenario, the denominator is much larger, meaning very little product is formed when the system reaches its balanced state. A very small \(K\), perhaps \(10^{-5}\), indicates that the reaction barely proceeds past the starting materials.
When the value of \(K\) is near one (typically between \(0.01\) and \(100\)), it signifies that the mixture at equilibrium contains substantial amounts of both reactants and products. The equilibrium constant only describes the final composition of the mixture; it offers no information regarding the rate or speed at which the reaction reaches this balanced state.