Unit 8: Chemical Equilibrium

Introduction to Equilibrium

In chemistry, many reactions proceed in one direction until the reactants are consumed. However, a significant number of reactions are reversible, meaning that products can react to reform the original reactants. When a reversible reaction occurs in a closed system, it eventually reaches a state where the rates of the forward and backward reactions become equal, and the net change in concentrations of reactants and products ceases. This state is known as equilibrium.

Understanding chemical equilibrium is crucial for predicting the outcome of reactions, optimizing industrial processes, and comprehending biological systems.

1. Physical and Chemical Equilibrium

Equilibrium is a state where opposing processes occur at equal rates, leading to no net change in the macroscopic properties of the system. We can observe equilibrium in both physical and chemical changes.

Physical Equilibrium

Physical equilibrium refers to a state where there is an equilibrium between different phases or physical states of the same substance. While the system appears static at a macroscopic level, processes are continuously occurring at the molecular level at equal rates in opposite directions.

• Solid-Liquid Equilibrium (Melting/Freezing)

  Consider ice and water coexisting at 0°C and 1 atm pressure in a closed container. At this specific temperature and pressure, the rate at which ice melts into water is equal to the rate at which water freezes into ice. The amount of ice and water remains constant, although individual water molecules are constantly transitioning between the solid and liquid phases.

  H2O(s) ⇌ H2O(l)
• Liquid-Vapor Equilibrium (Evaporation/Condensation)

  If water is placed in a closed container at a constant temperature, some water molecules will evaporate and become vapor. As the concentration of water vapor increases, some vapor molecules will condense back into liquid. Eventually, the rate of evaporation will equal the rate of condensation. At this point, the vapor pressure above the liquid becomes constant, and the system is in liquid-vapor equilibrium.

  H2O(l) ⇌ H2O(g)
• Solid-Vapor Equilibrium (Sublimation)

  Some solids, like iodine or dry ice (solid CO₂), can directly convert into vapor without passing through the liquid phase. In a closed container, equilibrium is established when the rate of sublimation equals the rate of deposition.

  I2(s) ⇌ I2(g) CO2(s) ⇌ CO2(g)
• Solution Equilibrium (Dissolution/Precipitation)

  When a solid solute like sugar or salt is added to a solvent, it dissolves. If enough solute is added, the solution becomes saturated. At this point, the rate at which the solute dissolves equals the rate at which the dissolved solute crystallizes out of the solution. The concentration of the dissolved solute remains constant.

  NaCl(s) ⇌ Na+(aq) + Cl-(aq)

Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rate of the forward reaction equals the rate of the backward (reverse) reaction. Consequently, the concentrations of reactants and products remain constant over time, provided the system is closed and conditions (like temperature) are unchanged.

Key characteristics of chemical equilibrium:

• It can only be achieved in a closed system where no matter can enter or leave.
• The reaction is reversible, meaning reactants form products, and products can reform reactants.
• The rate of the forward reaction equals the rate of the backward reaction.
• The concentrations of reactants and products remain constant at equilibrium. It's important to note that these concentrations are not necessarily equal, but rather their net change is zero.
• It is dynamic in nature, not static.

A classic example is the Haber process for ammonia synthesis:

Initially, nitrogen and hydrogen react to form ammonia. As ammonia concentration increases, it starts decomposing back into nitrogen and hydrogen. Eventually, the rate of ammonia formation equals the rate of its decomposition, and the system reaches equilibrium.

2. Dynamic Nature of Chemical Equilibrium

One of the most crucial aspects of chemical equilibrium is its dynamic nature. Although the macroscopic properties of a system at equilibrium (like concentrations, pressure, color) appear constant, the reactions have not stopped. Instead, both the forward and backward reactions continue to occur simultaneously, but at exactly equal rates.

Imagine a busy intersection with traffic flowing in two opposite directions. If the number of cars entering the intersection from one side is equal to the number of cars leaving from the opposite side, the total number of cars within the intersection might remain constant. However, the individual cars are continuously moving and changing their positions. Similarly, at chemical equilibrium, individual molecules are constantly reacting and interconverting between reactants and products.

• Forward and backward reactions continue: Molecules of reactants are still forming products, and molecules of products are still forming reactants.
• Equal rates: The speed at which reactants are converted to products is exactly matched by the speed at which products are converted back to reactants.
• Net change in concentration is zero: Because the rates are equal, there is no overall change in the amounts of reactants or products over time.
• Reaction does not stop: This distinguishes equilibrium from a reaction that has simply run to completion or stopped due to the consumption of a limiting reactant.

The dynamic nature of equilibrium can be experimentally demonstrated using isotopic labeling. For example, if radioactive iodine (¹³¹I₂) is added to a system at equilibrium: H2(g) + I2(g) ⇌ 2HI(g), the radioactivity is soon found in both I2 and HI, indicating that the forward and reverse reactions are still proceeding even at equilibrium.

3. Law of Mass Action

The Law of Mass Action, proposed by Cato Guldberg and Peter Waage in 1864, quantifies the relationship between the rate of a reaction and the concentrations of the reacting species. It states:

At a given temperature, the rate of a chemical reaction is directly proportional to the product of the molar concentrations of the reactants, each raised to the power of its stoichiometric coefficient as appearing in the balanced chemical equation.

Consider a general reversible reaction:

where a, b, c, d are the stoichiometric coefficients, and A, B, C, D are the reacting species.

According to the Law of Mass Action:

• The rate of the forward reaction (reactants to products) is: Ratef = kf[A]a[B]b

  Here, kf is the rate constant for the forward reaction, and [A] and [B] are the molar concentrations of reactants A and B, respectively.

• The rate of the backward (reverse) reaction (products to reactants) is: Rateb = kb[C]c[D]d

  Here, kb is the rate constant for the backward reaction, and [C] and [D] are the molar concentrations of products C and D, respectively.

At equilibrium, by definition, the rate of the forward reaction is equal to the rate of the backward reaction:

This fundamental relationship forms the basis for defining the equilibrium constant.

Example: For the reaction 2NO2(g) ⇌ N2O4(g)

• Forward rate: Ratef = kf[NO2]2
• Backward rate: Rateb = kb[N2O4]
• At equilibrium: kf[NO2]2 = kb[N2O4]

4. Equilibrium Constant (Kc and Kp)

From the Law of Mass Action, we established that at equilibrium, kf[A]a[B]b = kb[C]c[D]d. We can rearrange this equation to define a constant ratio:

This ratio of rate constants is called the equilibrium constant.

Concentration Equilibrium Constant (Kc)

When the concentrations of reactants and products are expressed in molarity (moles per liter), the equilibrium constant is denoted as Kc.

For the general reaction aA + bB ⇌ cC + dD, the expression for Kc is:

where [A], [B], [C], [D] represent the equilibrium molar concentrations of the respective species.

Characteristics of Kc:

• Temperature Dependent: The value of Kc is constant for a particular reaction at a given temperature. Any change in temperature will change the value of Kc.
• Independent of Initial Concentrations: Regardless of the initial amounts of reactants or products, the system will always reach equilibrium such that the ratio defined by Kc remains the same at a constant temperature.
• Independent of Catalyst: A catalyst speeds up both the forward and backward reactions equally, thus allowing the system to reach equilibrium faster, but it does not change the equilibrium concentrations or the value of Kc.
• Units of Kc: The units of Kc depend on the stoichiometry of the reaction. For example, if Δn = (c+d) - (a+b), the units would be (mol/L)Δn. Often, Kc is treated as dimensionless in advanced contexts, but for introductory chemistry, calculating units is common.

Significance of Kc:

The magnitude of Kc provides valuable information about the extent to which a reaction proceeds towards products at equilibrium:

• Large K_c (K_c >> 1, e.g., 10³ or more): The reaction goes almost to completion. Products are highly favored at equilibrium, and very little reactant remains. The equilibrium lies far to the right.
• Small K_c (K_c << 1, e.g., 10^-3 or less): Very little product is formed at equilibrium. Reactants are highly favored. The equilibrium lies far to the left.
• Intermediate K_c (K_c ≈ 1): Significant amounts of both reactants and products are present at equilibrium.

Writing Equilibrium Constant Expressions:

When writing Kc expressions, it is crucial to remember the following rule:

• Only include species whose concentrations can change significantly. This means gases (g) and aqueous solutions (aq) are included.
• Pure solids (s) and pure liquids (l) are excluded from the equilibrium expression because their concentrations (or more precisely, their activities) are considered constant and are incorporated into the value of Kc itself.

Examples:

1. Homogeneous Equilibrium (all species in the same phase): N2(g) + 3H2(g) ⇌ 2NH3(g) Kc = [NH3]2 / ([N2][H2]3)
2. Heterogeneous Equilibrium (species in different phases): CaCO3(s) ⇌ CaO(s) + CO2(g)

   Since CaCO3 and CaO are pure solids, they are excluded.

   Kc = [CO2]
3. Acid Dissociation (aqueous equilibrium): CH3COOH(aq) + H2O(l) ⇌ CH3COO-(aq) + H3O+(aq)

   H2O is a pure liquid solvent, so it is excluded.

   Kc = [CH3COO-][H3O+] / [CH3COOH]

Pressure Equilibrium Constant (Kp)

For reactions involving gases, it is often more convenient to express the equilibrium constant in terms of the partial pressures of the gaseous reactants and products, rather than their molar concentrations. This is denoted as Kp.

For the general gaseous reaction aA(g) + bB(g) ⇌ cC(g) + dD(g), the expression for Kp is:

where PA, PB, PC, PD represent the equilibrium partial pressures of the respective gaseous species.

Like Kc, Kp is also temperature-dependent and independent of initial conditions or catalysts.

Example: For the Haber process:

5. Relationship between Kp and Kc

The ideal gas law, PV = nRT, can be used to establish a relationship between partial pressure and molar concentration. Since n/V is molar concentration (C), we can write P = CRT. Substituting this into the Kp expression yields the relationship between Kp and Kc.

The relationship is given by the equation:

Where:

• R is the ideal gas constant, 0.0821 L·atm/(mol·K).
• T is the absolute temperature in Kelvin.
• Δn (delta n) is the change in the number of moles of gaseous species in the balanced chemical equation. It is calculated as: Δn = (moles of gaseous products) - (moles of gaseous reactants)

Important Cases:

• When Δn = 0: If the total number of moles of gaseous products equals the total number of moles of gaseous reactants, then Δn = 0. In this case, (RT)0 = 1, so: Kp = Kc

  Example: H2(g) + I2(g) ⇌ 2HI(g)

  Here, moles of gaseous products = 2. Moles of gaseous reactants = 1 + 1 = 2.

  Δn = 2 - 2 = 0. Therefore, Kp = Kc.

• When Δn ≠ 0: If the number of moles of gaseous products is different from the number of moles of gaseous reactants, then Kp and Kc will have different values.

  Example 1: N2(g) + 3H2(g) ⇌ 2NH3(g)

  Moles of gaseous products = 2. Moles of gaseous reactants = 1 + 3 = 4.

  Δn = 2 - 4 = -2. Therefore, Kp = Kc(RT)-2 = Kc / (RT)2.

  Example 2: PCl5(g) ⇌ PCl3(g) + Cl2(g)

  Moles of gaseous products = 1 + 1 = 2. Moles of gaseous reactants = 1.

  Δn = 2 - 1 = 1. Therefore, Kp = Kc(RT)1 = KcRT.

6. Le Chatelier's Principle

Le Chatelier's Principle, formulated by French chemist Henri Le Chatelier, is a powerful qualitative tool used to predict the direction in which a system at equilibrium will shift in response to a disturbance. It states:

If a system at equilibrium is subjected to a change in temperature, pressure, or concentration of a reactant or product, the system will shift its equilibrium position in a direction that tends to counteract the effect of the change.

Essentially, the system tries to relieve the "stress" imposed upon it.

Applications of Le Chatelier's Principle

a. Effect of Change in Concentration

When the concentration of a reactant or product is changed, the system will shift to consume the added substance or to produce more of the removed substance.

• Adding a Reactant: The equilibrium will shift to the forward (product) direction to consume the added reactant.
• Removing a Product: The equilibrium will shift to the forward (product) direction to replenish the removed product.
• Removing a Reactant: The equilibrium will shift to the backward (reactant) direction to replace the removed reactant.
• Adding a Product: The equilibrium will shift to the backward (reactant) direction to consume the added product.

Example: Haber process: N2(g) + 3H2(g) ⇌ 2NH3(g)

• If N2 or H2 is added, the equilibrium shifts to the right, producing more NH3.
• If NH3 is continuously removed (e.g., by liquefaction), the equilibrium shifts to the right, increasing the yield of NH3. This is how the industrial Haber-Bosch process maximizes ammonia production.

b. Effect of Change in Pressure (for Gaseous Reactions)

Changes in pressure primarily affect reactions involving gases. The system attempts to reduce the stress caused by the pressure change by favoring the side with fewer or more moles of gas.

• Increasing Pressure (by decreasing volume): The equilibrium will shift towards the side with fewer moles of gas to reduce the total number of gas molecules and thus relieve the pressure.
• Decreasing Pressure (by increasing volume): The equilibrium will shift towards the side with more moles of gas to increase the total number of gas molecules and thus counteract the pressure drop.
• No Change in Moles of Gas (Δn = 0): If the number of moles of gaseous reactants equals the number of moles of gaseous products, a change in pressure will have no effect on the equilibrium position.

Example 1: N2(g) + 3H2(g) ⇌ 2NH3(g)

Reactant side has 1 + 3 = 4 moles of gas. Product side has 2 moles of gas.

• Increase pressure: Shifts right (towards 2 moles of gas).
• Decrease pressure: Shifts left (towards 4 moles of gas).

Example 2: PCl5(g) ⇌ PCl3(g) + Cl2(g)

Reactant side has 1 mole of gas. Product side has 1 + 1 = 2 moles of gas.

• Increase pressure: Shifts left (towards 1 mole of gas).
• Decrease pressure: Shifts right (towards 2 moles of gas).

Example 3: H2(g) + I2(g) ⇌ 2HI(g)

Reactant side has 1 + 1 = 2 moles of gas. Product side has 2 moles of gas. (Δn = 0)

• Change in pressure: No effect on equilibrium position.

c. Effect of Change in Temperature

Temperature changes affect equilibrium by altering the rates of both forward and backward reactions unequally, and crucially, by changing the value of the equilibrium constant itself. We can treat heat as either a reactant or a product.

• Exothermic Reactions (ΔH < 0): These reactions release heat, so heat can be considered a product. Reactants ⇌ Products + Heat
  • Increase Temperature (add heat): The equilibrium shifts to the backward (reactant) direction to consume the added heat. The value of Kc decreases.
  • Decrease Temperature (remove heat): The equilibrium shifts to the forward (product) direction to produce more heat. The value of Kc increases.

  Example: Haber process: N2(g) + 3H2(g) ⇌ 2NH3(g) ; ΔH = -92 kJ/mol

  This is an exothermic reaction. To maximize NH3 yield, a lower temperature is preferred. However, too low a temperature makes the reaction too slow, so an optimal intermediate temperature is used in industry.

• Endothermic Reactions (ΔH > 0): These reactions absorb heat, so heat can be considered a reactant. Reactants + Heat ⇌ Products
  • Increase Temperature (add heat): The equilibrium shifts to the forward (product) direction to consume the added heat. The value of Kc increases.
  • Decrease Temperature (remove heat): The equilibrium shifts to the backward (reactant) direction to produce more heat. The value of Kc decreases.

  Example: Decomposition of dinitrogen tetroxide: N2O4(g) + Heat ⇌ 2NO2(g) ; ΔH = +57 kJ/mol

  N2O4 is colorless, while NO2 is brown. Increasing the temperature shifts the equilibrium to the right, making the mixture appear darker brown. Decreasing the temperature shifts it to the left, making it lighter.

d. Effect of Adding a Catalyst

A catalyst is a substance that increases the rate of a chemical reaction without being consumed in the process. It does this by providing an alternative reaction pathway with a lower activation energy.

• A catalyst speeds up both the forward and backward reactions equally.
• Therefore, a catalyst has no effect on the position of equilibrium. It does not change the equilibrium concentrations of reactants and products.
• A catalyst does not change the value of Kc or Kp.
• Its only effect is to help the system reach equilibrium faster. This is industrially important for processes that would otherwise be too slow.

e. Effect of Adding an Inert Gas

An inert gas is a non-reactive gas that does not participate in the equilibrium reaction.

• At Constant Volume: If an inert gas is added to a system at equilibrium while the volume is kept constant, the total pressure of the system increases. However, the partial pressures (and thus concentrations) of the reacting gases remain unchanged. Since the equilibrium depends on the partial pressures/concentrations of the reacting species, adding an inert gas at constant volume has no effect on the equilibrium position.
• At Constant Pressure: If an inert gas is added to a system at equilibrium while the pressure is kept constant, the volume of the system must increase to accommodate the added gas. This increase in volume leads to a decrease in the partial pressures of all reacting gases. The system will then respond as if the pressure has been decreased, shifting the equilibrium towards the side with more moles of gas.

Conclusion

The principles of chemical equilibrium are fundamental to understanding how chemical reactions proceed and respond to changes in their environment. From the basic definitions of physical and chemical equilibrium to the quantitative expressions of the Law of Mass Action and equilibrium constants (Kc and Kp), and finally to the predictive power of Le Chatelier's Principle, this unit provides a comprehensive framework for analyzing reversible reactions. These concepts are indispensable for chemical engineers designing industrial processes, environmental scientists studying atmospheric reactions, and biochemists exploring metabolic pathways.