Introduction to Chemical Equilibrium

Intro to Equilibrium

Overview

Chemical equilibrium is a fundamental concept in chemistry that describes the state in which the rate of the forward reaction equals the rate of the reverse reaction. This topic is essential for understanding how chemical reactions behave in closed systems and is widely applicable in both biological and physical sciences.

13.1 Equilibrium

Dynamic Equilibrium

• Dynamic equilibrium occurs when the rate of one process is equal to the rate of the reverse process in a chemical reaction.

• At equilibrium, reactants become products and products become reactants at the same rate.

• The amounts of reactants and products remain constant over time, but are not necessarily equal.

• Equilibrium can result in:

  • All reactants

  • All products

  • Any ratio in between

• The position of equilibrium describes how much of the products are present compared to reactants.

13.2 Equilibrium Constant

Definition and Expression

• The equilibrium constant (K) expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature.

• For a general reaction: aA + bB ⇌ cC + dD, the equilibrium constant expression is: $K = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Coefficients become exponents in the K expression.

• Only substances in the aqueous (aq) or gaseous (g) phase are included in the K expression. Solids (s) and liquids (l) are omitted (their activity is considered 1).

• The value of K is unique for every chemical reaction at a given temperature.

Examples

• For the reaction: $O_2 + NO \rightarrow NO_3$ $K = \frac{[NO_3]}{[O_2][NO]}$

• For: $2 NO_2 (g) \rightarrow N_2 (g) + 2 O_2 (g)$ $K = \frac{[N_2][O_2]^2}{[NO_2]^2}$

• For: $HBr(l) \rightarrow H_2(g) + Br_2(g)$ $K = [H_2][Br_2]$

• If no (aq) or (g) species are present, the K expression is set to 1.

Interpreting the Value of K

The magnitude of K indicates the relative amounts of products and reactants at equilibrium.

Value of K	Example	Description
Much greater than 1	K ≈ 1000	Almost all products, very little reactants
Around 1	K ≈ 1	Almost equal products to reactants
Much less than 1	K ≈ 0.001	Almost all reactants, very little products

Properties of the Equilibrium Constant

• K cannot be negative.

• K can be any positive number, depending on the reaction.

Manipulating Equilibrium Equations

• If a reaction is reversed, the new K is the reciprocal: $K_{reverse} = \frac{1}{K_{forward}}$

• If the coefficients in a reaction are multiplied by n, the new K is raised to the nth power: $K_{new} = (K_{original})^n$

• If two reactions are added, the new K is the product of the individual Ks: $K_{overall} = K_1 \times K_2$

Example

• For $4 Al(s) + 3 O_2(g) \rightarrow 2 Al_2O_3(s)$, the K expression is: $K = \frac{1}{[O_2]^3}$

13.2 Kc and Kp

Types of Equilibrium Constants

• Kc measures equilibrium when all concentrations are reported in molarity (M).

• Kp measures equilibrium when all concentrations are reported in atmospheres (atm) (for gases).

• The relationship between Kc and Kp is: $K_p = K_c(RT)^{\Delta n}$ where R = 0.08206 L·atm/(mol·K), T is temperature in Kelvin, and Δn = (moles of gaseous products) - (moles of gaseous reactants).

13.1 The Reaction Quotient (Q)

Definition and Use

• The reaction quotient (Q) is calculated using the same expression as K, but with initial (not equilibrium) concentrations.

• Q is used to determine the direction in which a reaction will proceed to reach equilibrium:

  • If Q < K: The reaction will proceed to the right (toward products).

  • If Q > K: The reaction will proceed to the left (toward reactants).

  • If Q = K: The system is at equilibrium.

Example

• For $FO_2(aq) \rightleftharpoons F_2(aq) + O_2(aq)$, with initial concentrations:

  • [F2] = 0.0008 M

  • [O2] = 0.0011 M

  • [FO2] = 0.0005 M

  $Q = \frac{[F_2][O_2]}{[FO_2]} = \frac{0.0008 \times 0.0011}{0.0005} = 0.00176$ If K = 0.20, since Q < K, the reaction will proceed to the right to reach equilibrium.

13.3 Le Chatelier’s Principle

Response to Disturbance

• Le Chatelier’s Principle states that if a system at equilibrium is disturbed, the system will shift in a direction that minimizes the disturbance and re-establishes equilibrium.

• Disturbances include changes in concentration, pressure, or temperature.

Summary Table: Effects of Changes on Equilibrium

Change	Effect on Q	Shift Direction
Add Reactant	Decrease in Q	Shifts to the right (products)
Add Product	Increase in Q	Shifts to the left (reactants)
Remove Reactant	Increase in Q	Shifts to the left (reactants)
Remove Product	Decrease in Q	Shifts to the right (products)

Example

• For $PCl_3(g) + Cl_2(g) \rightleftharpoons PCl_5(g)$, if more $PCl_5$ is added, the reaction will shift to the left to reduce the disturbance.

Practice and Application

• Predict the direction of shift for various reactions when reactants or products are added or removed.

• Use Q and K to determine if a reaction will shift left, right, or is at equilibrium.

Key Terms

• Dynamic equilibrium: A state where the forward and reverse reactions occur at the same rate.

• Equilibrium constant (K): A numerical value that expresses the ratio of product to reactant concentrations at equilibrium.

• Reaction quotient (Q): A value calculated like K, but with initial concentrations, used to predict the direction of reaction shift.

• Le Chatelier’s Principle: The principle that a system at equilibrium will adjust to counteract a disturbance.

Additional info: These notes are suitable for introductory college-level chemistry or general biology courses that include chemical equilibrium as a topic.