Question

Explain how to write the equilibrium-constant equation for a reversible process.

Short answer

The equilibrium-constant equation is written as \( K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \) for solutes and \( K_p \) for gas reactions, reflecting reactant and product concentrations at equilibrium.

Step-by-step solution

Understanding the Equilibrium Constant

The equilibrium constant, denoted as \( K \), is a dimensionless number that expresses the relationship between the concentrations of reactants and products of a reversible chemical reaction at equilibrium. It is specific for a particular reaction at a given temperature.

Identifying the Reaction

Start by writing down the balanced chemical equation for the reaction. Let's consider the general reversible reaction: \[ aA + bB ightleftharpoons cC + dD \]where \( A \) and \( B \) are reactants, \( C \) and \( D \) are products, and \( a, b, c, \) and \( d \) are their respective stoichiometric coefficients.

Writing the Equilibrium-Constant Expression

According to the law of mass action, the equilibrium constant expression \( K \) for the reaction is given by: \[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \]where \([C], [D], [A], \) and \([B]\) are the molar concentrations of the respective chemical species at equilibrium.

Application to Gaseous Reactions

For gaseous reactions, the equilibrium constant can also be expressed in terms of partial pressures, denoted as \( K_p \), instead of concentrations. For the same reaction, the expression becomes:\[ K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b} \]where \( P_A, P_B, P_C, \) and \( P_D \) are the partial pressures of the reactants \( A, B \) and products \( C, D \) at equilibrium.

Considering Units and Temperature

Remember that the equilibrium constant is mathematically dimensionless, but the reaction's context determines how concentrations or pressures cancel out stoichiometrically. Also, \( K \) values are specific to particular temperatures, so temperature information should be provided or assumed constant in problems involving \( K \).

Key concepts

Reversible Reactions

In chemistry, reversible reactions are fascinating processes where the reactants and the products can interconvert. This means that the reaction can proceed in both forward and backward directions. For example, in a chemical equation, we represent this with a double-headed arrow such as \( \rightleftharpoons \). In equilibrium, forward and reverse reactions occur at the same rate, creating a balanced system.
Some characteristics of reversible reactions include:

• They do not go to completion; instead, they reach a balance or equilibrium.
• The system will respond to changes in conditions (like concentration, temperature, and pressure) in a way that tries to re-establish equilibrium, often referred to as Le Chatelier's principle.

A familiar example is the synthesis of ammonia in the Haber process. In this industrial chemical reaction, nitrogen and hydrogen gases react continuously to form ammonia, which can decompose back into nitrogen and hydrogen under the right conditions.

Law of Mass Action

The law of mass action provides a vital framework for understanding the dynamics within a chemical reaction at equilibrium. It states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants, each raised to a power equal to its stoichiometric coefficient.
For a typical chemical equation \( aA + bB \rightleftharpoons cC + dD \), according to the law of mass action, the equilibrium-constant expression is written as:

• \( K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \)

The equilibrium constant \( K \) is a helpful parameter that remains constant at a given temperature for a particular reaction, allowing predictions of the equilibrium concentrations of reacting species. It's crucial because it ties the concentration or pressure of reactants and products to their transformation, guiding chemists in reaction planning and analysis.

Partial Pressures

When dealing with reactions involving gases, understanding partial pressures becomes essential. Partial pressure refers to the pressure exerted by an individual gas in a mixture. In equilibrium expressions for gaseous reactions, partial pressures replace concentrations, denoted as \( K_p \).
In gaseous reactions, similar to concentrations, the equilibrium constant in terms of partial pressures can be written as:

• \( K_p = \frac{P_C^c P_D^d}{P_A^a P_B^b} \)

Here, \( P_A, P_B, P_C, \) and \( P_D \) stand for the partial pressures of the related chemical species at equilibrium. The use of partial pressures is particularly advantageous in high-temperature reactions where gases are predominantly the concern.

Chemical Equilibrium

Chemical equilibrium is a dynamic state of a reversible chemical reaction where the rates of the forward and backward reactions are equal. This means that, over time, the concentrations of the reactants and products remain constant, not because the reactions have stopped, but because they occur at the same rate.
Key points to remember about chemical equilibrium include:

• It is dependent on the system remaining closed, so no substances escape or are added.
• The equilibrium position can shift when external conditions, like temperature and pressure, are altered.
• It is not static but a constant, dynamic process of interconversion.

In practice, understanding chemical equilibrium helps in predicting how a system will respond to changes, allowing scientists and engineers to control conditions for maximum yield in industrial chemical processes.