Characteristics of Equilibrium

Oct 13, 2025 by miodeya.com 135 views

Introduction

In chemistry, equilibrium is a state where the rates of forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. The equilibrium system we will be discussing is the dissociation of a gas, AB(g), into its constituent gases, A(g) and B(g). In this article, we will explore the process of achieving equilibrium in a sealed vessel when 1 mole of pure AB(g) is added.

The Equilibrium System

The equilibrium system is represented by the following equation:

${ \text{AB}(g) \rightleftharpoons \text{A}(g) + \text{B}(g) }$

This equation indicates that the gas AB(g) dissociates into two moles of gases, A(g) and B(g). The equilibrium constant (K) for this reaction can be expressed as:

${ K = \frac{[\text{A}][\text{B}]}{[\text{AB}]} }$

where [A], [B], and [AB] are the concentrations of gases A, B, and AB, respectively.

Initial Conditions

When 1 mole of pure AB(g) is added to a sealed vessel, the initial concentration of AB(g) is 1 mole per unit volume (1 M). Since the vessel is sealed, there is no net change in the volume of the gases. Therefore, the initial concentrations of A(g) and B(g) are zero.

Achieving Equilibrium

To achieve equilibrium, the following steps occur:

Step 1: Dissociation of AB(g)

The first step is the dissociation of AB(g) into A(g) and B(g). This process is represented by the forward reaction:

${ \text{AB}(g) \rightarrow \text{A}(g) + \text{B}(g) }$

As the dissociation occurs, the concentration of AB(g) decreases, while the concentrations of A(g) and B(g) increase.

Step 2: Reversal of the Forward Reaction

As the concentrations of A(g) and B(g) increase, the reverse reaction begins to occur:

${ \text{A}(g) + \text{B}(g) \rightarrow \text{AB}(g) }$

This reaction is known as the reverse reaction or the recombination reaction.

Step 3: Equilibrium is Achieved

As the forward and reverse reactions continue to occur, the concentrations of A(g), B(g), and AB(g) reach a state of equilibrium. At this point, the rates of the forward and reverse reactions are equal, and there is no net change in the concentrations of the reactants and products.

Characteristics of Equilibrium

At equilibrium, the following characteristics are observed:

The concentrations of A(g), B(g), and AB(g) remain constant.
The rates of the forward and reverse reactions are equal.
The equilibrium constant (K) is a constant value that depends on the temperature and the concentrations of the reactants and products.

Conclusion

Achieving equilibrium in a sealed vessel involves the dissociation of AB(g) into A(g) and B(g), followed by the reversal of the forward reaction. As the concentrations of A(g) and B(g) increase, the reverse reaction begins to occur, and eventually, equilibrium is achieved. At equilibrium, the concentrations of A(g), B(g), and AB(g) remain constant, and the rates of the forward and reverse reactions are equal.

Mathematical Representation of Equilibrium

The equilibrium constant (K) can be expressed as:

${ K = \frac{[\text{A}][\text{B}]}{[\text{AB}]} }$

where [A], [B], and [AB] are the concentrations of gases A, B, and AB, respectively.

Example Problem

Suppose we have a sealed vessel containing 1 mole of pure AB(g). If the equilibrium constant (K) is 2.0, what is the concentration of A(g) at equilibrium?

To solve this problem, we can use the equilibrium expression:

${ K = \frac{[\text{A}][\text{B}]}{[\text{AB}]} }$

Since the initial concentration of AB(g) is 1 mole per unit volume (1 M), the concentration of AB(g) at equilibrium is also 1 M. Let [A] and [B] be the concentrations of A(g) and B(g) at equilibrium, respectively.

Substituting the values into the equilibrium expression, we get:

${ 2.0 = \frac{[\text{A}][\text{B}]}{1} }$

Since the concentrations of A(g) and B(g) are equal at equilibrium, we can write:

${ [\text{A}] = [\text{B}] = x }$

Substituting this into the equilibrium expression, we get:

${ 2.0 = x^2 }$

Solving for x, we get:

${ x = \sqrt{2.0} = 1.41 }$

Therefore, the concentration of A(g) at equilibrium is 1.41 M.

Conclusion

Achieving equilibrium in a sealed vessel involves the dissociation of AB(g) into A(g) and B(g), followed by the reversal of the forward reaction. At equilibrium, the concentrations of A(g), B(g), and AB(g) remain constant, and the rates of the forward and reverse reactions are equal. The equilibrium constant (K) can be expressed as:

${ K = \frac{[\text{A}][\text{B}]}{[\text{AB}]} }$

Introduction

In our previous article, we discussed the process of achieving equilibrium in a sealed vessel when 1 mole of pure AB(g) is added. In this article, we will answer some frequently asked questions (FAQs) related to achieving equilibrium in a sealed vessel.

Q: What is equilibrium in a sealed vessel?

A: Equilibrium in a sealed vessel is a state where the rates of forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products.

Q: What is the equilibrium constant (K)?

A: The equilibrium constant (K) is a constant value that depends on the temperature and the concentrations of the reactants and products. It can be expressed as:

${ K = \frac{[\text{A}][\text{B}]}{[\text{AB}]} }$

where [A], [B], and [AB] are the concentrations of gases A, B, and AB, respectively.

Q: How is equilibrium achieved in a sealed vessel?

A: Equilibrium is achieved in a sealed vessel through the dissociation of AB(g) into A(g) and B(g), followed by the reversal of the forward reaction.

Q: What are the characteristics of equilibrium in a sealed vessel?

A: The characteristics of equilibrium in a sealed vessel are:

The concentrations of A(g), B(g), and AB(g) remain constant.
The rates of the forward and reverse reactions are equal.
The equilibrium constant (K) is a constant value that depends on the temperature and the concentrations of the reactants and products.

Q: How do I calculate the equilibrium constant (K)?

A: To calculate the equilibrium constant (K), you need to know the concentrations of A(g), B(g), and AB(g) at equilibrium. You can use the equilibrium expression:

${ K = \frac{[\text{A}][\text{B}]}{[\text{AB}]} }$

Q: What is the significance of the equilibrium constant (K)?

A: The equilibrium constant (K) is a measure of the extent to which a reaction occurs. A large value of K indicates that the reaction is favorable, while a small value of K indicates that the reaction is unfavorable.

Q: Can equilibrium be achieved in a sealed vessel at any temperature?

A: No, equilibrium cannot be achieved in a sealed vessel at any temperature. The temperature must be within the range where the reaction is feasible.

Q: How do I determine the temperature range for achieving equilibrium in a sealed vessel?

A: To determine the temperature range for achieving equilibrium in a sealed vessel, you need to know the activation energy of the reaction. The activation energy is the minimum energy required for the reaction to occur.

Q: What is the activation energy of a reaction?

A: The activation energy of a reaction is the minimum energy required for the reaction to occur. It is a measure of the energy barrier that must be overcome for the reaction to occur.

Q: How do I calculate the activation energy of a reaction?

A: To calculate the activation energy of a reaction, you need to know the rate constant (k) and the temperature (T) at which the reaction occurs. You can use the Arrhenius equation:

${ k = Ae^{-E_a/RT} }$

where k is the rate constant, A is the pre-exponential factor, E_a is the activation energy, R is the gas constant, and T is the temperature.

Conclusion

Achieving equilibrium in a sealed vessel involves the dissociation of AB(g) into A(g) and B(g), followed by the reversal of the forward reaction. The equilibrium constant (K) is a measure of the extent to which a reaction occurs, and it can be calculated using the equilibrium expression. The temperature range for achieving equilibrium in a sealed vessel must be within the range where the reaction is feasible, and the activation energy of the reaction must be known to determine this range.