Question

The number of degrees of freedom for the system \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s}) \rightleftharpoons \mathrm{NH}_{4} \mathrm{Cl}(\mathrm{g}) \rightleftharpoons \mathrm{NH}_{3}(\mathrm{~g})+\mathrm{HCl}(\mathrm{g})\) is (a) 1 (b) 3 (c) 0 (d) 2

Short answer

The number of degrees of freedom for the given system is 3. So, option (b) 3 is the correct answer.

Step-by-step solution

Identify the Number of Components (C)

The components are the chemically independent constituents of the system. Here, the components are \(NH_{4}Cl\), \(NH_{3}\), and \(HCl\). Therefore, \(C = 3\).

Identify the Number of Phases (P)

The phases are the physically distinct and mechanically separable portion of the system. Here, the phases are the solid phase (\(NH_{4}Cl\)) and the gas phase (\(NH_{3}, HCl, NH_{4}Cl\)). Therefore, \(P = 2\).

Substitute C and P values into the formula

Use the formula \(F = C - P + 2\) and substitute the values discovered in steps 1 and 2 into the formula. So, \(F = 3 - 2 + 2 = 3\).

Key concepts

Phase Rule

Understanding the Phase Rule is essential for comprehending the degrees of freedom in a chemical system. The degrees of freedom, often symbolized as F, represent the number of variables that can be independently varied without changing the number of phases. Gibbs' Phase Rule formula, which is expressed as \(F = C - P + 2\), is pivotal in physical chemistry for analyzing multiphase systems.

In the formula, \(C\) stands for the number of components, which are the chemically unique constituents of the system. In the context of the exercise involving ammonium chloride, ammonia, and hydrogen chloride, the number of components is 3.

The symbol \(P\) denotes the number of phases, such as solid, liquid, and gas, which are physically different forms that exist separately within the system. For the provided chemical equilibrium, there are two phases — solid and gas.

• By applying the formula, one can assess that the degrees of freedom for \(NH_4Cl(s)\) converting to \(NH_3(g)\) and \(HCl(g)\) is 3.
• This means that there are 3 variables (such as pressure, temperature, or composition) that can be independently adjusted without altering the equilibrium nature of the system.

Chemical Equilibrium

Chemical equilibrium is a fundamental concept in physical chemistry where the rate of the forward chemical reaction equals the rate of the reverse reaction. At this point, the concentrations of reactants and products remain constant over time. It is a dynamic balance, not a static one, since molecules continue to react, but do so in a way that maintains equilibrium.

In the exercise scenario, ammonium chloride is in equilibrium between its solid and gaseous forms, which further decompose into ammonia and hydrogen chloride gases.

• This state allows us to define equilibrium constants based on the concentrations of the involved species, which are indicators of the reaction's position at equilibrium.
• The fact that there are degrees of freedom in the system indicates that conditions such as temperature or pressure may be altered to shift the position of the equilibrium, following Le Châtelier's Principle.

Understanding how to manipulate these conditions can provide insights into efficiently driving reactions towards the desired products or reactants.

Chemical Thermodynamics

Chemical thermodynamics deals with the energy changes associated with chemical reactions and the direction in which processes occur. It gives insight into the spontaneity of reactions and the equilibrium position. Three main laws of thermodynamics provide a framework for understanding the flow of energy and the behavior of substances in a chemical process.

The First Law, known also as the Law of Energy Conservation, states that energy cannot be created or destroyed, only transformed. The Second Law introduces the concept of entropy, declaring that systems tend towards higher disorder.

• In the context of the reaction \(NH_{4}Cl(s) \rightleftharpoons NH_{4}Cl(g) \rightleftharpoons NH_{3}(g) + HCl(g)\), thermodynamics would drive the understanding of whether the reaction releases or absorbs energy (enthalpy change).
• It also helps predict how changes in temperature or pressure can shift the reaction towards the products or reactants (Gibbs free energy).
• Moreover, the Third Law of Thermodynamics, which relates to absolute zero temperature, defines the entropy of a perfect crystal at zero degrees Kelvin as zero, setting a baseline for measuring entropy changes.

This theoretical framework guides the prediction of reaction behavior under different conditions, crucial for methods applied in various industries, including pharmaceuticals and materials science.