91Ó°ÊÓ

Antimony(V) chloride, denoted as \( \text{SbCl}_5 \), undergoes thermal decomposition. This process transforms \( \text{SbCl}_5 \) into antimony(III) chloride, \( \text{SbCl}_3 \), and chlorine gas, \( \text{Cl}_2 \), when heated. The chemical equation representing this reversible reaction is:

• \( \text{SbCl}_5 (g) \rightleftharpoons \text{SbCl}_3 (g) + \text{Cl}_2 (g) \)

Understanding this decomposition is crucial as it forms the basis of achieving chemical equilibrium in the reaction system.
This reaction takes place in a gaseous state within a closed vessel, which is essential because it allows gases to reach equilibrium without losing any material to the surroundings.
This setup also ensures that the system’s volume remains constant, which is important for calculating concentrations and pressures during the reaction.

The equilibrium constant, \( K_c \), is a crucial part of understanding chemical equilibria. It is used to quantify the concentrations of reactants and products at equilibrium in a chemical reaction. For the decomposition of \( \text{SbCl}_5 \), the expression for \( K_c \) is given by:

• \( K_c = \frac{[\text{SbCl}_3][\text{Cl}_2]}{[\text{SbCl}_5]} \)

Here,

• \([\text{SbCl}_3]\), \([\text{Cl}_2]\), and \([\text{SbCl}_5]\) represent the molar concentrations of each substance.

Given that \( K_c \) is \( 2.50 \times 10^{-2} \), this tells us that at 248°C, the system favors the decomposition of \( \text{SbCl}_5 \), since a lower value of \( K_c \) suggests the reactants are still significantly present at equilibrium.
Calculating the equilibrium position involves setting and solving equations based on the initial amounts and changes (using an 'ICE' - Initial, Change, Equilibrium - table), to find the concentrations of each component at equilibrium.

The Ideal Gas Law is a fundamental principle used in chemistry to relate the state variables of a gas. The formula is given by:

• \( PV = nRT \)

Where

• \( P \) is the pressure, \( V \) is the volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

In the context of the antimony chloride decomposition, it enables the calculation of the total pressure in the vessel at equilibrium. After determining the amount of decomposition that occurs, the Ideal Gas Law is used to calculate the final pressure by substituting the equilibrium moles and system conditions into the equation.
This application highlights the interdependence of gas properties, such as volume and temperature, with the pressure and quantity of gas, which are modulated to maintain equilibrium under defined conditions.

Phase equilibrium describes the balance between different phases of matter, such as solid, liquid, and gas, within a system. In chemical reactions like the decomposition of \( \text{SbCl}_5 \), phase equilibrium is crucial to ensure that all reactants and products can exist and interact.

• Here, the entire reaction occurs in the gas phase, where variables such as pressure and volume play a decisive role.
• This kind of equilibrium is particularly sensitive to temperature and pressure changes, fundamental in processes occurring at high temperatures, like 248°C in this case.

Achieving phase equilibrium in closed systems helps in maintaining the consistency of the reaction environment, thereby enabling the calculation of equilibrium constants and application of the Ideal Gas Law.
Understanding phase equilibrium is essential for predicting the behavior of reactions under different conditions, which aids in controlling industrial chemical processes.