Question

From the following data, the heat of formation of \(\mathrm{PCl}_{5}\) \(2 \mathrm{P}(\mathrm{s})+3 \mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{PCl}_{3}(\mathrm{~g}) ; \Delta H=151.8 \mathrm{kcal}\) \(\mathrm{PCl}_{3}+\mathrm{Cl}_{2}(\mathrm{~g}) \rightarrow \mathrm{PCl}_{5}(\mathrm{~g}) ; \Delta H=32.8 \mathrm{kcal}\) (1) \(217.4 \mathrm{kcal}\) (2) \(+217.4 \mathrm{kcal}\) (3) \(108.7 \mathrm{kcal}\) (4) \(+108.7 \mathrm{kcal}\)

Short answer

+108.7 kcal

Step-by-step solution

Analyze Given Reactions

Review the given chemical reactions and their enthalpy changes. 1. \( 2 \mathrm{P} (\mathrm{s}) + 3 \mathrm{Cl_2} (\mathrm{g}) \rightarrow 2 \mathrm{PCl_3} (\mathrm{g}) ; \Delta H = 151.8 \mathrm{kcal} \) 2. \( \mathrm{PCl_3} (\mathrm{g}) + \mathrm{Cl_2} (\mathrm{g}) \rightarrow \mathrm{PCl_5} (\mathrm{g}) ; \Delta H = 32.8 \mathrm{kcal} \)

Determine Desired Reaction

The goal is to find the heat of formation of \( \mathrm{PCl_5} (\mathrm{g}) \) from its elemental form: \[ \mathrm{P} (\mathrm{s}) + \frac{5}{2}\mathrm{Cl_2} (\mathrm{g}) \rightarrow \mathrm{PCl_5} (\mathrm{g}) \]

Adjust Stoichiometry

Modify the given equations to align with the desired reaction. The first equation is already given for the formation of \( \mathrm{PCl_3} \), and it can be divided by 2. \( \mathrm{P} (\mathrm{s}) + \frac{3}{2}\mathrm{Cl_2} (\mathrm{g}) \rightarrow \mathrm{PCl_3} (\mathrm{g}) ; \frac{\Delta H}{2} = 75.9 \mathrm{kcal} \)

Combine Reactions

Add the two modified reactions to get the formation reaction for \( \mathrm{PCl_5} (\mathrm{g}) \). \( \mathrm{P} (\mathrm{s}) + \frac{3}{2} \mathrm{Cl_2} (\mathrm{g}) \rightarrow \mathrm{PCl_3} (\mathrm{g}) ; \Delta H = 75.9 \mathrm{kcal} \) \( \mathrm{PCl_3} (\mathrm{g}) + \mathrm{Cl_2} (\mathrm{g}) \rightarrow \mathrm{PCl_5} (\mathrm{g}) ; \Delta H = 32.8 \mathrm{kcal} \)

Compute Final Enthalpy

Sum the enthalpy changes from the two reactions to determine the heat of formation for \( \mathrm{PCl_5} (\mathrm{g}) \): \( 75.9 \mathrm{kcal} + 32.8 \mathrm{kcal} = 108.7 \mathrm{kcal} \)

Key concepts

enthalpy change

Enthalpy change, represented as \( \Delta H \), is a measure of the heat absorbed or released during a chemical reaction at constant pressure. It indicates whether a reaction is endothermic (absorbs heat) or exothermic (releases heat). For example, in our exercise, we have two reactions with known enthalpy changes:

• 2P(s) + 3Cl₂(g) → 2PCl₃(g); ΔH = 151.8 kcal (endothermic).


• PCl₃(g) + Cl₂(g) → PCl₅(g); ΔH = 32.8 kcal (endothermic).

Enthalpy change helps us understand the heat dynamics of these reactions, providing insights for calculating the total heat of formation for compounds like PCl₅(g). When you sum the enthalpy changes of intermediate steps, it gives the net enthalpy change of the overall reaction.

chemical reactions

A chemical reaction is a process where reactants transform into products by breaking and forming chemical bonds. In the given exercise, we work with two chemical reactions:

• 2P(s) + 3Cl₂(g) → 2PCl₃(g)


• PCl₃(g) + Cl₂(g) → PCl₅(g)

The goal of the exercise is to find the enthalpy change for the formation of PCl₅(g) from elemental phosphorus and chlorine. Chemical reactions follow the law of conservation of mass, meaning the same amount of atoms is present in the reactants as in the products. Understanding this helps us balance these reactions and calculate the heat changes accurately.

stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's key to understanding how much of each reactant is needed and how much product will be formed. In our exercise, stoichiometry helps us align the given reactions with the desired formation reaction for PCl₅(g).

• The first reaction: 2P(s) + 3Cl₂(g) → 2PCl₃(g), has to be divided by 2 to match the desired product formation.


• The second reaction: PCl₃(g) + Cl₂(g) → PCl₅(g) remains as it is.

By adjusting stoichiometric coefficients, we ensure the number of moles in the reactions correctly combine to form the target product, PCl₅(g).

thermochemistry

Thermochemistry focuses on the study of heat involved in chemical processes. It is closely related to the concept of enthalpy change. In our exercise, thermochemistry principles are used to determine the heat of formation for PCl₅(g).

We start by examining the enthalpy changes of the given reactions. By applying Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes of individual steps, we adjust and combine the reactions. This holistic approach in thermochemistry helps calculate the overall energy change, providing essential insights into the energetics of the chemical process.