Problem 52 - Chemistry and Chemical Reactivity

Question

You wish to know the enthalpy change for the formation of liquid \(\mathrm{PCl}_{3}\) from the elements. $$ \mathrm{P}_{4}(\mathrm{s})+6 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{3}(\ell) \quad \Delta_{r} H^{\circ}=? $$ The enthalpy change for the formation of \(\mathrm{PCl}_{5}\) from the elements can be determined experimentally, as can the enthalpy change for the reaction of \(\mathrm{PCl}_{3}(\ell)\) with more chlorine to give \(\mathrm{PCl}_{5}(\mathrm{s}):\) \(\mathrm{P}_{4}(\mathrm{s})+10 \mathrm{Cl}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{PCl}_{5}(\mathrm{s})\) \(\Delta_{i} H^{\circ}=-1774.0 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}\) \(\mathrm{PCl}_{3}(\ell)+\mathrm{Cl}_{2}(\mathrm{g}) \rightarrow \mathrm{PCl}_{5}(\mathrm{s})\) $$ \Delta_{r} H^{\circ}=-123.8 \mathrm{kJ} / \mathrm{mol}-\mathrm{Dxn} $$ Use these data to calculate the enthalpy change for the formation of 1.00 mol of \(\mathrm{PCl}_{3}(\ell)\) from phosphorus and chlorine.

Step-by-Step Solution

Answer

The enthalpy change is \(-319.7 \, \mathrm{kJ/mol}\) for \(\mathrm{PCl}_3(\ell)\).

Step 1: Identify Given Reactions

First, identify the two given reactions: the formation of \(\mathrm{PCl}_5\) and the reaction of \(\mathrm{PCl}_3\) with chlorine to form \(\mathrm{PCl}_5\). These are: \(\mathrm{P}_4(s) + 10 \mathrm{Cl}_2(g) \rightarrow 4 \mathrm{PCl}_5(s)\) with \(\Delta_i H^\circ = -1774.0 \, \mathrm{kJ/mol}\) and \(\mathrm{PCl}_3(\ell) + \mathrm{Cl}_2(g) \rightarrow \mathrm{PCl}_5(s)\) with \(\Delta_r H^\circ = -123.8 \, \mathrm{kJ/mol}\).

Step 2: Determine Target Reaction

The target reaction is the formation of \(\mathrm{PCl}_3\) from its elements: \(\mathrm{P}_4(s) + 6 \mathrm{Cl}_2(g) \rightarrow 4 \mathrm{PCl}_3(\ell)\). We need to find \(\Delta_r H^\circ\) for this reaction.

Step 3: Break Down Given Enthalpies Using Hess's Law

Apply Hess's Law: the target reaction can be derived by subtracting the \(\mathrm{PCl}_3\) conversion to \(\mathrm{PCl}_5\) from the total \(\mathrm{PCl}_5\) formation. \(\Delta H^\circ_{\text{target reaction}} = \Delta_i H^\circ - 4 \times \Delta_r H^\circ = (-1774.0) - 4(-123.8)\).

Step 4: Calculate Required Enthalpy Change

Compute the enthalpy change for the target reaction: \(\Delta H^\circ_{\text{target reaction}} = -1774.0 + 495.2 = -1278.8 \, \mathrm{kJ/mol}\). Since this gives the change for 4 moles of \(\mathrm{PCl}_3\), divide by 4 for 1 mole: \(-1278.8/4 = -319.7 \, \mathrm{kJ/mol}\).

Step 5: Present Final Enthalpy Change

The enthalpy change for the formation of \(1 \) mole of \(\mathrm{PCl}_3(\ell)\) is \(-319.7 \, \mathrm{kJ/mol}\).

Key Concepts

Hess's Law

Hess's Law is a fundamental principle in chemical thermodynamics that helps us calculate the enthalpy change in chemical reactions. It states that the total enthalpy change in a reaction is the same, regardless of the route taken to obtain the products from the reactants. This means you can add up the enthalpy changes of multiple steps to determine the overall enthalpy change of a reaction.

In the provided exercise, Hess's Law allows us to deduce the enthalpy change for forming liquid phosphorus trichloride (\(\text{PCl}_3\)) from phosphorus (\(\text{P}_4\)) and chlorine (\(\text{Cl}_2\)). By using known enthalpy changes for forming phosphorus pentachloride (\(\text{PCl}_5\)) and another reaction involving \(\text{PCl}_3\), we rearrange these steps to achieve the desired reaction path.
This method is incredibly useful in practical chemistry and helps us understand intricate reaction mechanisms.

• Applies to reactions that cannot be directly measured.
• Allows for comparison between theoretical and experimental data.
• Essential for calculating enthalpy of reactions in complex reaction networks.

chemical thermodynamics

Chemical thermodynamics explores the energy changes in chemical reactions and matter's physical transformations. It concerns itself with enthalpy, entropy, and free energy, which all play pivotal roles in chemical processes.

Enthalpy change is one of the cornerstones of thermodynamics, measuring the heat absorbed or released during a chemical reaction. When a reaction occurs, the bonds in reactants break, and new bonds form in the products, either consuming or releasing energy.
Thermodynamics principles, like Hess's Law, offer tools to compile, analyze, and predict these energy changes in reactions that aren't directly measurable.

• Predicts if a reaction will occur spontaneously (depends on both enthalpy and entropy).
• Helps determine the efficiency and energy requirements of industrial processes.
• Explains the energy sustainability of chemical processes and systems.

enthalpy formation

Enthalpy formation refers to the change in enthalpy when one mole of a compound is formed from its elements in their standard states. This is usually represented as the standard enthalpy of formation, denoted by \(\Delta_f H^{\circ}\).

In this exercise, we focus on finding the enthalpy change for creating \(\text{PCl}_3(\ell)\) from its constituent elements, phosphorus, and chlorine. This involves considering all possible reaction routes and utilizing known enthalpies of related processes. Using these values, we can calculate the formation enthalpy clearly and accurately.
Understanding enthalpy formation is crucial in assessing the stability and energy potential of chemical compounds.

• Standardize conditions to provide a reference point.
• Key in calculating reaction enthalpies using Hess's Law.
• Determines whether compound formation is exothermic or endothermic.