Problem 16 - Chemistry and Chemical Reactivity

Question

Use the following data to calculate the enthalpy of solution of sodium perchlorate, \(\mathrm{NaClO}_{4}\): $$\begin{aligned} \Delta H_{f}^{\circ}(\mathrm{s}) &=-382.9 \mathrm{kJ} / \mathrm{mol} \\\ \Delta H_{f}^{\circ}(\mathrm{aq}, 1 m) &=-369.5 \mathrm{kJ} / \mathrm{mol} \end{aligned}$$

Step-by-Step Solution

Answer

The enthalpy of solution for sodium perchlorate is \( 13.4 \, \mathrm{kJ/mol} \).

Step 1: Identify the Given Data

We are given the standard enthalpy of formation for sodium perchlorate in solid form, \( \Delta H_{f}^{\circ}(\mathrm{s}) = -382.9 \, \mathrm{kJ/mol} \), and for sodium perchlorate in aqueous solution form, \( \Delta H_{f}^{\circ}(\mathrm{aq}, 1 \mathrm{m}) = -369.5 \, \mathrm{kJ/mol} \).

Step 2: Understand the Concept of Enthalpy of Solution

The enthalpy of solution, \( \Delta H_{\text{solution}} \), represents the heat change when one mole of solute dissolves in a solvent to form an infinitely dilute solution. It can be calculated using the difference between the enthalpies of formation of the compound in aqueous and solid states.

Step 3: Calculate Enthalpy of Solution

To find the enthalpy of solution, subtract the enthalpy of formation for the solid form from the enthalpy of formation for the aqueous form. Use the formula: \[ \Delta H_{\text{solution}} = \Delta H_{f}^{\circ}(\mathrm{aq}, 1 \mathrm{m}) - \Delta H_{f}^{\circ}(\mathrm{s}) \]Plugging in the values gives: \[ \Delta H_{\text{solution}} = (-369.5) - (-382.9) = 13.4 \, \mathrm{kJ/mol} \]

Step 4: Interpret the Result

The positive value of \(13.4 \, \mathrm{kJ/mol} \) indicates that the dissolution of sodium perchlorate in water is an endothermic process, requiring heat to proceed.

Key Concepts

Sodium Perchlorate

Sodium perchlorate, or NaClO₄, is a compound formed from the combination of sodium and perchlorate ions. It is commonly used in chemistry labs and even in certain industrial applications like explosives and rocket propellant. However, for students, it is mostly encountered when exploring dissolution reactions and energy changes.
Sodium perchlorate is a soluble salt, meaning it easily dissolves in water. This solubility is significant because it involves breaking the ionic bonds in the solid crystal and then forming interactions between the ions and water molecules.

• The solid form has sodium ions held together with perchlorate ions, requiring energy to separate.
• Once dissolved, the ions are free to move in the aqueous solution.
• Understanding solubility aids in grasping how heat interactions occur in such processes.

Knowing about sodium perchlorate creates a foundation for studying thermodynamic concepts related to solutions.

Enthalpy of Formation

The enthalpy of formation refers to the heat change that occurs when one mole of a compound is formed from its constituent elements in their standard states. This is a crucial concept when calculating various energy changes in chemical reactions.
In this context, we have:

• The enthalpy of formation for sodium perchlorate in its solid form: \(-382.9 \text{ kJ/mol}\)
• The enthalpy of formation for sodium perchlorate in aqueous solution: \(-369.5 \text{ kJ/mol}\)

The enthalpy of formation provides a useful way of understanding the energy needed to form a compound. Knowing these values helps calculate the energy changes when substances change states, such as dissolving a solid in water.
If you need to calculate the enthalpy of solution, these values become instrumental as you take the difference between their aqueous and solid state enthalpies to find the heat change upon dissolution.

Endothermic Process

An endothermic process is one in which heat is absorbed from the surroundings, leading to an increase in the energy of the system. In our case, the positive enthalpy change indicates that the dissolution of sodium perchlorate in water requires the absorption of heat.
When sodium perchlorate is dissolved:

• The initial separation of ions consumes energy.
• The interaction of these free ions with water molecules creates new interactions, which also require energy.
• The absorption of heat results in a cooler solution, since heat from the surroundings is used.

Understanding endothermic processes helps explain why some substances feel cold when they dissolve. In such reactions, the system compensates by drawing in heat from the outside, leaving a noticeable endothermic effect.