Problem 16 - Chemistry and Chemical Reactivity

Question

Use the following data to calculate the enthalpy of solution of sodium perchlorate, \(\mathrm{NaClO}_{4}\) \(\Delta_{f} H^{\circ}(\mathrm{s})=-382.9 \mathrm{kJ} / \mathrm{mol} \quad\) and $$ \Delta_{f} H^{\circ}(\mathrm{aq}, 1 \mathrm{m})=-369.5 \mathrm{kJ} / \mathrm{mol} $$

Step-by-Step Solution

Answer

The enthalpy of solution for \( \text{NaClO}_4 \) is \( 13.4 \, \text{kJ/mol} \).

Step 1: Understand the Problem

To find the enthalpy of solution for sodium perchlorate \( \text{NaClO}_4 \), we need to calculate the change in enthalpy when the solid dissolves in water, forming an aqueous solution.

Step 2: Identify Known Values

We are given the standard enthalpy of formation for solid sodium perchlorate \( \Delta_{f}H^{\circ}(\text{s}) = -382.9 \, \text{kJ/mol} \) and for 1 molal aqueous sodium perchlorate \( \Delta_{f}H^{\circ}(\text{aq}) = -369.5 \, \text{kJ/mol} \).

Step 3: Apply the Formula for Enthalpy of Solution

The enthalpy of solution \( \Delta_{\text{sol}}H^{\circ} \) can be calculated as the difference between the enthalpy of formation of the aqueous solution and the solid form: \[\Delta_{\text{sol}}H^{\circ} = \Delta_{f}H^{\circ}(\text{aq}) - \Delta_{f}H^{\circ}(\text{s})\]

Step 4: Calculate the Enthalpy of Solution

Substitute the known values into the formula: \[\Delta_{\text{sol}}H^{\circ} = (-369.5) - (-382.9) \, \text{kJ/mol} \]Calculate the difference:\[\Delta_{\text{sol}}H^{\circ} = 13.4 \, \text{kJ/mol}\]

Step 5: Interpret the Results

The positive value of \( 13.4 \, \text{kJ/mol} \) indicates that the dissolution of sodium perchlorate in water is an endothermic process, meaning it absorbs heat from the surroundings.

Key Concepts

Sodium Perchlorate

Sodium perchlorate is an ionic compound represented by the formula \( \text{NaClO}_4 \). It consists of sodium ions \( \text{Na}^+ \) and perchlorate ions \( \text{ClO}_4^- \). When it is dissolved in water, the compound dissociates into these ions, forming an aqueous solution.
Understanding its behavior in solution is crucial, especially in studying thermodynamic properties like enthalpy changes.
Sodium perchlorate is used in various applications, including as a strong oxidizing agent. This property comes from the oxygen-rich perchlorate ion, making it valuable in chemical synthesis and even in explosives.
When calculating the enthalpy of its solution, knowing the enthalpies of formation in different states, like solid and aqueous, is essential.

Enthalpy of Formation

The enthalpy of formation \( \Delta_{f} H^{\circ} \) is a vital concept in thermochemistry. It refers to the change in enthalpy when one mole of a substance is formed from its elements in their standard states.
It serves as a baseline to compare different thermodynamic processes. For sodium perchlorate, we have the standard enthalpy of formation for both its solid form \( -382.9 \text{ kJ/mol} \) and its aqueous form \( -369.5 \text{ kJ/mol} \).
This information helps us determine how much energy is involved in the dissolution process.
Calculating the change in enthalpy from one form to another, as we see in enthalpy of solution, gives insights into whether a process is endothermic or exothermic.
Such calculations allow chemists to predict how materials will behave under different conditions.

Endothermic Process

An endothermic process is one that absorbs energy from its surroundings, often in the form of heat. This process results in a cooling effect in the environment.
In the case of sodium perchlorate dissolving in water, the enthalpy of solution was calculated to be \( 13.4 \text{ kJ/mol} \). This positive enthalpy value indicates that heat is absorbed during the dissolving process.
Understanding whether a reaction is endothermic or exothermic is crucial in controlling chemical reactions and is significant in industrial processes.
Endothermic processes require input of energy, which can be essential information when designing reactions or choosing appropriate conditions for chemical production.