Question

The enthalpies of solution of \(\mathrm{BaCl}_{2}\) (s) and \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) (s) are \(-20.6\) and \(8.8 \mathrm{~kJ} \mathrm{~mol}^{-1}\) respectively. The enthalpy change for the hydration of \(\mathrm{BaCl}_{2}(\mathrm{~s})\) is (a) \(29.8 \mathrm{~kJ}\) (b) \(-11.8 \mathrm{~kJ}\) (c) \(-20.6 \mathrm{~kJ}\) (d) \(-29.4 \mathrm{~kJ}\).

Short answer

(a) 29.8 kJ/mol.

Step-by-step solution

Understanding the Given Values

We are given the enthalpies of solution for \( \mathrm{BaCl}_{2} \) as \(-20.6 \, \mathrm{kJ/mol}\) and for \( \mathrm{BaCl}_{2} \cdot 2\mathrm{H}_{2} \mathrm{O} \) as \(8.8 \, \mathrm{kJ/mol}\). These represent the energy changes when each of these compounds dissolve in water.

Defining the Hydration Enthalpy

The enthalpy of hydration is the enthalpy change when a substance transitions from a solid state to its hydrated form (including water of crystallization). Here, it is the enthalpy change for converting \( \mathrm{BaCl}_{2} \) to \( \mathrm{BaCl}_{2} \cdot 2\mathrm{H}_{2} \mathrm{O} \).

Applying the Enthalpy Change Formula

Using Hess's law, the enthalpy change for the hydration can be determined: \( \Delta H_{\text{hydration}} = \Delta H_{\text{solution of hydrated}} - \Delta H_{\text{solution of anhydrous}} \). Here, it simplifies to \( 8.8 \, \mathrm{kJ/mol} - (-20.6 \, \mathrm{kJ/mol}) \).

Calculating the Hydration Enthalpy

Perform the calculation: \( 8.8 \, \mathrm{kJ/mol} + 20.6 \, \mathrm{kJ/mol} = 29.4 \, \mathrm{kJ/mol} \). This value represents the enthalpy change for the hydration of \( \mathrm{BaCl}_{2} \).

Key concepts

Enthalpy of Solution

The enthalpy of solution refers to the heat energy change when one mole of a substance dissolves in a solvent. In our exercise, we deal with the dissolution of barium chloride (\( \mathrm{BaCl}_2 \)) both in anhydrous form and as a dihydrate (\( \mathrm{BaCl}_{2}\cdot 2 \mathrm{H}_{2} \mathrm{O} \)). When \( \mathrm{BaCl}_2 \) dissolves, energy either gets absorbed from or released into the surroundings, resulting in an enthalpy value. The negative value of \(-20.6 \, \mathrm{kJ/mol}\) for the anhydrous form indicates that the process is exothermic, meaning it releases heat. On the other hand, the dihydrate form has a positive enthalpy of \(8.8 \, \mathrm{kJ/mol}\), showing an endothermic process, which absorbs heat from the surroundings. This difference underscores how physical states and molecular interactions impact energy changes.

Hydration Enthalpy

Hydration enthalpy is the energy change when an ionic compound absorbs water molecules and forms a hydrated structure. It's an essential part of the overall enthalpy change in dissolving ionic compounds. In the exercise, the transition of \( \mathrm{BaCl}_2 \) to \( \mathrm{BaCl}_{2}\cdot 2\mathrm{H}_2\mathrm{O} \) involves this concept. The hydration process can influence whether the overall process is exothermic or endothermic. The hydration enthalpy can be inside the total energy balance of solution enthalpy. This means that when a compound like barium chloride interacts with water to form a hydrated salt, the release or absorption of heat during this process is encapsulated in the hydration enthalpy.

Hess's Law

Hess's Law is a fundamental principle in thermochemistry. It states that the total enthalpy change for a reaction is the same, no matter how it is achieved, considering initial and final states only. This principle allows us to calculate unknown enthalpy changes by summing known values along a reaction pathway. In the exercise, Hess’s Law helps calculate the hydration enthalpy by using the enthalpies of the dihydrate and anhydrous forms of barium chloride. The formula used is: \[ \Delta H_{\text{hydration}} = \Delta H_{\text{solution of hydrated}} - \Delta H_{\text{solution of anhydrous}} \]This allows us to determine the energy required or released during the formation of the hydrated salt from its anhydrous counterpart.

Thermochemistry

Thermochemistry is the study of energy changes, particularly heat, during chemical reactions and changes in state. It involves analyzing how energy flows and converts during chemical transformations, including processes like dissolution, hydration, and reaction energetics. Although most chemical reactions involve either releasing or absorbing energy, the precise nature of this energy change (whether exothermic or endothermic) can significantly impact reaction conditions and outcomes. Understanding these changes is crucial because they affect practical applications, including the design of chemical processes and the manipulation of reaction environments. This exercise emphasizes these thermochemical concepts by highlighting how compounds dissolve and relate to overall energy transformations. Recognizing the link between enthalpy values and reaction types helps in grasping the broader scope of thermochemistry in real-world reactions.