Problem 47 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Enthalpies of solution of \(\mathrm{BaCl}_{2}(\mathrm{~s})\) and \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) are \(-20.6 \mathrm{~kJ} / \mathrm{mol}\) and \(8.8 \mathrm{~kJ} / \mathrm{mol}\), respectively. \(\Delta H\) hydration of \(\mathrm{BaCl}_{2}(\mathrm{~s})\) to \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) is (a) \(-29.4 \mathrm{~kJ}\) (b) \(-11.8 \mathrm{~kJ}\) (c) \(29.6 \mathrm{~kJ}\) (d) \(11.8 \mathrm{~kJ}\)

Step-by-Step Solution

Answer

\(\Delta H_\text{hydration}\) of \(\mathrm{BaCl}_{2}(\mathrm{~s})\) to \(\mathrm{BaCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) is 29.4 \mathrm{~kJ/mol}.

Step 1: Understanding Enthalpy Changes

There are several types of enthalpy changes involved here: the enthalpy of solution when a substance dissolves in water and the enthalpy of hydration when water molecules attach to the ions of the dissolved substance. Here we are interested in the difference between the two given enthalpy of solution values to determine the enthalpy change of hydration.

Step 2: Calculate the Enthalpy Change of Hydration

The change in enthalpy of hydration, \( \Delta H_\text{hydration} \), can be calculated using the enthalpy of solution for the anhydrous and hydrated form. This is done by subtracting the enthalpy of solution of the anhydrous salt from the enthalpy of solution of the hydrated salt: \( \Delta H_\text{hydration} = \Delta H_\text{solution, hydrated} - \Delta H_\text{solution, anhydrous} \).

Step 3: Substitute the Given Values

Substitute in the given enthalpy values to find the enthalpy change of hydration: \( \Delta H_\text{hydration} = (8.8 \, \text{kJ/mol}) - (-20.6 \, \text{kJ/mol}) \).

Step 4: Perform the Calculation

Adding the two values gives the enthalpy change of hydration: \( \Delta H_\text{hydration} = 8.8 \, \text{kJ/mol} + 20.6 \, \text{kJ/mol} = 29.4 \, \text{kJ/mol} \).

Step 5: Determine the Sign of \(\Delta H\)

If the overall enthalpy change should be endothermic (as heat is absorbed from the surroundings), the sign of \( \Delta H_\text{hydration} \) should be positive. If it should be exothermic (as heat is released to the surroundings), it should be negative. Since we are adding enthalpies, the sign will be positive.

Key Concepts

Enthalpy of Solution

The enthalpy of solution, often denoted as can be an endothermic or exothermic process, signifies the heat change when a solute dissolves in a solvent to form a solution. This value is crucial in understanding how substances interact with solvents like water. For instance, when a salt dissolves in water, it may require energy to break the ionic bonds in the solid (an endothermic process), and energy may be released when new interactions between the ions and water molecules are established (an exothermic process). The overall enthalpy of solution is the net effect of these opposing energy changes. Comprehending the enthalpy of solution facilitates the prediction of solution behavior and stability.

Moreover, the explanation in the exercise improvement advice suggests the importance of distinguishing the enthalpy of solution for anhydrous and hydrated forms. This differentiation allows us to address a common oversight, ensuring that the energy associated with the hydration shell of water molecules is properly considered when calculating the total enthalpy changes during the dissolving process.

Hydration of Ions

The process of hydration of ions is a key concept in physical chemistry, involving ions from a soluble ionic compound being surrounded by water molecules. Each water molecule has a polarity - a distinct separation of charges, with the oxygen atom having a partial negative charge, and the hydrogen atoms having a partial positive charge. When an ionic compound dissolves, these polar water molecules interact with the positive and negative ions, stabilizing them in solution through hydration shells.

Significance in Thermochemistry

The hydration of ions is not only vital for the solubility of compounds but also plays a significant role in thermochemistry. When ions are hydrated, energy is typically released since forming interactions between ions and water molecules is exothermic. However, the amount of energy varies depending on the ion's charge density. For educational clarity and student comprehension, detailing how cations and anions interact with water, and how hydration shells are formed, can greatly improve understanding of the hydration process.

Thermochemistry in Physical Chemistry

Thermochemistry is a branch of physical chemistry that deals with the quantity of heat evolved or absorbed during chemical reactions and physical changes. One key concept is the conservation of energy, which states that energy cannot be created or destroyed, only transformed. This principle underlies calculations like those for enthalpy changes; where energy changes in a system must equal those in the surroundings.

Applying Concepts to Solutions

For students, understanding thermochemical principles is fundamental when approaching exercises on solution energetics. It's pivotal to realize that the enthalpy of solution and the enthalpy of hydration involve energy exchanges. To improve exercise content, it is often helpful to emphasize the real-world implications of these concepts, such as their role in environmental processes and industrial applications. Providing students with relatable examples can enhance their grasp of how thermochemical principles govern the behavior of substances in various contexts.