Question

The enthalpies of solution of \(\mathrm{BaCl}_{2}\) (s) and \(\mathrm{BaCl}_{2} .2 \mathrm{H}_{2} \mathrm{O}\) (s) are \(-20.6\) and \(8.8 \mathrm{~kJ} \mathrm{~mol}^{2}\) 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

The enthalpy change for the hydration of \( \mathrm{BaCl}_2 \) is 29.4 kJ/mol.

Step-by-step solution

Understand the Data Given

We are provided with the enthalpies of solution for \( \mathrm{BaCl}_2 (s) \) which is \(-20.6 \, \mathrm{kJ/mol} \) and \( \mathrm{BaCl}_2 \cdot 2 \mathrm{H}_2 \mathrm{O} (s) \) which is \( 8.8 \, \mathrm{kJ/mol} \). We need to calculate the enthalpy change for the hydration of \( \mathrm{BaCl}_2 (s) \).

Use the Formula for Hydration Enthalpy

The enthalpy change for the hydration process can be calculated using the formula:\[ \Delta H_{hydration} = \Delta H_{solution, \mathrm{BaCl}_2 \cdot 2\mathrm{H}_2 \mathrm{O}} - \Delta H_{solution, \mathrm{BaCl}_2} \]

Substitute the Given Values

Replace the variables in the equation with the given values:\[ \Delta H_{hydration} = 8.8 \mathrm{\, kJ/mol} - (-20.6 \mathrm{\, kJ/mol}) \]

Simplify the Expression

Simplify the expression by performing the subtraction:\[ \Delta H_{hydration} = 8.8 \mathrm{\, kJ/mol} + 20.6 \mathrm{\, kJ/mol} \]

Calculate the Final Result

Add the values to find the enthalpy change for hydration:\[ \Delta H_{hydration} = 29.4 \mathrm{\, kJ/mol} \]

Choose the Correct Option

The calculated enthalpy change for the hydration of \( \mathrm{BaCl}_2 \) is \( 29.4 \mathrm{\, kJ/mol} \). Therefore, the correct answer is option (a) \( 29.8 \mathrm{\, kJ/mol} \).

Key concepts

Thermodynamics

Thermodynamics is the study of energy, heat, work, and how they interrelate. In the context of thermodynamics, enthalpy is a key concept representing the total heat content of a system. Enthalpy changes (\(\Delta H\)) occur during chemical reactions or phase changes, telling us how heat is absorbed or released.

When dealing with processes like the hydration of a substance, thermodynamics can help predict the direction of heat flow and the feasibility of the process. This branch of science uses laws and equations to describe how systems behave:

• The First Law of Thermodynamics states that energy cannot be created or destroyed, only transformed from one form to another.
• The Second Law of Thermodynamics introduces the concept of entropy, a measure of disorder, highlighting that energy transformations lead to increased disorder in the universe.

Thermodynamics thus provides a framework for understanding why some processes, like solution energetics, are spontaneous or require energy input.

Hydration Process

The hydration process involves the interaction of a substance with water molecules. More specifically, it is the process by which ions from a salt are surrounded by water molecules in a solution. In the case of \(\mathrm{BaCl}_2\), when it dissolves, it undergoes hydration by water molecules.

During hydration, water molecules surround and stabilize the ions. These interactions are due to the polarity of water molecules. This stabilization typically releases energy, contributing to a negative enthalpic change associated with hydration, known as enthalpy of hydration.

• Hydration helps in breaking the ionic bonds of salt, facilitating its dissolution in water.
• The extent of hydration can significantly influence the solubility and behavior of salts in aqueous solutions.

Overall, hydration is integral in chemical processes and impacts everything from solubility to thermal and physical properties.

Chemical Thermodynamics

Chemical thermodynamics deals with the interrelation of chemical reactions and energy changes. It provides the theoretical basis for understanding chemical behavior, reactions, and changes, focusing on concepts like enthalpy, entropy, and free energy.

In chemical thermodynamics, enthalpy (\(\Delta H\)) is crucial for understanding whether a reaction will release or absorb heat. For instance, when \(\mathrm{BaCl}_2\) forms a solution with water, the enthalpy of solution reflects the net effect of breaking ionic bonds and forming new interactions with water.

• Exothermic reactions release heat (\(\Delta H < 0\)), often resulting in a temperature rise.
• Endothermic reactions absorb heat (\(\Delta H > 0\)), which can cause cooling in the system.

Using chemical thermodynamics, we can predict the warmth or coolness of a solution forming process and understand energy transformations involved in reactions.

Solution Energetics

Solution energetics refers to the study of energy changes as substances interact to form solutions. It examines how the energetics of solute and solvent interactions impact the overall energy changes or enthalpy of the solution process.

For \(\mathrm{BaCl}_2\) and its hydrated form, enthalpy of solution indicates the energy associated with dissolving the compound in water. To determine the enthalpy of hydration, one can assess the difference between the hydrated and anhydrous states' enthalpy of solution:

• When \(\mathrm{BaCl}_2\) interacts with water, the resulting solution's enthalpy change incorporates breaking down ionic structures and forming new interactions.
• Both experimental data and theoretical calculations can be used to quantify these changes, facilitating a deeper understanding of how solvation impacts chemical thermodynamics.

Solution energetics is central to processes such as dissolution, precipitation, and even pharmaceutical drug delivery, as it governs the energy dynamics within solution systems.