Question

Lithium sulfate dissolves exothermically in water. (a) Is the enthalpy of solution for \(\mathrm{Li}_{2} \mathrm{SO}_{4}\) positive or negative? (b) Write the chemical equation for the dissolving process. (c) Which is larger for lithium sulfate, the lattice enthalpy or the enthalpy of hydration?

Short answer

The enthalpy of solution for lithium sulfate is negative, the chemical equation for the dissolving process is \(\mathrm{Li}_{2}SO_{4}(s) \rightarrow 2\mathrm{Li}^+(aq) + \mathrm{SO}_{4}^{2-}(aq)\), and the enthalpy of hydration is larger than the lattice enthalpy for lithium sulfate.

Step-by-step solution

Determine the Sign of the Enthalpy of Solution

The enthalpy of solution can be determined based on whether the dissolving process is exothermic or endothermic. Since the problem states that lithium sulfate dissolves exothermically, it releases heat to the surroundings. Therefore, the process must have a negative enthalpy of solution.

Write the Dissolving Chemical Equation

To write the chemical equation for the dissolving process of lithium sulfate in water, dissociate the solid ionic compound into its ions. The equation is \(\mathrm{Li}_{2}SO_{4}(s) \rightarrow 2\mathrm{Li}^+(aq) + \mathrm{SO}_{4}^{2-}(aq)\).

Compare Lattice Enthalpy and Enthalpy of Hydration

Since the overall process of dissolving is exothermic, the exothermic enthalpy of hydration must be greater than the endothermic lattice enthalpy to result in a release of energy. Thus, the enthalpy of hydration is larger than the lattice enthalpy for lithium sulfate.

Key concepts

Exothermic Reactions

Understanding exothermic reactions is key to grasping the concept of the enthalpy of solution. In an exothermic reaction, energy is released into the surroundings, usually in the form of heat. This is often observed as an increase in the temperature of the surroundings.

For the enthalpy of solution, this means that when the solute dissolves, the overall energy transferred out from the substance into the water leads to a release of heat. Indications that a reaction is exothermic include terms like 'heat is released', 'temperature rises', or, as mentioned in the lithium sulfate example, the substance 'dissolves exothermically'.

Chemical Equation

The chemical equation for a dissolving process displays how the reactants (the substances starting the reaction) turn into products. It's a symbolic representation that provides a snapshot of the process taking place at the molecular level.

For our lithium sulfate example, the chemical equation is straightforward: \(\mathrm{Li}_{2}SO_{4}(s) \rightarrow 2\mathrm{Li}^+(aq) + \mathrm{SO}_{4}^{2-}(aq)\). This tells us that solid lithium sulfate separates into lithium ions and sulfate ions when it dissolves in water. Remember that 's' stands for solid and 'aq' implies that the ions are aqueous, or dissolved in water.

Lattice Enthalpy

Lattice enthalpy is a measure of the strength of the forces between the ions in an ionic solid. It's defined as the energy required to separate one mole of a solid ionic compound into gaseous ions.

This value is always positive because breaking bonds requires energy input. In simple terms, it's the energy price to pay for pulling ions apart. Lattice enthalpy values are high for ionic compounds with strongly charged ions and small ionic radii because the electrostatic forces are stronger, requiring more energy to overcome.

Enthalpy of Hydration

Conversely, the enthalpy of hydration is the energy change when one mole of gaseous ions become surrounded by water molecules, forming an aqueous solution. This process is typically exothermic, meaning energy is released during the interaction as the ions are 'stabilized' by water.

The extent of this energy change depends on the charge and size of the ions; higher charges and smaller sizes lead to more negative (or more exothermic) enthalpy of hydration values. For lithium sulfate, the enthalpy of hydration exceeds the lattice enthalpy, meaning more energy is released in hydrating the ions than is consumed in breaking the ionic solid apart.