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Chapter 9: Problem 33

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

Expert verified
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

01

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.
02

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 \(\mathrm{Li}_{2}SO_{4}(s) \rightarrow 2\mathrm{Li}^+(aq) + \mathrm{SO}_{4}^{2-}(aq)\).
03

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.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

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.

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Most popular questions from this chapter

Benzene, \(\mathrm{C}_{6} \mathrm{H}_{6}\), and toluene, \(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}\), form an ideal solution. The vapor pressure of benzene is \(94.6\) Torr and that of toluene is \(29.1\) Torr at \(25^{\circ} \mathrm{C}\). Calculate the vapor pressure of each of the following solutions and the mole fraction of each substance in the vapor phase above those solutions at \(25^{\circ} \mathrm{C}\) : (a) \(1.50 \mathrm{~mol}\) \(\mathrm{C}_{6} \mathrm{H}_{6}\) mixed with \(0.50 \mathrm{~mol} \mathrm{} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3} ;\) (b) \(15.0 \mathrm{~g}\) of benzene mixed with \(64.3 \mathrm{~g}\) of toluene.

Calculate the concentrations of each of the following solutions: (a) the molality of \(13.63 \mathrm{~g}\) of sucrose, \(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\), dissolved in \(612 \mathrm{~mL}\) of water; (b) the molality of CsCl in a \(10.00 \%\) by mass aqueous solution; (c) the molality of acetone in an aqueous solution with a mole fraction for acetone of \(0.197 .\)

Consider an apparatus in which \(A\) and B are two \(1.00-\mathrm{L}\) flasks joined by a stopcock \(\mathrm{C}\). The volume of the stopcock is negligible. Initially, \(\mathrm{A}\) and \(\mathrm{B}\) are evacuated, the stopcock \(\mathrm{C}\) is dosed, and \(1.50 \mathrm{~g}\) of diethyl ether, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5}\), is introduced into flask A. The vapor pressure of diethyl ether is 57 Torr at \(-45^{\circ} \mathrm{C}\), 185 Torr at \(0 .{ }^{\circ} \mathrm{C}, 534\) Torr at \(25^{\circ} \mathrm{C}\), and negligible below \(-86^{\circ} \mathrm{C}\). (a) If the stopcock is left closed and the flask is brought to equilibrium at \(-45^{\circ} \mathrm{C}\), what will be the pressure of diethyl ether in flask A? (b) If the temperature is raised to \(25^{\circ} \mathrm{C}\), what will be the pressure of diethyl ether in the flask? (c) If the temperature of the assembly is returned to \(-45^{\circ} \mathrm{C}\) and the stopcock \(\mathrm{C}\) is opened, what will be the pressure of diethyl ether in the apparatus? (d) If flask \(\mathrm{A}\) is maintained at \(-45^{\circ} \mathrm{C}\) and flask B is cooled with liquid nitrogen (boiling point, \(-196^{\circ} \mathrm{C}\) ) with the stopcock open, what changes will take place in the apparatus? Assume ideal behavior.

Calculate the osmotic pressure at \(20^{\circ} \mathrm{C}\) of each of the following solutions; assume complete dissociation of ionic compounds: (a) \(3.0 \times 10^{-3} \mathrm{M}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(\mathrm{aq}) ;\) (b) \(2.0 \times 10^{-3} \mathrm{M}\) \(\mathrm{CaCl}_{2}(\mathrm{aq}) ;\) (c) \(0.010 \mathrm{M} \mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{aq})\).

Which would be the better solvent, water or tetrachloromethane, for each of the following substances: (a) \(\mathrm{NH}_{3}\); (b) \(\mathrm{HNO}_{3} ;\) (c) \(\mathrm{N}_{2}\) ?
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