Question

Potassium perchlorate \(\left(\mathrm{KClO}_{4}\right)\) has a lattice energy of \(-599 \mathrm{~kJ} / \mathrm{mol}\) and a heat of hydration of \(-548 \mathrm{~kJ} / \mathrm{mol}\). Find the heat of solution for potassium perchlorate and determine the temperature change that occurs when \(10.0 \mathrm{~g}\) of potassium perchlorate is dissolved with enough water to make \(100.0 \mathrm{~mL}\) of solution. (Assume a heat capacity of \(4.05 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\) for the solution and a density of \(1.05 \mathrm{~g} / \mathrm{mL}\).)

Short answer

The heat of solution for potassium perchlorate is -1147 kJ/mol. When 10.0 g is dissolved in water to make 100.0 mL of solution, the temperature decreases by 19.06°C.

Step-by-step solution

Calculate the Heat of Solution

The heat of solution can be calculated using the lattice energy and the heat of hydration. It is given by the formula: Heat of Solution = Lattice Energy + Heat of Hydration. Substitute the given values: Heat of Solution = (-599 kJ/mol) + (-548 kJ/mol) = (-1147 kJ/mol).

Find Moles of Potassium Perchlorate

First, find the molar mass of KClO4 by adding the atomic masses of K (39.10 g/mol), Cl (35.45 g/mol), and 4 O atoms (4 x 16.00 g/mol). Molar mass of KClO4 = 39.10 + 35.45 + (4 x 16.00) = 138.55 g/mol. Use this to find the moles of 10.0 g KClO4: Moles of KClO4 = 10.0 g / 138.55 g/mol = 0.0722 mol.

Calculate the Total Heat Released on Solution

Multiply the moles of KClO4 by the heat of solution per mole to find the total heat released: Total Heat = 0.0722 mol x (-1147 kJ/mol) x 1000 J/kJ. Total Heat = -82867.4 J.

Determine Mass of the Solution

To find the mass of the solution, multiply the volume of the solution by the density: Mass of Solution = Volume x Density = 100.0 mL x 1.05 g/mL = 105 g.

Calculate the Temperature Change

Using the formula q=mcΔT, where q is the heat released, m is the mass of the solution, c is the heat capacity of the solution, and ΔT is the change in temperature. Rearrange to solve for ΔT: ΔT = q / (m x c). ΔT = -82867.4 J / (105 g x 4.05 J/g⋅°C) = -19.06°C.

Key concepts

Lattice Energy

Lattice energy is a measure of the bond strength holding ionic compounds together. In simple terms, it's the energy required to separate one mole of a solid ionic compound into its gaseous ionic constituents. For example, the substance potassium perchlorate (\(\mathrm{KClO}_{4}\))) mentioned in the exercise, has its constituent ions firmly held together in the solid state, and the lattice energy is a negative value of -599 kJ/mol, indicating an exothermic process required to break the bonds during the dissolution process.
The larger the lattice energy, the more stable the ionic compound and the more energy it will take to break these ionic bonds. It's a critical factor in understanding the heat of solution, as the process of dissolving involves overcoming this lattice energy.

Heat of Hydration

Heat of hydration is the amount of energy released when one mole of ions is dissolved in water, specifically when they become surrounded by water molecules. Imagine a crowd of fans (water molecules) surrounding a celebrity (an ion) — this gives an ion a sort of energetic 'comfort.' For \(\mathrm{KClO}_{4}\), the heat of hydration is -548 kJ/mol. This process is usually exothermic, as demonstrated by the negative sign, meaning that it releases heat.
During the dissolution of ionic compounds, ions are pulled apart due to the lattice energy, and then each ion is stabilized in solution by hydration. The combination of heat of hydration with the lattice energy helps determine whether the overall process of dissolving will be exothermic or endothermic — a key step in finding the heat of solution.

Molar Mass

The molar mass of a substance is the weight in grams of one mole of that substance. It's like a molecular 'price tag' indicating how heavy one mole of a material is. The molar mass of potassium perchlorate (\(\mathrm{KClO}_{4}\)) is calculated by summing the masses of its constituent atoms: potassium (K), chlorine (Cl), and oxygen (O). For \(\mathrm{KClO}_{4}\), the molar mass turns out to be 138.55 g/mol. Understanding molar mass is fundamental in stoichiometry, allowing scientists and students to convert between mass and moles, a critical step in quantifying the amounts of substances involved in chemical reactions or processes like dissolving.

Enthalpy Change

Enthalpy change is essentially the change in heat content for a system during a reaction or process, at constant pressure. It's denoted by \(\Delta H\) and measured in joules or kilojoules per mole. The enthalpy change for a reaction can be exothermic (heat is released, \(\Delta H\) is negative) or endothermic (heat is absorbed, \(\Delta H\) is positive).
The heat of solution for \(\mathrm{KClO}_{4}\) is found by adding the lattice energy and the heat of hydration, another way of considering the enthalpy change of dissolving \(\mathrm{KClO}_{4}\) in water. Besides, the temperature change of the resulting solution can be directly related to the enthalpy change, linking to the concept of heat capacity and giving us practical insight into how a chemical process can affect its surroundings.