Question

A saturated solution prepared at \(70^{\circ} \mathrm{C}\) contains \(32.0 \mathrm{g}\) CuSO \(_{4}\) per 100.0 g solution. A 335 g sample of this solution is then cooled to \(0^{\circ} \mathrm{C}\) and \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) crystallizes out. If the concentration of a saturated solution at \(0^{\circ} \mathrm{C}\) is \(12.5 \mathrm{g} \mathrm{CuSO}_{4} / 100 \mathrm{g}\) soln, what mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) would be obtained? [Hint: Note that the solution composition is stated in terms of \(\mathrm{CuSO}_{4}\) and that the solid that crystallizes is the hydrate \(\left.\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} .\right]\)

Short answer

The mass of CuSO4·5H2O that would be obtained from cooling the solution is 102 g.

Step-by-step solution

Calculate the Initial Amount of CuSO4

Firstly, calculate the amount of CuSO4 initially present in the 335 g sample of the solution. Use the given concentration of the solution at \(70^{\circ}C\) which is 32.0 g CuSO4 per 100.0 g solution. The mass of CuSO4 can be calculated by proportion: \((32.0 g CuSO4 / 100.0 g solution) * 335 g solution = 107.2 g CuSO4\).

Calculate the Amount of CuSO4 Remaining in Solution

Next, calculate how much CuSO4 stays in the solution after it has cooled down. Use the given concentration of the saturated solution at \(0^{\circ}C\), that is 12.5 g CuSO4 per 100g solution. The mass of CuSO4 in this case can also be calculated by proportion: \((12.5 g CuSO4 / 100 g solution) * 335 g solution = 41.9 g CuSO4\). The difference between the initial amount of CuSO4 and that remaining in the solution after cooling is the amount of CuSO4 that crystallize out.

Calculate the Mass of CuSO4·5H2O Crystallized

The mass of CuSO4 that crystallized out can be calculated as \(107.2 g CuSO4 - 41.9 g CuSO4 = 65.3 g CuSO4\). This mass of copper sulfate crystallizes out as an hydrate CuSO4·5H2O. To convert this mass into the mass of the hydrate, use the molar masses of CuSO4 and CuSO4·5H2O. Considering that the molar mass of CuSO4 is 159.60 g/mol and the molar mass of CuSO4·5H2O is 249.70 g/mol the mass of the hydrate can be determined by the equation: \((65.3 g CuSO4 * 249.70 g CuSO4·5H2O) / 159.60 g CuSO4 = 102 g CuSO4·5H2O\).

Key concepts

Copper Sulfate

Copper sulfate, with the chemical formula \(\text{CuSO}_4\), is a blue crystal commonly used in various applications, such as in agriculture as a fungicide and in chemistry for various reactions. It is an ionic compound, meaning it is made of copper (Cu) cations and sulfate (SO₄) anions. This results in its ability to dissolve in water, which is fundamental for creating solutions and performing chemical reactions.

• Copper sulfate is often stored in its pentahydrate form, \(\text{CuSO}_4 \, \cdot \, 5\text{H}_2\text{O}\), which means it contains five water molecules bound in its crystal structure.
• When heated or dissolved, copper sulfate can lose these water molecules, changing its physical properties.
• The solubility of copper sulfate in water is temperature-dependent, which is key to its behavior in solutions.

Understanding the properties of copper sulfate is essential for predicting its behavior during experiments, especially when dealing with solutions and crystallization.

Hydration Crystallization

Hydration crystallization occurs when the hydrated form of a compound crystallizes out of a solution. This process significantly involves copper sulfate in its pentahydrate form, \(\text{CuSO}_4 \, \cdot \, 5\text{H}_2\text{O}\). During crystallization, the copper sulfate incorporates water molecules into its crystal lattice, leading to the hydrate form.

• As a solution cools, solubility changes can lead to the formation of solid crystals.
• For copper sulfate, the cooling process allows \(\text{CuSO}_4\) to bind with water and form \(\text{CuSO}_4 \, \cdot \, 5\text{H}_2\text{O}\).
• This process is visible as the emergence of blue crystals from the solution.

Hydration crystallization is useful because it influences the form and purity of the substance being crystallized, which is crucial in chemical procedures and industrial applications.

Temperature Dependence of Solubility

Solubility refers to the ability of a substance to dissolve in a solvent, such as water. For copper sulfate, solubility is heavily dependent on temperature. This means that as the temperature changes, so does the amount of copper sulfate that can dissolve in water.

• At higher temperatures, more copper sulfate can dissolve in water.
• Conversely, when the temperature decreases, the solubility decreases, leading to crystallization of the excess solute.
• This property is used to separate substances through cooling the solution, causing crystallization of less soluble compounds.

Understanding the temperature dependence of solubility is vital in various industries, from chemistry to environmental science, because it helps predict how substances will behave under different conditions.