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Chapter 13: Problem 107

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

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

Step by step solution

01

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: \((32.0 g CuSO4 / 100.0 g solution) * 335 g solution = 107.2 g CuSO4\).
02

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.
03

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: \((65.3 g CuSO4 * 249.70 g CuSO4·5H2O) / 159.60 g CuSO4 = 102 g CuSO4·5H2O\).

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Most popular questions from this chapter

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