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Chapter 3: Problem 141

A \(0.755-\mathrm{g}\) sample of hydrated copper(II) sulfate \(\mathrm{CuSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\) was heated carefully until it had changed completely to anhydrous copper(II) sulfate \(\left(\mathrm{CuSO}_{4}\right)\) with a mass of \(0.483 \mathrm{~g}\). Determine the value of \(x\). [This number is called the number of waters of hydration of copper(II) sulfate. It specifies the number of water molecules per formula unit of \(\mathrm{CuSO}_{4}\) in the hydrated crystal.]

Short Answer

Expert verified
The number of waters of hydration for the hydrated copper(II) sulfate (\(\mathrm{CuSO}_4\cdot\ x\mathrm{H}_2\mathrm{O}\)) is \(x = 5\). This means there are five water molecules per formula unit in the hydrated crystal, making the hydrated copper(II) sulfate \(\mathrm{CuSO}_4\cdot 5\mathrm{H}_2\mathrm{O}\).

Step by step solution

01

1. Calculate the mass of water lost during the heating process

To calculate the mass of water lost, subtract the mass of anhydrous copper(II) sulfate from the initial mass of the hydrated sample: Mass of water lost = Initial mass - Mass of anhydrous CuSO4 Mass of water lost = \(0.755 g - 0.483 g = 0.272 g\)
02

2. Calculate moles for water and copper(II) sulfate

To calculate the moles of water and copper(II) sulfate, we first need the molar masses. For water (H2O): the molar mass is \(2 \times1.008 + 16 = 18.016 g/mol\) For copper(II) sulfate (CuSO4): the molar mass is \(63.546 + 32.066 + 4 \times 16 = 159.62 g/mol\) Now, we can calculate the moles: Moles of water = \(\cfrac{0.272 g}{18.016 g/mol} \approx 0.0151mol\) Moles of copper(II) sulfate = \(\cfrac{0.483 g}{159.62 g/mol} \approx 0.00303 mol\)
03

3. Determine the ratio between moles of water and copper(II) sulfate

Now we have to find the mole ratio between water (H2O) and copper(II) sulfate (CuSO4) by dividing the moles of water by the moles of copper(II) sulfate: Mole ratio = \(\cfrac{0.0151 mol}{0.00303 mol} \approx 4.98\)
04

4. Determine the value of x

Since the mole ratio \(approx 4.98\) is close to 5, and considering the number of moles must be a whole number, we can conclude that the value of x in CuSO4·xH2O is 5. Therefore, the hydrated copper(II) sulfate is CuSO4·5H2O, and the number of waters of hydration is 5.

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