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Chapter 5: Problem 141

A 0.755-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 (CuSO_) with a mass of 0.483 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 hydrated copper(II) sulfate formula is CuSO\(_4 \cdot 5\)H\(_2\)O, where the value of \(x\) is 5.

Step by step solution

01

Calculate the mass of water evaporated during heating

Subtract the mass of anhydrous copper(II) sulfate from the mass of hydrated copper(II) sulfate to find the mass of water evaporated: mass of water evaporated = mass of hydrated copper(II) sulfate - mass of anhydrous copper(II) sulfate mass of water evaporated = 0.755 g - 0.483 g = 0.272 g
02

Calculate the molar mass of anhydrous copper(II) sulfate (CuSO\(_4\)) and water (H\(_2\)O)

To find the value of \(x\), we need to know the molar mass of the substances involved. Use the periodic table to find the molar mass of each element and then add them up accordingly: Molar mass of CuSO\(_4\) = 63.55 (Cu) + 32.07 (S) + 4 * 16.00 (O) = 159.62 g/mol Molar mass of H\(_2\)O = 2 * 1.01 (H) + 16.00 (O) = 18.02 g/mol
03

Calculate the moles of CuSO\(_4\) and water (H\(_2\)O) involved

Divide the masses of each substance by their respective molar mass to find the number of moles: moles of CuSO\(_4\) = mass of CuSO\(_4\) / molar mass of CuSO\(_4\) = 0.483 g / 159.62 g/mol ≈ 0.00303 mol moles of H\(_2\)O = mass of H\(_2\)O / molar mass of H\(_2\)O = 0.272 g / 18.02 g/mol ≈ 0.0151 mol
04

Determine the value of \(x\) considering the ratio of moles of CuSO\(_4\) and H\(_2\)O

Divide the moles of H\(_2\)O by the moles of CuSO\(_4\) to find the value of \(x\): x = moles of H\(_2\)O / moles of CuSO\(_4\) = 0.0151 mol / 0.00303 mol ≈ 5 Since \(x\) must be an integer, we can conclude that \(x = 5\). Hence, the hydrated copper(II) sulfate formula should be written as: CuSO\(_4 \cdot 5\)H\(_2\)O

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