Question

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

The value of x in the hydrated copper(II) sulfate compound CuSO4 · xH2O is found to be 5, meaning the compound can be written as CuSO4 · 5H2O.

Step-by-step solution

Find the mass of water lost during heating

Initial mass of hydrated copper(II) sulfate = 0.755 g Final mass of anhydrous copper(II) sulfate = 0.483 g Mass of water lost = Initial mass - Final mass = 0.755 g - 0.483 g = 0.272 g

Calculate the moles of anhydrous copper(II) sulfate and water

Moles of CuSO4 = Mass of CuSO4 / Molar mass of CuSO4 = 0.483 g / (63.55 g/mol + 32.07 g/mol + (4 × 16.00 g/mol)) = 0.483 g / 159.62 g/mol = 0.00303 mol Moles of H2O = Mass of H2O / Molar mass of H2O = 0.272 g / (2 × 1.01 g/mol + 16.00 g/mol) = 0.272 g / 18.02 g/mol = 0.0151 mol

Determine the value of x

x = Moles of H2O / Moles of CuSO4 = 0.0151 mol / 0.00303 mol = 4.984 Since the number of waters of hydration is usually an integer, we can round the value of x to the nearest whole number. Therefore, x = 5. The value of x in CuSO4 · xH2O is 5, meaning the hydrated copper(II) sulfate compound can be written as CuSO4 · 5H2O.

Key concepts

Hydrated Copper(II) Sulfate

Hydrated copper(II) sulfate, commonly represented as \textbf{CuSO\(_4\)・xH\(_2\)O}, is a vivid blue, crystalline substance that includes water molecules within its crystal structure. The 'x' in its chemical formula stands for the hydration number, which tells us the exact number of water molecules associated with each copper(II) sulfate unit in the crystal. The process of heating the hydrated salt can cause it to lose these water molecules, turning it into an anhydrous substance.

Understanding hydration is essential, as the properties of a compound, like color and reactivity, can drastically change upon losing water. For example, hydrated copper(II) sulfate is blue, but when it becomes anhydrous, its color changes to white or gray, indicating a significant structural alteration in the compound.

Anhydrous Copper(II) Sulfate

When hydrated copper(II) sulfate loses all its water molecules upon heating, it becomes anhydrous copper(II) sulfate, abbreviated as \textbf{CuSO\(_4\)}. This process involves heating the hydrated form until it ceases to lose mass, implying that all the water of hydration has been removed. Anhydrous copper(II) sulfate is quite different from its hydrated counterpart, not just in color but also in terms of its absorption properties. It is often used as a test for water because it readily absorbs water from its surroundings, regaining its blue color upon doing so. This physical property is particularly handy in laboratories for detecting the presence of water in various substances or environments.

Stoichiometry

Stoichiometry refers to the quantitative relationships between substances as they participate in chemical reactions. In this context, it is used to relate the mass of the hydrated copper(II) sulfate to the mass of water lost upon heating and hence to deduce the number of water molecules corresponding to a fixed number of copper(II) sulfate formula units. By utilizing the molar masses of these substances and measuring the mass change during the dehydration process, we can calculate the number of moles involved and eventually find the hydration number, 'x'. Stoichiometry is a foundational concept in chemistry because it allows scientists to predict the quantities of reactants needed and products formed in a chemical reaction.

Molecular Formulas

Molecular formulas represent the actual number of atoms of each element in a compound. For hydrated compounds, the molecular formula includes the number of water molecules associated with each formula unit, which are integral to the structure of the compound. In the case of hydrated copper(II) sulfate, once we determine the hydration number 'x' using stoichiometry, we can accurately write its molecular formula as \textbf{CuSO\(_4\)・xH\(_2\)O}. Furthermore, knowing the molecular formula is crucial for understanding the compound's stoichiometry, as it directly influences the proportions of elements and compounds involved in chemical reactions. Therefore, for scientists and students alike, mastering the interpretation and use of molecular formulas is essential for successful chemistry.