Question

Each copper(II) sulfate unit is associated with five water molecules in crystalline copper(II) sulfate pentahydrate \(\left(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\right) .\) When this compound is heated in air above \(100^{\circ} \mathrm{C},\) it loses the water molecules and also its blue color: $$ \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CuSO}_{4}+5 \mathrm{H}_{2} \mathrm{O} $$ If \(9.60 \mathrm{~g}\) of \(\mathrm{CuSO}_{4}\) is left after heating \(15.01 \mathrm{~g}\) of the blue compound, calculate the number of moles of \(\mathrm{H}_{2} \mathrm{O}\) originally present in the compound.

Short answer

0.300 moles of water were originally present.

Step-by-step solution

Understand the Reaction

The chemical reaction presented is: \( \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{CuSO}_{4} + 5 \mathrm{H}_{2} \mathrm{O} \). This indicates that each formula unit of copper(II) sulfate pentahydrate loses 5 water molecules upon heating. We are given the mass of the initial compound and the mass of the anhydrous compound after heating.

Determine Mass of Water Lost

To find the mass of water lost, subtract the mass of \( \mathrm{CuSO}_{4} \) remaining after heating from the initial mass of \( \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \): \( 15.01 \mathrm{~g} - 9.60 \mathrm{~g} = 5.41 \mathrm{~g} \) of water was lost.

Calculate Moles of Water

Use the molar mass of water \( \mathrm{H}_{2} \mathrm{O} \) which is approximately \( 18.02 \mathrm{~g/mol} \), to calculate the number of moles of water lost: \[ \text{Moles of } \mathrm{H}_{2} \mathrm{O} = \frac{5.41 \mathrm{~g}}{18.02 \mathrm{~g/mol}} \approx 0.300 \text{ moles} \].

Verify Moles Correspond to Reaction

According to the balanced equation, the 0.300 moles of water corresponds to the 5 moles of water that originate from a complete mole of \( \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \). This confirms that our calculations match the stoichiometry of the reaction.

Key concepts

Stoichiometry

Stoichiometry is the core concept that helps chemists understand the quantitative relationships between reactants and products in a chemical reaction. In the case of Copper(II) Sulfate Pentahydrate, stoichiometry tells us how the breakdown of compounds happens when heated. The balanced chemical equation is given by:\[ \mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{CuSO}_{4} + 5 \mathrm{H}_{2} \mathrm{O} \]This equation indicates that each molecule of Copper(II) Sulfate Pentahydrate will yield five molecules of water and one molecule of anhydrous Copper(II) Sulfate. From the stoichiometric coefficients (numbers in front of the chemical formulas), you can see the direct relationship between how much of each substance is involved.
Understanding these relationships helps ensure that when we calculate moles, mass, or volumes of reactants and products, the conservation of mass is respected. Making stoichiometry an essential tool in any chemical analysis.

Chemical Reaction

A chemical reaction is a process where substances, called reactants, are transformed into new substances, known as products. In this scenario, Copper(II) Sulfate Pentahydrate is a reactant, and when heated beyond 100°C, a chemical change results in producing anhydrous Copper(II) Sulfate and water, our products.
Understanding the nature of this change is important:

• Heating causes a physical removal of water molecules linked to the Copper(II) Sulfate, resulting in a color change (blue to white or grayish).
• Essentially, the crystalline structure loses its water of hydration.
• These transformations are often reversible if water vapor is added back, returning the original hydrated salt color.

Interpreting chemical reactions not only through written equations but by observing physical changes, like color shifts, supports a deeper comprehension of chemical processes.

Mole Calculation

Mole calculations allow chemists to convert between mass units and the number of molecules, which helps quantify the substances involved in a reaction. In this exercise, you determined how many moles of water were originally present in Copper(II) Sulfate Pentahydrate.The calculation process included:1. **Determine Mass of Water Lost**: This was found by subtracting the mass of remaining Copper(II) Sulfate from the starting hydrated compound mass: 15.01 g - 9.60 g = 5.41 g of water.2. **Convert Mass to Moles**: Using the molar mass of water (18.02 g/mol), the moles of water are calculated: \[ \text{Moles of } \mathrm{H}_{2} \mathrm{O} = \frac{5.41 \mathrm{~g}}{18.02 \mathrm{~g/mol}} \approx 0.300 \text{ moles} \]Understanding mole calculations involves injecting the relations described in stoichiometry alongside the chemical equations, allowing you to precisely know how much of each reactant was present or has been used. Keeping these calculations clear ensures accuracy and reinforces knowledge gained from practicing.