Problem 121 - Chemistry The Science in Context

Question

As a solution of copper sulfate slowly evaporates, beautiful blue crystals made of copper(II) and sulfate ions form such that water molecules are trapped inside the crystals. The overall formula of the compound is \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) a. What is the percent water in this compound? b. At high temperatures, the water in the compound is driven off as steam. What mass percentage of the original sample of the blue solid is lost as a result?

Step-by-Step Solution

Answer

Answer: The percent water in the compound CuSO4 · 5H2O is 36.08%, and the mass percentage of the original sample of the blue solid lost when the water is driven off as steam is also 36.08%.

Step 1: Calculate molar mass of the compound components CuSO4 and H2O

First, we need to find the molar mass of the individual components of the compound. The molar masses are: Copper (Cu) = 63.55 g/mol Sulfur (S) = 32.07 g/mol Oxygen (O) = 16.00 g/mol Hydrogen (H) = 1.01 g/mol Now, calculate the molar mass of CuSO4 and H2O: CuSO4: (1 x 63.55) + (1 x 32.07) + (4 x 16.00) = 63.55 + 32.07 + 64.00 = 159.62 g/mol H2O: (2 x 1.01) + (1 x 16.00) = 2.02 + 16.00 = 18.02 g/mol

Step 2: Calculate molar mass of the entire compound

Now, let's find the molar mass of the entire compound CuSO4 · 5H2O using the molar masses calculated in step 1: Molar mass of CuSO4 · 5H2O = (1 x 159.62) + (5 x 18.02) = 159.62 + 90.10 = 249.72 g/mol

Step 3: Calculate the percentage of water in the compound CuSO4 · 5H2O

To find the percentage of water, we will divide the molar mass of the water portion by the total molar mass of the compound and multiply by 100: Percentage of water = (mass of water component / total molar mass of compound) × 100 Percentage of water = (90.10 g/mol / 249.72 g/mol) × 100 = 36.08% The percent of water in the compound CuSO4 · 5H2O is 36.08%.

Step 4: Calculate the mass percentage of the original sample lost when water is driven off as steam

When the water is driven off as steam, the blue solid loses its water component (5H2O). To find the mass percentage of the original sample lost, we will again divide the molar mass of the water portion by the total molar mass of the compound and multiply by 100: Mass percentage lost = (mass of water component / total molar mass of compound) × 100 Mass percentage lost = (90.10 g/mol / 249.72 g/mol) × 100 = 36.08% The mass percentage of the original sample of the blue solid lost as a result is 36.08%.

Key Concepts

Molar Mass Calculation

Understanding the molar mass of a compound is foundational in chemistry for stoichiometric calculations, where quantitative relationships in a chemical reaction are determined. The molar mass represents the mass of one mole (Avogadro's number, or approximately 6.022 x 10^23 particles) of a substance and is usually expressed in grams per mole (g/mol).

To calculate the molar mass of a compound, sum the molar masses of all the atoms that make up the compound based on the periodic table values. For example, in a molecule of water (H₂O), the molar mass is calculated by adding twice the molar mass of hydrogen to the molar mass of oxygen. Hence, H₂O has a molar mass of (2 x 1.01) + 16.00 = 18.02 g/mol. For copper sulfate pentahydrate (CuSO₄·5H₂O), the molar mass is the sum of the molar masses of one copper (Cu), one sulfur (S), four oxygen (O) atoms, and five water molecules.

Hydrate Compounds

Hydrate compounds, also known as hydrated crystals, are substances that contain water molecules within their crystal structure. The water present in hydrate compounds is not merely trapped physically but is chemically bonded to the salt and can be removed by heating. This process is known as dehydration, where the water is released, usually as steam. The hydrate is characterized by a specific number of water molecules per formula unit of the salt, indicated in the chemical formula by a dot followed by the appropriate number of water molecules, such as in copper sulfate pentahydrate (CuSO₄·5H₂O).

The formula tells us there are five water molecules for each unit of copper sulfate. These hydrates have specific properties and uses due to the presence of water molecules. In the field of chemistry, understanding the formula of hydrate compounds is vital for calculations involving the compound’s molar mass and percentage composition.

Copper Sulfate Pentahydrate

Copper sulfate pentahydrate (CuSO₄·5H₂O) is a commonly encountered hydrate compound. It appears as beautiful blue crystals and is widely used in agriculture as a fungicide, in public health for water purification, and in education for demonstrating properties of hydrates. Each formula unit of the substance consists of one CuSO₄ and five water molecules (H₂O), totaling five moles of water per mole of copper sulfate.

The importance of determining the percent composition of water in copper sulfate pentahydrate lies in understanding its empirical formula and working with reactions where water plays a role. When heated, copper sulfate pentahydrate loses water and turns into anhydrous copper sulfate, which has a white or gray color. This color change is an indication of the dehydration process and is utilized in experiments and practical applications. Knowledge of its molar mass and water composition is essential for chemists when calculating concentrations, reactant quantities, and in predicting the outcomes of chemical reactions.