Problem 185 - Chemistry Matter and Change

Question

Gypsum is hydrated calcium sulfate. A 4.89-g sample of this hydrate was heated. After the water was removed, 3.87 g anhydrous calcium sulfate remained. Determine the formula for this hydrate and name the compound.

Step-by-Step Solution

Answer

The formula for the hydrate is CaSO4·2H2O, and the compound is named Calcium sulfate dihydrate.

Step 1: Calculate moles of anhydrous CaSO4

To find the moles of CaSO4, use the molar mass of CaSO4, which is 136.14 g/mol, and the mass of the anhydrous sample, which is 3.87 g. Moles of CaSO4 = mass of CaSO4 / molar mass of CaSO4 = \( \frac{3.87\,g}{136.14\,g/mol} \) = 0.0284 mol.

Step 2: Calculate the mass of water lost

Find the mass of water that was present in the hydrate by subtracting the mass of anhydrous CaSO4 from the mass of the sample: Mass of water = mass of hydrate - mass of anhydrous CaSO4 = 4.89 g - 3.87 g = 1.02 g.

Step 3: Calculate moles of water

To find the moles of water, use the molar mass of water, which is 18.015 g/mol, and the mass of the water that was lost: Moles of water = mass of water / molar mass of water = \( \frac{1.02\,g}{18.015\,g/mol} \) = 0.0567 mol.

Step 4: Calculate the mole ratio of water to CaSO4

Divide the moles of water by the moles of CaSO4 to determine their mole ratio: Mole ratio = \( \frac{moles\,of\,water}{moles\,of\,CaSO4} \) = \( \frac{0.0567\,mol}{0.0284\,mol} \) ≈ 2. The mole ratio is approximately 2, which means that there are 2 moles of water for every mole of CaSO4 in the hydrate.

Step 5: Determine the formula of the hydrate and name the compound

Since the mole ratio of water to CaSO4 is approximately 2, the formula of the hydrate is CaSO4·2H2O. The name of the compound is Calcium sulfate dihydrate.

Key Concepts

Hydrate

In chemistry, a hydrate is a compound that includes water molecules within its structure. These water molecules can be part of the crystal lattice, forming an important part of the compound's molecular arrangement. Hydrates are significant because the water can influence both the mass and the chemical behavior of the compound.
Upon heating, hydrates lose their water content, turning into an anhydrous form. This was observed in the given problem where the hydrate gypsum (calcium sulfate dihydrate) loses water upon heating.

• Hydrate Example: Gypsum, or calcium sulfate dihydrate, with the formula CaSO4·2H2O.
• Anhydrous Form: Calcium sulfate (CaSO4) after losing water.

The structure usually determines the ratio of water molecules to the rest of the compound, which can be determined through experimentation such as heating and weighing.

Moles

A mole in chemistry is an essential unit of measurement that links the microscopic world of atoms and molecules to the macroscopic quantities we can measure. It is the amount of substance that contains as many particles, such as atoms, molecules, ions, or electrons, as there are atoms in 12 grams of carbon-12. This amounts to Avogadro's number, approximately \(6.022 \times 10^{23}\) entities.

• Moles allow chemists to convert between the mass of a substance and the number of atoms or molecules it contains.
• In the exercise, the moles of anhydrous calcium sulfate and water were calculated to determine the hydrate's ratio.

Reasoning in terms of moles allows scientists to relate complex chemical reactions on paper to actual lab experimentation and processes.

Molar Mass

Molar mass is the mass of one mole of a given substance. It is usually expressed in grams per mole (g/mol) and is crucial in many chemical calculations, including converting between mass and moles.

• To find the moles of a substance, divide the mass of the sample by the molar mass.
• For instance, in the solution, the molar mass of calcium sulfate (CaSO4) used was 136.14 g/mol.

The molar mass concept ensures that chemists accurately measure and calculate the properties of substances needed to proceed with reactions and to interpret experimental data. In solving chemical formulas and making predictions, knowing the molar mass is essential.

Mole Ratio

In chemical reactions, the mole ratio indicates the proportions in which substances react or are produced. It is derived from the coefficients of each substance in the balanced chemical equation and helps predict the amount of reactants needed or products formed.

• Mole ratios are a fundamental aspect of reaction stoichiometry, providing the basis for reactions and formula calculations.
• In the situation at hand, the mole ratio of water to calcium sulfate was calculated as 2:1. This revealed there are 2 moles of water for every mole of calcium sulfate in the hydrate.

Understanding mole ratios is essential to determining the relationship and quantities within compounds, as demonstrated in the establishment of the chemical formula for calcium sulfate dihydrate (CaSO4·2H2O).