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 CaSO\(_4\)·2H\(_2\)O, also known as calcium sulfate dihydrate.

Step 1: Identify the Composition of the Hydrate

The problem states that gypsum is hydrated calcium sulfate, meaning it has water molecules attached to it. The goal is to find out how many water molecules are associated with each formula unit of calcium sulfate in the hydrate.

Step 2: Determine the Mass of Water Removed

Calculate the mass of water by subtracting the mass of the anhydrous calcium sulfate (3.87 g) from the total mass of the hydrate (4.89 g):\[\text{mass of water} = 4.89\, g - 3.87\, g = 1.02\, g\]

Step 3: Calculate Moles of Anhydrous Calcium Sulfate

Find the molar mass of anhydrous calcium sulfate (CaSO\(_4\)) which is 40.08 (Ca) + 32.07 (S) + (4*16.00) (O) = 136.14 g/mol. Calculate the moles:\[\text{moles of } \text{CaSO}_4 = \frac{3.87\, g}{136.14\, g/mol} \approx 0.0284\, mol\]

Step 4: Calculate Moles of Water

Find the molar mass of water (H\(_2\)O), which is 18.02 g/mol.Calculate the moles:\[\text{moles of } \text{H}_2\text{O} = \frac{1.02\, g}{18.02\, g/mol} \approx 0.0566\, mol\]

Step 5: Determine the Mole Ratio

Find the mole ratio between water and calcium sulfate:\[\text{mol ratio} = \frac{0.0566\, mol\, \text{H}_2\text{O}}{0.0284\, mol\, \text{CaSO}_4} = 2\]This suggests that there are approximately 2 moles of water for every mole of anhydrous calcium sulfate.

Step 6: Determine the Formula of the Hydrate

Given the 1:2 molar ratio, the formula for the hydrate can be written as CaSO\(_4\)·2H\(_2\)O, which means this is calcium sulfate dihydrate.

Key Concepts

Mole Calculations

Understanding mole calculations is crucial in chemistry, especially when dealing with chemical compounds. The mole is a unit used to measure the amount of a substance in terms of the number of atoms, molecules, or particles it contains. Think of a mole like a scientist's "dozen". Instead of 12, a mole equals Avogadro's number, which is approximately \(6.022 \times 10^{23}\) particles. This allows chemists to work with the macroscopic scale of matter in laboratories.

• To calculate the number of moles, use the formula: \(\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\).

In the context of the original exercise, this calculation is applied by measuring the mass of each component and then using the molar masses of the compounds involved. For instance, for calcium sulfate and water, the moles were calculated to determine their respective amounts present in the compound. Keeping track of these moles allows one to determine the proportion of each component in a compound.

Formula Determination

Determining the chemical formula of a compound involves understanding the proportions of each type of atom present in the compound. Once you know the quantities of each element in moles, you can establish a ratio, which helps you determine the compound's empirical formula.

• The empirical formula represents the simplest whole-number ratio of atoms in a compound.

In the exercise, after finding the moles of anhydrous calcium sulfate and water, these values were used to create a mole ratio. The mole ratio \(\frac{0.0566\, \text{mol}\, \text{H}_2\text{O}}{0.0284\, \text{mol}\, \text{CaSO}_4} = 2\) was determined, meaning two moles of water per mole of anhydrous calcium sulfate. This leads to the formula CaSO\(_4\)·2H\(_2\)O, representing calcium sulfate dihydrate. Such derivations are critical for understanding the composition and properties of chemical compounds.

Gypsum

Gypsum is a naturally occurring mineral, chiefly composed of calcium sulfate dihydrate (CaSO\(_4\)·2H\(_2\)O). It is a soft sulfate mineral widely used in construction and agriculture. In construction, it is a key component in plaster, drywall, and even in cement.

• Gypsum is also known for its role in the creation of sculptures and decorative elements due to its workability.

It can also be used as a soil conditioner in agriculture to improve soil's drainage and fertility. The formula CaSO\(_4\)·2H\(_2\)O signifies that gypsum includes two water molecules for each molecule of calcium sulfate. This hydration is what gives gypsum its characteristic properties, such as its ability to be molded and shaped when mixed with water.

Anhydrous and Hydrated Compounds

Understanding the difference between anhydrous and hydrated compounds is important in chemistry. Anhydrous compounds are those which contain no water molecules, while hydrated compounds include water molecules within their structure.

• Hydrated compounds are often formed when water molecules integrate into their crystal structure, which is common in many minerals.
• When heated, hydrous compounds can lose their water content, becoming anhydrous.

In the case of gypsum from the exercise, before heating, it was a hydrated compound, with the formula CaSO\(_4\)·2H\(_2\)O. After heating and losing water, it turns into anhydrous calcium sulfate, represented as CaSO\(_4\). This transition is crucial in many industrial applications where the removal of water is necessary to alter the compound for specific uses.