Question

What is the molar concentration of a saturated solution of calcium sulfate that contains \(0.209 \mathrm{~g}\) of solute in \(100.0 \mathrm{~mL}\) of solution?

Short answer

The molar concentration of the solution is 0.01535 mol/L.

Step-by-step solution

Identify solute's molar mass

Calcium sulfate ( ext{CaSO}_4) is composed of Calcium, Sulfur, and Oxygen. Calculate its molar mass by adding their atomic masses: \(1\times 40.08 + 1\times 32.07 + 4\times 16.00 = 136.14 \, \text{g/mol}\).

Calculate moles of solute

Convert the mass of calcium sulfate from grams to moles using its molar mass: \(\frac{0.209 \, \text{g}}{136.14 \, \text{g/mol}} = 0.001535 \, \text{mol}\).

Convert solution volume to liters

Convert the volume of the solution from milliliters to liters: \(100.0 \, \text{mL} = 0.1000 \, \text{L}\).

Calculate molarity

Molarity is moles of solute per liter of solution. Calculate the molarity: \(\frac{0.001535 \, \text{mol}}{0.1000 \, \text{L}} = 0.01535 \, \text{mol/L}\).

Key concepts

Calcium Sulfate

Calcium sulfate, with the chemical formula \( \text{CaSO}_4 \), is a chemical compound made up of one calcium (Ca) atom, one sulfur (S) atom, and four oxygen (O) atoms. It appears as a white, crystalline solid, and is naturally occurring in different mineral forms such as gypsum. Calcium sulfate is commonly used in laboratories and industries.

In the context of solutions, calcium sulfate is known for its relatively low solubility in water, meaning it doesn't dissolve very easily compared to other salts. When we talk about a saturated solution of calcium sulfate, we're referring to the maximum amount of this compound that can be dissolved in a given amount of water to form a solution. Beyond this point, adding more calcium sulfate will not dissolve and will instead remain as a solid in the mixture. Understanding the solubility of calcium sulfate helps us predict and calculate how much can dissolve in a specific volume of water. This property is crucial in chemistry when preparing solutions or when its calcium or sulfate ions are needed for reactions.

Molar Mass Calculation

The molar mass of a compound is an essential concept in chemistry, referring to the mass of one mole of a substance expressed in grams per mole (g/mol). To calculate the molar mass, you need to sum the atomic masses of all the atoms in a molecule of the compound.

Let's break down the calculation of calcium sulfate's molar mass:

• Calcium (Ca) has an atomic mass of approximately 40.08 g/mol.
• Sulfur (S) has an atomic mass of about 32.07 g/mol.
• Oxygen (O) has an atomic mass close to 16.00 g/mol, and since there are four oxygen atoms in calcium sulfate, we multiply this by four resulting in 64.00 g/mol.

By adding together these atomic masses, we get the total molar mass: \[ 40.08 + 32.07 + 64.00 = 136.14 \text{ g/mol} \]. This calculation is critical because it allows us to convert between mass and moles, facilitating the analysis and stoichiometry of chemical reactions and solutions.

Solution Chemistry

Solution chemistry involves the study of how substances dissolve in solvents to form homogenous mixtures. A fundamental aspect of solution chemistry is the concept of molarity, which is a way to express the concentration of a solute in a solution. Molarity is defined as the number of moles of solute per liter of solution, indicated in mol/L (M).

To calculate the molarity of our calcium sulfate solution:

• First, we find the moles of solute by using the formula: \[ \text{moles} = \frac{\text{mass of solute (g)}}{\text{molar mass (g/mol)}}\]. With our example: \( \frac{0.209 \text{ g}}{136.14 \text{ g/mol}} = 0.001535 \text{ mol} \).
• Next, we ensure our solution's volume is in liters. Here, 100.0 mL equals 0.1000 L.
• Finally, we calculate molarity: \[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution (L)}} = \frac{0.001535 \text{ mol}}{0.1000 \text{ L}} = 0.01535 \text{ mol/L} \].

Understanding these calculations helps students and scientists alike when working with reactions and preparing solutions of specific concentrations, which is a common requirement in both laboratory and industrial settings.