Question

A solution is prepared by dissolving 52.3 g cesium chloride in 60.0 g water. The volume of the solution is 63.3 \(\mathrm{mL}\) . Calculate the mass percent, molarity, molality, and mole fraction of the CsCl solution.

Short answer

The mass percent of cesium chloride (CsCl) in the solution is 46.5%. The molarity of the solution is 12.42 M, and the molality is 13.16 m. The mole fraction of CsCl in the solution is 0.0501.

Step-by-step solution

Calculate the moles of CsCl

To calculate the moles of CsCl, we will use its molar mass: CsCl = 132.9 g/mol. moles of CsCl = (mass of CsCl) / (molar mass of CsCl) = \(\frac{52.3 \ \mathrm{g}}{132.9 \ \mathrm{g/mol}}\) Calculate the moles of CsCl using the equation above.

Calculate the moles of water

To calculate the moles of water, we use its molar mass: H2O = 18.015 g/mol. moles of H2O = (mass of H2O) / (molar mass of H2O) = \(\frac{60.0 \ \mathrm{g}}{18.015 \ \mathrm{g/mol}}\) Calculate the moles of water using the equation above.

Calculate mass percent

Mass percent = \(\frac{\text{mass of solute}}{\text{mass of solution}} \times 100\) Mass of the solution = mass of CsCl + mass of water = 52.3 g + 60.0 g Calculate the mass percent of CsCl using the mass of solute and solution.

Calculate molarity

Molarity = \(\frac{\text{moles of solute}}{\text{volume of the solution in liters}}\) First, convert the volume of the solution from mL to liters: 63.3 mL × \(\frac{1 \ \mathrm{L}}{1000 \ \mathrm{mL}}\) = 0.0633 L Next, calculate the molarity of the solution using the moles of CsCl and volume of the solution in liters.

Calculate molality

Molality = \(\frac{\text{moles of solute}}{\text{mass of solvent in kg}}\) First, convert the mass of water (the solvent) from grams to kilograms: 60 g × \(\frac{1 \ \mathrm{kg}}{1000 \ \mathrm{g}}\) Next, calculate the molality of the solution using the moles of CsCl and the mass of water (solvent) in kilograms.

Calculate mole fraction

Mole fraction = \(\frac{\text{moles of solute}}{\text{total moles in the solution}}\) Total moles = moles of CsCl + moles of H2O Calculate the mole fraction of CsCl using the moles of CsCl and total moles in the solution.

Key concepts

Mass Percent

Mass percent tells us how much of a solute is present in a solution in comparison to the total mass of the solution. It is expressed as a percentage and gives us a clear idea of the concentration by mass. To find the mass percent, use the formula:

• Mass percent = \( \frac{\text{mass of solute}}{\text{mass of solution}} \times 100 \)

In our example, cesium chloride is the solute, and water is the solvent. By combining the mass of cesium chloride (52.3 g) and water (60.0 g) we find the mass of the solution. Plug these values into the formula above to determine the mass percent of cesium chloride in the solution. The mass percent indicates how concentrated the solution is, by showing the portion of cesium chloride relative to the total mass.

Molarity

Molarity measures the concentration of a solute in a solution relative to the volume. Specifically, it’s the number of moles of solute per liter of solution. Molarity is important when mixing chemicals because it tells you the exact concentration, allowing for consistency in experiments. To calculate molarity, apply the formula:

• Molarity = \(\frac{\text{moles of solute}}{\text{volume of solution in liters}} \)

In the solution exercise, first convert the volume from milliliters to liters. With 63.3 mL given, this becomes 0.0633 L. Using the previously calculated moles of cesium chloride, use this formula to calculate the molarity. Molarity helps us understand how concentrated the cesium chloride is in every liter of the solution.

Molality

Molality is another way to express concentration, based instead on the mass of the solvent. Unlike molarity, which can change with temperature and pressure due to volume changes, molality is temperature-independent as it is based on mass. The formula for molality is:

• Molality = \(\frac{\text{moles of solute}}{\text{mass of solvent in kg}} \)

In the problem statement, convert the mass of the water from grams to kilograms. With 60 g of water present, that converts to 0.060 kg. With the moles of cesium chloride already known, calculate the molality using the formula above. Molality provides another measure of concentration, particularly useful in scenarios involving temperature variations.

Mole Fraction

Mole fraction is a dimensionless number that compares the number of moles of one component to the total number of moles in the solution. It provides insight into the composition of a solution without relying on mass or volume. To find the mole fraction, use the following formula:

• Mole fraction = \(\frac{\text{moles of solute}}{\text{total moles in the solution}} \)

First, find the number of moles for each component—cesium chloride and water. Next, add them together to obtain the total moles. Use the moles of cesium chloride and the total moles to solve for the mole fraction. This value tells us how dominant cesium chloride is relative to water in the solution. Mole fraction is especially useful in thermodynamic calculations and applications involving phase changes.