Question

A solution is prepared by dissolving 52.3 g cesium chloride in \(60.0 \mathrm{g}\) 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 the cesium chloride solution is 46.56%, the molarity is 4.906 mol/L, the molality is 5.173 mol/kg, and the mole fraction of CsCl is 0.0852.

Step-by-step solution

Find the mass of the solution

To find the mass of the solution, add the mass of cesium chloride and mass of water. Mass of cesium chloride (CsCl) = 52.3 g Mass of water (H2O) = 60.0 g Mass of solution = mass of CsCl + mass of H2O = 52.3 g + 60.0 g = 112.3 g

Calculate the mass percent

Mass percent is calculated by dividing the mass of the solute (CsCl) by the mass of the solution and multiplying by 100 to get the percentage. Mass percent = (mass of CsCl / mass of solution) * 100 Mass percent = (52.3 g / 112.3 g) * 100 = 46.56 %

Calculate the molarity

First, find the moles of CsCl using its molar mass (Cs = 132.9 g/mol, Cl = 35.45 g/mol). Then, convert the volume of the solution into liters. Finally, we can calculate the molarity by dividing the moles of CsCl by the volume of the solution in liters. Molar mass of CsCl = 132.9 + 35.45 = 168.35 g/mol Moles of CsCl = 52.3 g / 168.35 g/mol ≈ 0.3104 mol Volume of solution = 63.3 mL = 0.0633 L Molarity = moles of CsCl / volume of solution (L) Molarity = 0.3104 mol / 0.0633 L ≈ 4.906 mol/L

Calculate the molality

Molality is the ratio of moles of solute (CsCl) to the mass of solvent (water) in kilograms. Mass of water in kg = 60 g / 1000 = 0.06 kg Molality = moles of CsCl / mass of solvent (kg) Molality = 0.3104 mol / 0.06 kg ≈ 5.173 mol/kg

Calculate the mole fraction

First, find the moles of water using its molar mass (18.015 g/mol). Then, calculate the total moles in the solution. Finally, divide the moles of CsCl by the total moles in the solution to find the mole fraction. Molar mass of water (H2O) = 18.015 g/mol Moles of water = 60 g / 18.015 g/mol ≈ 3.331 mol Total moles = moles of CsCl + moles of water = 0.3104 mol + 3.331 mol ≈ 3.6414 mol Mole fraction of CsCl = moles of CsCl / total moles = 0.3104 mol / 3.6414 mol ≈ 0.0852 Summary: Mass percent of CsCl = 46.56 % Molarity of CsCl solution = 4.906 mol/L Molality of CsCl solution = 5.173 mol/kg Mole fraction of CsCl = 0.0852

Key concepts

Understanding Molarity

Molarity is a way to express the concentration of a solution. It tells us how many moles of solute are present in one liter of solution. To calculate molarity, you first need the amount of solute in moles. You also need the volume of the solution in liters.
For example, if you have 0.3104 moles of cesium chloride (CsCl) dissolved in 0.0633 liters of solution, the molarity is determined by
the formula:
\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]Plugging in the numbers, you get a molarity of approximately 4.906 mol/L.

• Molarity provides a clear view of how concentrated a solution is.
• It is temperature dependent because it relies on volume, which can change with temperature.

Molarity is a standardized way to convey concentration in a variety of chemical contexts.

Understanding Molality

Molality is another measure of concentration. Unlike molarity, which depends on the total volume of the solution, molality is based on the mass of the solvent.
The formula for molality is:\[ \text{Molality} = \frac{\text{moles of solute}}{\text{mass of solvent in kilograms}} \]
For the CsCl solution, since there are 0.3104 moles of CsCl, and the mass of water (solvent) is 0.06 kg, the molality is approximately 5.173 mol/kg.

• Unlike molarity, molality is independent of temperature.
• This makes it a reliable concentration measure when working with fluctuating temperatures.

Understanding the difference between molality and molarity is crucial for precise concentration calculations.

Comprehending Mass Percent

Mass percent, or mass percentage, is a simple way to describe the concentration of a solute in a solution. It tells us what portion of the total mass of the solution is made up by the solute.

• To find it, use the formula:
  \[ \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \]
• In our example, the mass percent of CsCl is calculated as:
  \[ \left( \frac{52.3 \text{ g}}{112.3 \text{ g}} \right) \times 100 \approx 46.56\% \]
• Mass percent is useful for understanding the composition of mixtures without complex calculations.
• It is easy to convey and interpret, particularly when only mass measurements are available.

Mass percent is often used in industrial and laboratory settings for quick concentration assessments.

Exploring Mole Fraction

Mole fraction is a unique way to describe concentration by considering the ratio of moles of solute to the total moles in the solution. It is dimensionless, meaning it has no units, and it always results in a number between 0 and 1.

• To calculate, use:
  \[ \text{Mole fraction} = \frac{\text{moles of solute}}{\text{total moles in solution}} \]
• In our exercise, we determined the mole fraction of CsCl to be approximately 0.0852.
• The mole fraction is crucial in scenarios such as chemical equilibria and colligative properties.
• This approach to concentration can often be clearer when dealing with gases and mixtures in ideal solutions.

Understanding mole fraction is essential for various theoretical and practical chemistry applications.