An aqueous solution contains 25% HCl by mass. Calculate the molality and mole fraction of the solution.

Verified step by step guidance

1. Step 1: Define the given information. You have a solution that is 25% HCl by mass, which means 25 grams of HCl in every 100 grams of solution.
2. Step 2: Calculate the mass of the solvent (water) in the solution. Since the solution is 100 grams and contains 25 grams of HCl, the mass of water is 100 grams - 25 grams = 75 grams.
3. Step 3: Convert the mass of HCl to moles. Use the molar mass of HCl (approximately 36.46 g/mol) to find the number of moles: \( \text{moles of HCl} = \frac{25 \text{ g}}{36.46 \text{ g/mol}} \).
4. Step 4: Calculate the molality of the solution. Molality is defined as moles of solute per kilogram of solvent. Use the formula: \( \text{molality} = \frac{\text{moles of HCl}}{\text{mass of water in kg}} \).
5. Step 5: Calculate the mole fraction of HCl. First, find the moles of water using its molar mass (approximately 18.02 g/mol). Then, use the formula for mole fraction: \( \text{mole fraction of HCl} = \frac{\text{moles of HCl}}{\text{moles of HCl} + \text{moles of water}} \).

Key Concepts

Molality

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It is particularly useful in situations where temperature changes may affect the volume of the solution, as it is based on mass rather than volume. To calculate molality, one must first determine the moles of solute and the mass of the solvent in kilograms.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles of all components in the mixture. It is a dimensionless quantity and is useful for understanding the composition of solutions. To find the mole fraction, one must calculate the moles of both the solute and the solvent and then use these values in the mole fraction formula.

Mass Percent

Mass percent, or weight percent, is a way to express the concentration of a component in a mixture, calculated as the mass of the solute divided by the total mass of the solution, multiplied by 100. In this case, a 25% HCl solution means that there are 25 grams of HCl in every 100 grams of solution. Understanding mass percent is crucial for converting to other concentration units like molality and mole fraction.