An aqueous NaCl solution is made using 112 g of NaCl diluted to a total solution volume of 1.00 L. Calculate the molality of the solution. (Assume a density of 1.08 g/mL for the solution.)

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Calculate the moles of NaCl using its molar mass: \( \text{moles of NaCl} = \frac{\text{mass of NaCl}}{\text{molar mass of NaCl}} \).

Determine the mass of the solution using its volume and density: \( \text{mass of solution} = \text{volume of solution} \times \text{density of solution} \).

Calculate the mass of the solvent (water) by subtracting the mass of NaCl from the mass of the solution: \( \text{mass of water} = \text{mass of solution} - \text{mass of NaCl} \).

Convert the mass of the solvent from grams to kilograms: \( \text{mass of water in kg} = \frac{\text{mass of water in g}}{1000} \).

Calculate the molality of the solution using the formula: \( \text{molality} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \).

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주요 개념

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Molarity and Molality

Molarity (M) is defined as the number of moles of solute per liter of solution, while molality (m) is the number of moles of solute per kilogram of solvent. Understanding the difference is crucial for calculations involving concentrations, especially when dealing with solutions where temperature and volume may affect molarity but not molality.

Calculating Moles from Mass

To find the number of moles of a substance, you can use the formula: moles = mass (g) / molar mass (g/mol). For NaCl, the molar mass is approximately 58.44 g/mol. This calculation is essential for determining the concentration of the solute in the solution.

Density and Volume Relationships

Density is defined as mass per unit volume (g/mL or g/cm³). In this problem, the density of the solution is given as 1.08 g/mL, which allows us to convert the total volume of the solution into mass. This conversion is necessary to calculate the mass of the solvent (water) for determining molality.