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Ch.13 - Solutions & Their Properties
Chapter 13, Problem 78c

A 0.944 M solution of glucose, C6H12O6, in water has a density of 1.0624 g/mL at 20 °C. What is the concentration of this solution in the following units? (c) Molality

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Calculate the mass of 1 liter of the glucose solution using its density. Multiply the density of the solution (1.0624 g/mL) by the volume of the solution (1000 mL for 1 liter).
Determine the mass of glucose in 1 liter of solution. Use the molarity of the solution (0.944 M), which means 0.944 moles of glucose per liter. Multiply the number of moles by the molar mass of glucose (approximately 180.16 g/mol).
Find the mass of water in 1 liter of solution by subtracting the mass of glucose from the total mass of the solution.
Convert the mass of water from grams to kilograms for the calculation of molality.
Calculate the molality of the solution by dividing the number of moles of glucose by the mass of water in kilograms. Molality is expressed as moles of solute per kilogram of solvent.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molarity

Molarity (M) is a measure of concentration defined as the number of moles of solute per liter of solution. In this case, the glucose solution has a molarity of 0.944 M, indicating that there are 0.944 moles of glucose in every liter of the solution. Understanding molarity is essential for converting to other concentration units, such as molality.
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Molality

Molality (m) is defined as the number of moles of solute per kilogram of solvent. It differs from molarity as it focuses on the mass of the solvent rather than the total volume of the solution. To calculate molality, one must know the mass of the solvent, which can be derived from the solution's density and volume.
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Density

Density is the mass per unit volume of a substance, typically expressed in grams per milliliter (g/mL) or kilograms per liter (kg/L). In this problem, the density of the glucose solution is given as 1.0624 g/mL, which is crucial for determining the mass of the solvent when calculating molality. Density allows us to convert between volume and mass, facilitating the calculation of molality from the given molarity.
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Density Concepts