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Ch.13 - Properties of Solutions
Chapter 13, Problem 49b

The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH3OH in 98.7 mL of CH3CN. (b) What is the molality of the solution?

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First, we need to calculate the mass of each component. The mass of a substance can be calculated by multiplying its volume by its density. So, calculate the mass of CH<sub>3</sub>CN and CH<sub>3</sub>OH using their respective volumes and densities.
Next, convert the mass of CH<sub>3</sub>OH to moles. The molar mass of CH<sub>3</sub>OH is approximately 32.04 g/mol. Divide the mass of CH<sub>3</sub>OH by its molar mass to get the number of moles.
Molality is defined as the number of moles of solute (in this case, CH<sub>3</sub>OH) per kilogram of solvent (in this case, CH<sub>3</sub>CN). Convert the mass of CH<sub>3</sub>CN from grams to kilograms by dividing by 1000.
Finally, calculate the molality by dividing the number of moles of CH<sub>3</sub>OH by the mass of CH<sub>3</sub>CN in kilograms. This will give you the molality of the solution in mol/kg.
Remember that molality is a measure of the concentration of a solution. It tells us how many moles of solute are present in a certain amount of solvent. In this case, it tells us how many moles of methanol are present in a certain amount of acetonitrile.

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Key Concepts

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

Density

Density is defined as mass per unit volume and is typically expressed in grams per milliliter (g/mL) for liquids. It is a crucial property that helps determine how much mass of a substance is contained in a given volume. In this question, the densities of acetonitrile and methanol are provided, which will be used to calculate the mass of each component in the solution.
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Molality

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

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is essential for converting between grams and moles when performing calculations in chemistry. In this problem, the molar mass of methanol will be needed to convert the mass of methanol into moles, which is necessary for calculating the molality of the solution.
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Related Practice
Textbook Question

Ascorbic acid (vitamin C, C6H8O6) is a water-soluble vitamin. A solution containing 80.5 g of ascorbic acid dissolved in 210 g of water has a density of 1.22 g/mL at 55 °C. Calculate (a) the mass percentage,

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Textbook Question

Ascorbic acid (vitamin C, C6H8O6) is a water-soluble vitamin. A solution containing 80.5 g of ascorbic acid dissolved in 210 g of water has a density of 1.22 g/mL at 55 °C. Calculate (c) the molality,

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Textbook Question

The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH3OH in 98.7 mL of CH3CN. (a) What is the mole fraction of methanol in the solution?

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Textbook Question

The density of acetonitrile (CH3CN) is 0.786 g/mL and the density of methanol (CH3OH) is 0.791 g/mL. A solution is made by dissolving 22.5 mL of CH3OH in 98.7 mL of CH3CN. (c) Assuming that the volumes are additive, what is the molarity of CH3OH in the solution?

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Textbook Question

The density of toluene (C7H8) is 0.867 g/mL, and the density of thiophene (C4H4S) is 1.065 g/mL. A solution is made by dissolving 8.10 g of thiophene in 250.0 mL of toluene. (a) Calculate the mole fraction of thiophene in the solution.

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Textbook Question

The density of toluene (C7H8) is 0.867 g/mL, and the density of thiophene (C4H4S) is 1.065 g/mL. A solution is made by dissolving 8.10 g of thiophene in 250.0 mL of toluene. (b) Calculate the molality of thiophene in the solution.

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