Ch.13 - Solutions

Problem 67

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Chapter 13, Problem 67

An aqueous solution contains 36% HCl by mass. Calculate the molality and mole fraction of the solution.

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Identify the given information: 36% HCl by mass means 36 grams of HCl in 100 grams of solution.

Calculate the mass of the solvent (water) by subtracting the mass of HCl from the total mass of the solution: 100 g - 36 g = 64 g of water.

Convert the mass of HCl to moles using its molar mass (Molar mass of HCl = 1.01 g/mol for H + 35.45 g/mol for Cl = 36.46 g/mol).

Convert the mass of water to kilograms to use in the molality formula (1 kg = 1000 g).

Calculate the molality using the formula: molality (m) = moles of solute / kilograms of solvent, and calculate the mole fraction using the formula: mole fraction of HCl = moles of HCl / (moles of HCl + moles of water).

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Key Concepts

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

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 volume, 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 to express 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.

Mass Percent

Mass percent, or weight percent, is a way to express the concentration of a solute in a solution, calculated as the mass of the solute divided by the total mass of the solution, multiplied by 100. In this case, a 36% mass percent of HCl means that there are 36 grams of HCl in every 100 grams of solution. This information is crucial for converting mass to moles and subsequently calculating molality and mole fraction.

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Textbook Question

A solution is prepared by dissolving 20.2 mL of methanol (CH₃OH) in 100.0 mL of water at 25 °C. The final volume of the solution is 118 mL. The densities of methanol and water at this temperature are 0.782 g/mL and 1.00 g/mL, respectively. For this solution, calculate the concentration in each unit. e. mole percent

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Textbook Question

Household hydrogen peroxide is an aqueous solution containing 3.0% hydrogen peroxide by mass. What is the molarity of this solution? (Assume a density of 1.01 g/mL.)

One brand of laundry bleach is an aqueous solution containing 4.55% sodium hypochlorite (NaOCl) by mass. What is the molarity of this solution? (Assume a density of 1.02 g/mL.)

An aqueous solution contains 5.0% NaCl by mass. How do you calculate the molality and mole fraction of the solution?

Open Question

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Which solution has the highest vapor pressure? a. 20.0 g of glucose (C₆H₁₂O₆) in 100.0 mL of water b. 20.0 g of sucrose (C₁₂H₂₂O₁₁) in 100.0 mL of water c. 10.0 g of potassium acetate KC₂H₃O₂ in 100.0 mL of water

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