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Ch.14 - Solutions
All textbooksTro 5th EditionCh.14 - SolutionsProblem 120
Chapter 14, Problem 120

Find the mass of urea (CH4N2O) needed to prepare 50.0 g of a solution in water in which the mole fraction of urea is 0.0770.

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Identify the given information: the mole fraction of urea (CH4N2O) is 0.0770, and the total mass of the solution is 50.0 g.
Recall that the mole fraction of a component in a solution is the ratio of the moles of that component to the total moles of all components in the solution. Therefore, \( X_{\text{urea}} = \frac{n_{\text{urea}}}{n_{\text{urea}} + n_{\text{water}}} = 0.0770 \).
Express the moles of urea \( n_{\text{urea}} \) in terms of its mass \( m_{\text{urea}} \) and molar mass \( M_{\text{urea}} \): \( n_{\text{urea}} = \frac{m_{\text{urea}}}{M_{\text{urea}}} \). The molar mass of urea (CH4N2O) is approximately 60.06 g/mol.
Express the moles of water \( n_{\text{water}} \) in terms of its mass \( m_{\text{water}} \) and molar mass \( M_{\text{water}} \): \( n_{\text{water}} = \frac{m_{\text{water}}}{M_{\text{water}}} \). The molar mass of water (H2O) is approximately 18.02 g/mol.
Set up the equation for the mole fraction: \( 0.0770 = \frac{\frac{m_{\text{urea}}}{60.06}}{\frac{m_{\text{urea}}}{60.06} + \frac{50.0 - m_{\text{urea}}}{18.02}} \). Solve this equation for \( m_{\text{urea}} \) to find the mass of urea needed.

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Key Concepts

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

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the mixture. In this case, the mole fraction of urea indicates how much of the total solution is made up of urea, which is crucial for calculating the mass needed.
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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). For urea (CH4N2O), the molar mass can be calculated by summing the atomic masses of its constituent elements: carbon, hydrogen, nitrogen, and oxygen. Knowing the molar mass is essential for converting between moles and grams when determining how much urea is required for the solution.
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Mass Percent and Solution Preparation

Mass percent is the mass of a solute divided by the total mass of the solution, multiplied by 100. In this context, understanding how to relate the mass of urea to the total mass of the solution (50.0 g) is vital for preparing the desired solution. This involves using the mole fraction to find the number of moles of urea and then converting that to mass using the molar mass.
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Related Practice
Textbook Question

The vapor pressure of carbon tetrachloride, CCl4, is 0.354 atm, and the vapor pressure of chloroform, CHCl3, is 0.526 atm at 316 K. A solution is prepared from equal masses of these two compounds at this temperature. Calculate the mole fraction of the chloroform in the vapor above the solution. If the vapor above the original solution is condensed and isolated into a separate flask, what will the vapor pressure of chloroform be above this new solution?

Textbook Question

A solution contains 10.05 g of unknown compound dissolved in 50.0 mL of water. (Assume a density of 1.00 g/mL for water.) The freezing point of the solution is -3.16 °C. The mass percent composition of the compound is 60.97% C, 11.94% H, and the rest is O. What is the molecular formula of the compound?

Textbook Question

The osmotic pressure of a solution containing 2.10 g of an unknown compound dissolved in 175.0 mL of solution at 25 °C is 1.93 atm. The combustion of 24.02 g of the unknown compound produced 28.16 g CO2 and 8.64 g H2O. What is the molecular formula of the compound (which contains only carbon, hydrogen, and oxygen)?

Textbook Question

A 100.0-mL aqueous sodium chloride solution is 13.5% NaCl by mass and has a density of 1.12 g/mL. What would you add (solute or solvent) and what mass of it to make the boiling point of the solution 104.4 °C? (Use i = 1.8 for NaCl.)