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Ch.13 - Solutions
Tro - Chemistry: A Molecular Approach 4th Edition
Tro4th EditionChemistry: A Molecular ApproachISBN: 9780134112831Not the one you use?Change textbook
All textbooksTro 4th EditionCh.13 - SolutionsProblem 122
Chapter 13, Problem 122

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)?

Verified step by step guidance
1
Determine the molar mass of the unknown compound using the osmotic pressure formula: \( \Pi = \frac{n}{V}RT \), where \( \Pi \) is the osmotic pressure, \( n \) is the number of moles of solute, \( V \) is the volume of the solution in liters, \( R \) is the gas constant (0.0821 L atm K^{-1} mol^{-1}), and \( T \) is the temperature in Kelvin.
Convert the mass of the unknown compound (2.10 g) and the volume of the solution (175.0 mL) to appropriate units and plug them into the osmotic pressure equation to solve for the number of moles (\( n \)).
Calculate the molar mass of the compound by dividing the mass of the compound by the number of moles calculated in the previous step.
Analyze the combustion data to find the empirical formula. Convert the mass of CO2 and H2O produced into moles, and use these values to determine the moles of carbon and hydrogen in the original compound.
Use the molar mass found from the osmotic pressure data and the empirical formula from the combustion analysis to determine the molecular formula of the compound. Adjust the subscripts in the empirical formula to match the molar mass.

Key Concepts

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

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the molarity of the solute and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity, R is the ideal gas constant, and T is the temperature in Kelvin. Understanding this concept is crucial for determining the molar mass of the unknown compound from the given osmotic pressure.
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Combustion Analysis

Combustion analysis is a method used to determine the elemental composition of organic compounds by burning them in excess oxygen and measuring the amounts of CO2 and H2O produced. The mass of CO2 and H2O generated allows for the calculation of the moles of carbon and hydrogen in the compound. This information is essential for deducing the empirical formula of the unknown compound, which can then be used to find its molecular formula.
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Empirical and Molecular Formulas

The empirical formula represents the simplest whole-number ratio of elements in a compound, while the molecular formula indicates the actual number of atoms of each element in a molecule. To find the molecular formula, one must first determine the empirical formula and then use the molar mass obtained from osmotic pressure calculations to find the ratio between the empirical and molecular formulas. This distinction is vital for accurately identifying the unknown compound's composition.
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Related Practice
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.)

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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?

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