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Ch.13 - Solutions & Their Properties
All textbooksMcMurry 8th EditionCh.13 - Solutions & Their PropertiesProblem 146
Chapter 13, Problem 146

The steroid hormone estradiol contains only C, H, and O; combustion analysis of a 3.47 mg sample yields 10.10 mg CO2 and 2.76 mg H2O. When dissolving 7.55 mg of estradiol in 0.500 g of camphor, the melting point of camphor is depressed by 2.10 °C. What is the molecular weight of estradiol, and what is a probable formula? [For camphor, Kf = 37.7 °C kg/mol.]

Verified step by step guidance
1
Step 1: Determine the moles of carbon and hydrogen in the sample. Use the mass of CO2 to find the moles of carbon: \( \text{moles of C} = \frac{10.10 \text{ mg CO2}}{44.01 \text{ g/mol}} \times \frac{1 \text{ mol C}}{1 \text{ mol CO2}} \). Use the mass of H2O to find the moles of hydrogen: \( \text{moles of H} = \frac{2.76 \text{ mg H2O}}{18.02 \text{ g/mol}} \times \frac{2 \text{ mol H}}{1 \text{ mol H2O}} \).
Step 2: Calculate the mass of carbon and hydrogen in the sample. Convert moles of carbon to mass: \( \text{mass of C} = \text{moles of C} \times 12.01 \text{ g/mol} \). Convert moles of hydrogen to mass: \( \text{mass of H} = \text{moles of H} \times 1.008 \text{ g/mol} \).
Step 3: Determine the mass of oxygen in the sample. Subtract the mass of carbon and hydrogen from the total mass of the sample: \( \text{mass of O} = 3.47 \text{ mg} - \text{mass of C} - \text{mass of H} \).
Step 4: Calculate the moles of oxygen. Convert the mass of oxygen to moles: \( \text{moles of O} = \frac{\text{mass of O}}{16.00 \text{ g/mol}} \).
Step 5: Use the freezing point depression to find the molar mass of estradiol. Use the formula \( \Delta T_f = K_f \times m \), where \( m \) is the molality. Rearrange to find molality: \( m = \frac{\Delta T_f}{K_f} \). Then, use \( m = \frac{\text{moles of solute}}{\text{kg of solvent}} \) to find moles of estradiol, and calculate molar mass: \( \text{molar mass} = \frac{\text{mass of estradiol}}{\text{moles of estradiol}} \).

Key Concepts

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

Combustion Analysis

Combustion analysis is a method used to determine the elemental composition of organic compounds. In this process, a sample is burned in excess oxygen, and the resulting products, typically CO2 and H2O, are measured. The masses of these products allow for the calculation of the amounts of carbon, hydrogen, and oxygen in the original sample, which is essential for determining the empirical formula of the compound.
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Freezing Point Depression

Freezing point depression is a colligative property that describes the lowering of a solvent's freezing point when a solute is added. The extent of this depression is directly proportional to the molality of the solute and is quantified using the formula ΔTf = Kf * m, where Kf is the freezing point depression constant of the solvent. This concept is crucial for calculating the molar mass of the solute, in this case, estradiol, based on the observed change in freezing point.
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Molecular Weight and Empirical Formula

Molecular weight refers to the mass of a molecule calculated by summing the atomic weights of its constituent atoms. The empirical formula represents the simplest whole-number ratio of the elements in a compound. By determining the molecular weight from experimental data and the empirical formula from combustion analysis, one can deduce the molecular formula, which provides insight into the actual number of atoms of each element in a molecule of estradiol.
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Related Practice
Textbook Question
Desert countries like Saudi Arabia have built reverse osmo-sis plants to produce freshwater from seawater. Assume that seawater has the composition 0.470 M NaCl and 0.068 M MgCl2 and that both compounds are completelydissociated.(b) If the reverse osmosis equipment can exert a maximum pressure of 100.0 atm at 25.0 °C, what is the maximum volume of freshwater that can be obtained from 1.00 L of seawater?
Textbook Question
Elemental analysis of b@carotene, a dietary source of vitamin A, shows that it contains 10.51% H and 89.49% C. Dissolving 0.0250 g of b@carotene in 1.50 g of camphor gives a freezing- point depression of 1.17 °C. What are the molecular weight and formula of b@carotene? [Kf for camphor is 37.7 1°C kg2>mol.]
Textbook Question
Addition of 50.00 mL of 2.238 m H2SO4 1solution density= 1.1243 g>mL2 to 50.00 mL of 2.238 M BaCl2 gives a white precipitate.(b) If you filter the mixture and add more H2SO4 solution to the filtrate, would you obtain more precipitate? Explain.
Textbook Question

Treatment of 1.385 g of an unknown metal M with an excess of aqueous HCl evolved a gas that was found to have a volume of 382.6 mL at 20.0 °C and 755 mm Hg pressure. Heating the reaction mixture to evaporate the water and remaining HCl then gave a white crystalline compound, MClx. After dissolving the compound in 25.0 g of water, the melting point of the resulting solution was - 3.53 °C. (b) What mass of MClx is formed? (a) How many moles of H2 gas are evolved?

Textbook Question

Treatment of 1.385 g of an unknown metal M with an excess of aqueous HCl evolved a gas that was found to have a volume of 382.6 mL at 20.0 °C and 755 mm Hg pressure. Heating the reaction mixture to evaporate the water and remaining HCl then gave a white crystalline compound, MClx. After dis- solving the compound in 25.0 g of water, the melting point of the resulting solution was - 3.53 °C. (c) What is the molality of particles (ions) in the solution of MClx?