Textbook Question
The osmotic pressure of a 0.010 M aqueous solution of CaCl2 is found to be 0.674 atm at 25 °C. Calculate the van't Hoff factor, i, for the solution.
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Ch.13 - Properties of Solutions
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement140
- Ch.2 - Atoms, Molecules, and Ions192
- Ch.3 - Chemical Reactions and Reaction Stoichiometry172
- Ch.4 - Reactions in Aqueous Solution156
- Ch.5 - Thermochemistry151
- Ch.6 - Electronic Structure of Atoms137
- Ch.7 - Periodic Properties of the Elements127
- Ch.8 - Basic Concepts of Chemical Bonding143
- Ch.9 - Molecular Geometry and Bonding Theories167
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces97
- Ch.12 - Solids and Modern Materials129
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics175
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Acid-Base Equilibria127
- Ch.17 - Additional Aspects of Aqueous Equilibria133
- Ch.18 - Chemistry of the Environment88
- Ch.19 - Chemical Thermodynamics140
- Ch.20 - Electrochemistry137
- Ch.21 - Nuclear Chemistry99
- Ch.22 - Chemistry of the Nonmetals66
- Ch.23 - Transition Metals and Coordination Chemistry69
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry11
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
Chapter 13, Problem 79
Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of 0.64 g of adrenaline in 36.0 g of CCl4 elevates the boiling point by 0.49 °C. Calculate the approximate molar mass of adrenaline from this data.
Verified step by step guidance1
Identify the formula for boiling point elevation: \( \Delta T_b = i \cdot K_b \cdot m \), where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van't Hoff factor (which is 1 for non-electrolytes like adrenaline), \( K_b \) is the ebullioscopic constant of the solvent, and \( m \) is the molality of the solution.
Rearrange the formula to solve for molality \( m \): \( m = \frac{\Delta T_b}{i \cdot K_b} \).
Calculate the molality \( m \) using the given \( \Delta T_b = 0.49 \text{ °C} \) and the known \( K_b \) for carbon tetrachloride (CCl_4), which you can look up in a reference table.
Use the definition of molality: \( m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} \). Convert the mass of CCl_4 from grams to kilograms and use the calculated molality to find the moles of adrenaline.
Calculate the molar mass of adrenaline by dividing the mass of adrenaline (0.64 g) by the moles of adrenaline obtained in the previous step.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Colligative Properties
Colligative properties are physical properties of solutions that depend on the number of solute particles in a given amount of solvent, rather than the identity of the solute. Examples include boiling point elevation and freezing point depression. In this context, the boiling point elevation of CCl4 due to the addition of adrenaline is a key factor in determining the molar mass of adrenaline.
Boiling Point Elevation Formula
The boiling point elevation can be calculated using the formula ΔT_b = i * K_b * m, where ΔT_b is the change in boiling point, i is the van 't Hoff factor (which is 1 for non-electrolytes like adrenaline), K_b is the ebullioscopic constant of the solvent, and m is the molality of the solution. This formula allows us to relate the observed boiling point change to the concentration of the solute, which is essential for calculating molar mass.
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Boiling Point Elevation
Molar Mass Calculation
Molar mass is defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the molar mass of adrenaline in this scenario, we can rearrange the boiling point elevation formula to solve for the molar mass using the mass of adrenaline and the calculated molality from the boiling point change. This process involves understanding the relationship between mass, moles, and the properties of the solution.
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Related Practice
Textbook Question
Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing 0.150 g of this enzyme in 210 mL of solution has an osmotic pressure of 0.953 torr at 25 °C. What is the molar mass of lysozyme?
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Textbook Question
A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.605 atm at 25 °C. Assuming that the organic compound is a nonelectrolyte, what is its molar mass?
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