Chapter 13: Problem 42
What are colligative properties? What is the meaning of the word colligative in this context?
Short Answer
Expert verified
Colligative properties depend on the number of solute particles, not their identity, and "colligative" means "bound together."
Step by step solution
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Boiling Point Elevation
Boiling point elevation is a fascinating colligative property that occurs when a non-volatile solute is added to a solvent. It simply means that the boiling point of a solution is higher than that of the pure solvent. This happens because the solute particles disrupt the normal movement of the solvent molecules, requiring more energy and therefore a higher temperature to turn into vapor.
To predict the change in boiling point, we use the formula: \[ \Delta T_b = i \cdot K_b \cdot m \] where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van 't Hoff factor (number of particles the solute breaks into), \( K_b \) is the ebullioscopic constant (specific to each solvent), and \( m \) is the molal concentration of the solution.
Key takeaways:
To predict the change in boiling point, we use the formula: \[ \Delta T_b = i \cdot K_b \cdot m \] where \( \Delta T_b \) is the boiling point elevation, \( i \) is the van 't Hoff factor (number of particles the solute breaks into), \( K_b \) is the ebullioscopic constant (specific to each solvent), and \( m \) is the molal concentration of the solution.
Key takeaways:
- The more solute particles present, the higher the boiling point elevation.
- This property is used in real-life scenarios, such as in antifreeze solutions in car radiators.
Freezing Point Depression
Freezing point depression is another core colligative property. It occurs when the addition of a solute causes the freezing point of a liquid to drop. This is because solute particles disrupt the crystalline formation necessary for a solvent to solidify, thus requiring a lower temperature to freeze.
The mathematical expression for freezing point depression is:\[ \Delta T_f = i \cdot K_f \cdot m \]Here, \( \Delta T_f \) stands for the freezing point depression, \( K_f \) represents the cryoscopic constant (unique to each solvent), and the other variables retain the same meaning as in boiling point elevation.
Essential points to remember:
The mathematical expression for freezing point depression is:\[ \Delta T_f = i \cdot K_f \cdot m \]Here, \( \Delta T_f \) stands for the freezing point depression, \( K_f \) represents the cryoscopic constant (unique to each solvent), and the other variables retain the same meaning as in boiling point elevation.
Essential points to remember:
- It's the basis for using salt on icy roads, as it lowers the freezing point of water.
- The degree of freezing point depression depends solely on the number of solute particles.
Vapor Pressure Lowering
Vapor pressure lowering is a colligative property where the addition of a non-volatile solute to a solvent reduces the solution's vapor pressure. This is because the solute occupies surface area in the liquid, reducing the number of solvent particles that can escape into the vapor phase.
In simpler terms, there are fewer solvent molecules available at the surface to evaporate, which consequently lowers the vapor pressure. This principle is captured by Raoult's Law, which states: \[ P_1 = X_1 \cdot P_1^0 \]where \( P_1 \) is the vapor pressure of the solvent with solute, \( X_1 \) is the mole fraction of the solvent, and \( P_1^0 \) is the vapor pressure of the pure solvent.
Key insights:
In simpler terms, there are fewer solvent molecules available at the surface to evaporate, which consequently lowers the vapor pressure. This principle is captured by Raoult's Law, which states: \[ P_1 = X_1 \cdot P_1^0 \]where \( P_1 \) is the vapor pressure of the solvent with solute, \( X_1 \) is the mole fraction of the solvent, and \( P_1^0 \) is the vapor pressure of the pure solvent.
Key insights:
- Vapor pressure lowering is responsible for phenomena like humid air resulting in delayed evaporation.
- This property affects various practical applications, including the design of chemical processes.
Osmotic Pressure
Osmotic pressure is a critical colligative property involved in biological and chemical processes. It is the pressure required to halt solvent flow through a semipermeable membrane, counteracting osmosis. Osmosis is the movement of solvent molecules from a region of low solute concentration to high solute concentration.
The formula to calculate osmotic pressure is: \[ \Pi = i \cdot M \cdot R \cdot T \]Where \( \Pi \) is the osmotic pressure, \( i \) is the van 't Hoff factor, \( M \) is the molarity of the solution, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.
Important observations:
The formula to calculate osmotic pressure is: \[ \Pi = i \cdot M \cdot R \cdot T \]Where \( \Pi \) is the osmotic pressure, \( i \) is the van 't Hoff factor, \( M \) is the molarity of the solution, \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.
Important observations:
- Osmotic pressure is crucial in physiological processes like nutrient absorption and waste removal in living organisms.
- It provides a way to determine molecular weights of solutes.
