Question:
A solution containing 4g of polymer in a 4.0-litre solution at 27°C shows an osmotic pressure of 3.0×10-4 atm. The molar mass of the polymer in g/mol is
A solution containing 4g of polymer in a 4.0-litre solution at 27°C shows an osmotic pressure of 3.0×10-4 atm. The molar mass of the polymer in g/mol is
Updated On: Apr 11, 2025
- 820000
- 82000
- 8200
- 820
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The Correct Option is B
Solution and Explanation
The correct answer is option (B): 82000 g/mol
Explanation: The osmotic pressure formula is given by:
\(\pi = \frac{nRT}{V}\)
Where:
- \(\pi\) = osmotic pressure = \(3.0 \times 10^{-4}\) atm
- V = volume of solution = 4.0 L
- T = temperature = 27°C = 300 K
- R = gas constant = 0.08206 L·atm/mol·K
- n = number of moles = \( \frac{4}{M} \), where M is the molar mass (since mass = 4 g)
Substitute into the formula:
\[ 3.0 \times 10^{-4} = \frac{\left(\frac{4}{M}\right)(0.08206)(300)}{4} \]
Multiply both sides by 4:
\[ 1.2 \times 10^{-3} = \frac{(4)(0.08206)(300)}{M} \]
Solve for M:
\[ M = \frac{(4)(0.08206)(300)}{1.2 \times 10^{-3}} = \frac{98.472}{1.2 \times 10^{-3}} = 82060 \approx 82000 \text{ g/mol} \]
Hence, the molar mass of the polymer is approximately 82000 g/mol.
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Concepts Used:
Types of Solutions
Solutions are homogeneous mixtures of two or more substances, where the solute is uniformly dispersed in the solvent. Solutions can be classified into several types based on their composition and properties.
- Gas solutions: These are solutions where gases are dissolved in other gases, such as oxygen and nitrogen in air.
- Liquid solutions: These are solutions where a liquid is dissolved in another liquid, such as ethanol in water.
- Solid solutions: These are solutions where a solid is dissolved in another solid, such as an alloy of copper and zinc.
- Aqueous solutions: These are solutions where water is the solvent, such as saltwater or sugar water.
- Concentrated solutions: These are solutions where a large amount of solute is dissolved in the solvent, resulting in a high concentration.
- Dilute solutions: These are solutions where a small amount of solute is dissolved in the solvent, resulting in a low concentration.
- Saturated solutions: These are solutions where the maximum amount of solute has been dissolved in the solvent at a given temperature and pressure.
- Supersaturated solutions: These are solutions where more solute has been dissolved in the solvent than is normally possible at a given temperature and pressure.
- Colloidal solutions: These are solutions where the size of the dispersed particles is between 1 and 1000 nanometers. These solutions have unique properties such as Brownian motion and Tyndall effect.
Understanding the different types of solutions is important for understanding their properties, behavior, and applications in various fields, such as chemistry, biology, and engineering.