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
- 820000
- 82000
- 8200
- 820
The Correct Option is B
Solution and Explanation
The osmotic pressure (π) of a solution is given by the formula:
π=VnRT,
where n is the number of moles of solute, V is the volume of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.
In this case, we are given that the osmotic pressure (π) is 3.0×10−43.0×10−4 atm, the volume (V) is 4.0 liters, and the temperature (T) is 27°C = 300 K.
We need to find the number of moles (n) of the polymer. Given that the mass of the polymer is 4 g, we can use its molar mass (M) to calculate n using the formula:
n=molar massmass.
Substituting the values:
n=M4g.
Now, we can substitute the values of n, V, R, and T into the osmotic pressure formula and solve for M:
π=VnRT.
3.0×10−4 atm=4 g4.0 L××300 K3.0×10−4atm=4.0LM4g×R×300K.
Solving for M:
3.0×10−4atm×4.0L×R×300K4g.
Given that R is the ideal gas constant, which is approximately 0.08206 L atm/mol K0.08206L atm/mol K, we can substitute its value:
M=4 g3.0×10−4 atm×4.0 L×0.08206 L atm/mol K×300 KM=3.0×10−4atm×4.0L×0.08206L atm/mol K×300K4g.
Solving for M:
M=82000 g/molM=82000g/mol.
Hence, the molar mass of the polymer is approximately 82000 g/mol, which matches the given answer.
The correct option is(B): 82000
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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.