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 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.
Top Questions on Solutions
According to the generally accepted definition of the ideal solution there are equal interaction forces acting between molecules belonging to the same or different species. (This is equivalent to the statement that the activity of the components equals the concentration.) Strictly speaking, this concept is valid in ecological systems (isotopic mixtures of an element, hydrocarbons mixtures, etc.). It is still usual to talk about ideal solutions as limiting cases in reality since very dilute solutions behave ideally with respect to the solvent. This law is further supported by the fact that Raoult’s law empirically found for describing the behaviour of the solvent in dilute solutions can be deduced thermodynamically via the assumption of ideal behaviour of the solvent.
Answer the following questions:
(a) Give one example of miscible liquid pair which shows negative deviation from Raoult’s law. What is the reason for such deviation?
(b) (i) State Raoult’s law for a solution containing volatile components.
OR
(ii) Raoult’s law is a special case of Henry’s law. Comment.
(c) Write two characteristics of an ideal solution.- A solution of glucose (molar mass = 180 g mol\(^{-1}\)) in water has a boiling point of 100.20°C. Calculate the freezing point of the same solution. Molal constants for water \(K_f\) and \(K_b\) are 1.86 K kg mol\(^{-1}\) and 0.512 K kg mol\(^{-1}\) respectively.
- Define Azeotrope. What type of Azeotrope is formed by negative deviation from Raoult's law? Give an example.
- Give reasons:
(a) Cooking is faster in a pressure cooker than in an open pan.
(b) On mixing liquid X and liquid Y, volume of the resulting solution decreases. What type of deviation from Raoult's law is shown by the resulting solution? What change in temperature would you observe after mixing liquids X and Y? - An unripe mango placed in a concentrated salt solution to prepare pickle, shrivels because __________
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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.