The osmotic pressure of solutions of PVC in cyclohexanone at $300 K$ are plotted on the graph The molar mass of $PVC$ is ____$g \,mol ^{-1}$ (Nearest integer)
( Given : R = 0.083 L atm K-1 mol-1 )
( Given : R = 0.083 L atm K-1 mol-1 )
Correct Answer: 41500
Approach Solution - 1
The correct answer is 41500
If we assume graph between and
Assuming vs graph
Slope
Approach Solution -2
The van 't Hoff equation for osmotic pressure (\(\pi\)) is:
\[ \pi = CRT \]
Dividing both sides by concentration (\(C\)):
\[ \frac{\pi}{C} = RT \times \frac{1}{M} \]
From the graph, the slope (\(\frac{\pi}{C}\)) is determined to be 6.0 atm L g$^{-1}$.
Using the relation: \[ M = \frac{RT}{\text{slope}} \]
Substituting the values:
\[ M = \frac{0.083 \times 300}{6.0} = 41500 \, \text{g mol$^{-1}$}. \]
Thus, the molar mass of PVC is 41500 g \(mol^{-1}\).
The molar mass of a polymer like PVC can be calculated from osmotic pressure data using the van 't Hoff equation. The slope of the \(\pi / C\) graph provides critical information for this calculation.
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.