QUESTION NO. 2

(a) Calculate molecular weight of a non-volatile solute whose 3 gm dissolved in 60 gm of water has osmotic pressure 6.57 atm at 15°C. Given solution constant(s) = 0.082 atm L mol K-

To calculate the molecular weight of the non-volatile solute, we can use the formula for osmotic pressure ((\Pi)) of a solution:

[ \Pi = \frac{n}{V}RT ]

Where:

• (\Pi) is the osmotic pressure.
• (n) is the number of moles of solute.
• (V) is the volume of the solution in liters.
• (R) is the gas constant (0.082 atm L mol(^{-1}) K(^{-1})).
• (T) is the temperature in Kelvin.

First, let’s convert the temperature from Celsius to Kelvin:

[ T = 15^\circ C + 273.15 = 288.15 \, \text{K} ]

Next, we need to find the volume of the solution. Assuming the density of water is approximately 1 g/mL, 60 grams of water is equivalent to 60 mL or 0.060 L.

Given:

• Osmotic pressure ((\Pi)) = 6.57 atm
• Weight of solute = 3 grams
• Volume of solution (V) = 0.060 L
• Gas constant (R) = 0.082 atm L mol(^{-1}) K(^{-1})
• Temperature (T) = 288.15 K

We can rearrange the osmotic pressure formula to solve for (n):

[ n = \frac{\Pi V}{RT} ]

Substituting the given values:

[ n = \frac{6.57 \times 0.060}{0.082 \times 288.15} ]

Let’s calculate (n):

[ n = \frac{6.57 \times 0.060}{0.082 \times 288.15} \approx \frac{0.3942}{23.6263} \approx 0.0167 \, \text{moles} ]

Now, the number of moles ((n)) is also given by:

[ n = \frac{\text{mass}}{\text{molar mass}} ]

Rearranging to solve for molar mass (M):

[ \text{molar mass} = \frac{\text{mass}}{n} ]

Substituting the values:

[ \text{molar mass} = \frac{3 \, \text{g}}{0.0167 \, \text{moles}} \approx 179.64 \, \text{g/mol} ]

So, the molecular weight of the non-volatile solute is approximately 179.64 g/mol.

b) What is Osmotic pressure? Describe a method for determination of it.

Osmotic Pressure:

Osmotic pressure ((\Pi)) is the pressure required to stop the flow of solvent molecules through a semipermeable membrane from a dilute solution into a concentrated solution. It is a colligative property, meaning it depends on the number of solute particles in a given amount of solvent and not on the type of particles.

Mathematically, osmotic pressure can be expressed using the van’t Hoff equation:

[ \Pi = iCRT ]

Where:

• (\Pi) is the osmotic pressure.
• (i) is the van’t Hoff factor (number of particles the solute dissociates into).
• (C) is the molar concentration of the solute.
• (R) is the universal gas constant (0.0821 atm L mol(^{-1}) K(^{-1})).
• (T) is the temperature in Kelvin.

Determination of Osmotic Pressure:

One common method to determine osmotic pressure is by using an osmometer. Here’s a general procedure:

1. Preparation of Solution:

• Prepare the solution of the non-volatile solute whose osmotic pressure is to be determined. Ensure the solute is completely dissolved.

1. Setup of the Osmometer:

• An osmometer typically consists of a semipermeable membrane separating two chambers: one containing the solution and the other containing pure solvent (usually water).
• Place the solution in one chamber and the pure solvent in the other chamber.

1. Equilibrium Establishment:

• Allow the system to reach equilibrium. Solvent molecules will move from the pure solvent side through the semipermeable membrane to the solution side due to the difference in chemical potential.
• This movement will continue until the osmotic pressure builds up sufficiently to stop further movement of the solvent.

1. Measurement of Osmotic Pressure:

• The osmotic pressure can be measured using a manometer connected to the chamber containing the solution. The manometer will measure the pressure difference between the solution and the solvent.
• Alternatively, an electronic osmometer can be used, which provides a direct reading of the osmotic pressure.

1. Calculation of Osmotic Pressure:

• Using the van’t Hoff equation, the osmotic pressure can be calculated if the concentration of the solute and the temperature are known.

Example Procedure Using a Membrane Osmometer:

1. Set Up the Apparatus:

• Fill one compartment of the osmometer with the solution of known concentration.
• Fill the other compartment with pure solvent (water).

1. Observation:

• Allow the solvent to flow through the semipermeable membrane until equilibrium is reached.
• Note the height difference (if using a column setup) or the pressure reading (if using a manometer).

1. Recording Data:

• Measure the pressure difference across the membrane. This pressure difference corresponds to the osmotic pressure of the solution.

1. Calculations:

• Use the recorded pressure difference and the van’t Hoff equation to calculate the osmotic pressure.
• Ensure temperature and concentration are accurately measured for precise calculations.

By following these steps, the osmotic pressure of a solution can be determined accurately, providing valuable information about the solution’s properties and the solute’s behavior in the solvent.

(c) State and explain Raoult’s law of relative lowering of vapour pressure.

Raoult’s Law of Relative Lowering of Vapor Pressure:

Raoult’s law states that the vapor pressure of a solvent in an ideal solution is directly proportional to the mole fraction of the solvent in the solution. For a solution containing a non-volatile solute, Raoult’s law can be expressed as:

[ P_A = P_A^0 \cdot X_A ]

Where:

• ( P_A ) is the vapor pressure of the solvent in the solution.
• ( P_A^0 ) is the vapor pressure of the pure solvent.
• ( X_A ) is the mole fraction of the solvent in the solution.

When a non-volatile solute is added to a solvent, the vapor pressure of the solvent decreases. This decrease in vapor pressure is known as the relative lowering of vapor pressure. Raoult’s law of relative lowering of vapor pressure can be derived from the above expression.

Relative Lowering of Vapor Pressure

The relative lowering of vapor pressure is defined as the ratio of the decrease in vapor pressure of the solvent to the vapor pressure of the pure solvent. Mathematically, it is given by:

[ \frac{P_A^0 – P_A}{P_A^0} ]

Using Raoult’s law, we can substitute ( P_A = P_A^0 \cdot X_A ):

[ \frac{P_A^0 – (P_A^0 \cdot X_A)}{P_A^0} = \frac{P_A^0 (1 – X_A)}{P_A^0} = 1 – X_A ]

Since ( X_A + X_B = 1 ) (where ( X_B ) is the mole fraction of the solute):

[ 1 – X_A = X_B ]

Therefore, the relative lowering of vapor pressure is:

[ \frac{P_A^0 – P_A}{P_A^0} = X_B ]

This shows that the relative lowering of vapor pressure is equal to the mole fraction of the non-volatile solute in the solution.

Explanation of Raoult’s Law

1. Ideal Solutions:

• Raoult’s law applies to ideal solutions where the interactions between solute-solvent molecules are similar to those between solvent-solvent and solute-solute molecules. In such solutions, the enthalpy of mixing is zero, and the volume change upon mixing is negligible.

1. Non-Volatile Solute:

• When a non-volatile solute is added to a solvent, it does not contribute to the vapor pressure. The presence of solute particles reduces the number of solvent molecules at the surface, thus lowering the vapor pressure of the solvent.

1. Colligative Property:

• The lowering of vapor pressure is a colligative property, meaning it depends on the number of solute particles in the solution, not their identity. This property leads to other colligative effects such as boiling point elevation, freezing point depression, and osmotic pressure.

Applications of Raoult’s Law

1. Determination of Molar Mass:

• Raoult’s law can be used to determine the molar mass of a non-volatile solute by measuring the relative lowering of vapor pressure of the solvent.

1. Purity of Solvent:

• It can help in assessing the purity of a solvent. Any deviation from the expected vapor pressure indicates the presence of impurities.

1. Chemical Industry:

• Raoult’s law is used in designing processes like distillation, where the separation of components depends on differences in vapor pressures.

1. Formulation of Solutions:

• It aids in the formulation of solutions in pharmaceuticals, food industries, and other applications where specific concentrations are critical.

In summary, Raoult’s law of relative lowering of vapor pressure is a fundamental principle in solution chemistry, describing how the addition of a non-volatile solute affects the vapor pressure of a solvent and providing a basis for understanding various colligative properties.