1. Vapor pressure of pure water 2338 Pascle and Hydrogenation of aqueous solution 2295.8 pascle. What will be the osmosis pressure of the solution at 313 degree Kelvin?

To determine the osmotic pressure of the solution at 313 Kelvin, we can use the formula for osmotic pressure, which is derived from van't Hoff's law. The osmotic pressure (\( \Pi \)) can be calculated using the equation:

Understanding Osmotic Pressure

The formula for osmotic pressure is given by:

Π = iCRT

Where:

• Π = osmotic pressure (in atm or pascals)
• i = van't Hoff factor (number of particles the solute dissociates into)
• C = molarity of the solution (in moles per liter)
• R = ideal gas constant (0.0821 L·atm/(K·mol) or 8.314 J/(K·mol))
• T = temperature in Kelvin

Calculating the Osmotic Pressure

In your case, we need to find the osmotic pressure of an aqueous solution at 313 K. First, we need to determine the concentration of the solute in the solution. The vapor pressure of pure water is given as 2338 Pa, while the vapor pressure of the aqueous solution is 2295.8 Pa. This difference in vapor pressure can help us find the molality of the solution.

Finding the Mole Fraction

The change in vapor pressure can be used to find the mole fraction of the solute using Raoult's Law:

ΔP = P° - P

Where:

• ΔP = change in vapor pressure
• P° = vapor pressure of pure solvent (2338 Pa)
• P = vapor pressure of the solution (2295.8 Pa)

Calculating ΔP:

ΔP = 2338 Pa - 2295.8 Pa = 42.2 Pa

Using Raoult's Law

According to Raoult's Law, the change in vapor pressure is related to the mole fraction of the solute:

ΔP = P° * X_solute

Where \( X_{solute} \) is the mole fraction of the solute. Rearranging gives:

X_solute = ΔP / P°

Substituting the values:

X_solute = 42.2 Pa / 2338 Pa ≈ 0.018

Calculating Molarity

To find the molarity (C), we can relate the mole fraction to the number of moles of solute and solvent. Assuming we have 1 kg of water (which is approximately 55.5 moles), the number of moles of solute can be calculated as:

n_solute = X_solute * n_solvent

Substituting the values:

n_solute = 0.018 * 55.5 ≈ 1.0 moles

Now, the molarity (C) of the solution can be calculated as:

C = n_solute / volume of solution in liters

Assuming the volume of the solution is approximately 1 L (since the solute is small compared to the solvent), we have:

C ≈ 1.0 moles/L

Final Calculation of Osmotic Pressure

Now we can substitute the values into the osmotic pressure formula:

Π = iCRT

Assuming the solute does not dissociate (i = 1):

Π = 1 * 1.0 moles/L * 8.314 J/(K·mol) * 313 K

Converting J to Pa·m³ (1 J = 1 Pa·m³):

Π = 1 * 1.0 * 8.314 * 313 ≈ 2600 Pa

Thus, the osmotic pressure of the solution at 313 K is approximately 2600 Pa.