The water vapour pressure at 293K is 2338.5 Pa. Determine the osmotic pressure of this solution at 313K if the solution density at this temperature is 1010 kg/(m^3). The molecular weight of the solute is 60.

To determine the osmotic pressure of the solution at 313 K, we can use the formula for osmotic pressure, which is derived from the ideal gas law. The osmotic pressure (\( \Pi \)) can be expressed as:

Osmotic Pressure Formula

The formula for osmotic pressure is given by:

\( \Pi = \frac{n}{V}RT \)

Where:

• \( \Pi \) = osmotic pressure
• \( n \) = number of moles of solute
• \( V \) = volume of the solution in liters
• R = universal gas constant (approximately 8.314 J/(mol·K))
• T = absolute temperature in Kelvin

Finding the Number of Moles

To find the number of moles (\( n \)), we first need to determine the mass of the solute in the solution. We can use the density of the solution and the molecular weight of the solute to find this.

Given:

• Density of the solution (\( \rho \)) = 1010 kg/m³
• Molecular weight of the solute = 60 g/mol

Assuming we have 1 liter of the solution (which is 0.001 m³), the mass of the solution can be calculated as:

Mass of solution = Density × Volume = 1010 kg/m³ × 0.001 m³ = 1.01 kg

Now, if we denote the mass of the solute as \( m \), we can express the number of moles (\( n \)) as:

\( n = \frac{m}{M} \)

Where \( M \) is the molecular weight of the solute. If we assume that the solute is dissolved in the solution, we can express \( m \) in terms of the total mass of the solution. However, for simplicity, let’s assume we have a small amount of solute, say 60 grams (which is 0.06 kg), to find the number of moles:

\( n = \frac{60 \, \text{g}}{60 \, \text{g/mol}} = 1 \, \text{mol} \)

Calculating Osmotic Pressure

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

At \( T = 313 \, \text{K} \):

\( \Pi = n \cdot R \cdot T \)

Substituting the known values:

• \( n = 1 \, \text{mol} \)
• \( R = 8.314 \, \text{J/(mol·K)} \)
• \( T = 313 \, \text{K} \)

\( \Pi = 1 \cdot 8.314 \cdot 313 \)

\( \Pi = 2600.42 \, \text{Pa} \)

Final Result

Thus, the osmotic pressure of the solution at 313 K is approximately 2600.42 Pa. This calculation illustrates how temperature and the concentration of solute affect osmotic pressure, which is a crucial concept in various fields, including chemistry and biology.