To determine the osmotic pressure of the aqueous solution at 313 K, we can use the formula for osmotic pressure, which is given by the equation:
Osmotic Pressure Formula
The osmotic pressure (π) can be calculated using the formula:
π = iCRT
- i = van 't Hoff factor (which is 1 for non-electrolytes)
- C = molarity of the solution
- R = universal gas constant (approximately 8.314 J/(mol·K))
- T = temperature in Kelvin
Step 1: Calculate the Molarity of the Solution
First, we need to find the molarity (C) of the solution. Molarity is defined as the number of moles of solute per liter of solution. To find this, we can use the density of the solution and its molecular weight.
The density of the solution is given as 1010 kg/m³. To convert this to grams per liter, we multiply by 1000:
Density = 1010 kg/m³ = 1010 g/L
Next, we can find the number of moles of solute in 1 liter of solution. The molecular weight of the solute is given as 60 g/mol. Therefore, the number of moles of solute in 1 liter is:
Number of moles = Mass (g) / Molecular weight (g/mol) = 1010 g / 60 g/mol = 16.83 mol
Step 2: Calculate the Osmotic Pressure
Now that we have the molarity (C = 16.83 mol/L), we can substitute the values into the osmotic pressure formula. The temperature (T) is given as 313 K, and we will use the gas constant (R) as 8.314 J/(mol·K).
Substituting these values into the osmotic pressure formula:
π = (1)(16.83 mol/L)(8.314 J/(mol·K))(313 K)
Calculating this gives:
π = 1 * 16.83 * 8.314 * 313 ≈ 43,500.57 Pa
Final Result
The osmotic pressure of the aqueous solution at 313 K is approximately 43,500.57 Pa. This value indicates the pressure required to stop the flow of solvent into the solution through a semipermeable membrane, which is a key concept in understanding osmotic processes in biological and chemical systems.
