When 4.56 g of a nonelectrolyte solute is dissolved in water to make 275 mL of solution at 22 °C, the solution exerts an osmotic pressure of 873 torr.
10 years ago
11 months ago
To calculate the molar mass of the solute, we can use the formula for the osmotic pressure of a dilute solution:
π = MRT
Where:
π is the osmotic pressure in atm
M is the molar concentration of the solute in mol/L
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
First, we need to convert the osmotic pressure from torr to atm:
873 torr * (1 atm / 760 torr) = 1.15 atm
Next, we need to convert the temperature from Celsius to Kelvin:
22 °C + 273.15 = 295.15 K
Now, we can rearrange the formula to solve for the molar concentration (M):
M = π / (RT)
M = 1.15 atm / (0.0821 L·atm/mol·K * 295.15 K)
M ≈ 0.0445 mol/L
Since we know the molar concentration of the solute, we can calculate the moles of solute using the volume of the solution:
moles of solute = molar concentration * volume of solution
moles of solute = 0.0445 mol/L * 0.275 L
moles of solute ≈ 0.0122 mol
Finally, we can calculate the molar mass of the solute using the given mass of the solute:
molar mass = mass of solute / moles of solute
molar mass = 4.56 g / 0.0122 mol
molar mass ≈ 373.77 g/mol
Therefore, the molar mass of the nonelectrolyte solute is approximately 373.77 g/mol.