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.
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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.