Final answer:
The molar concentration is 0.0517 M, there are 0.0302 moles of solute, and the molar mass of the solute is 156.6 g/mol for a solution made by dissolving 4.73 g of a nonelectrolyte in 585 mL of water at 23 °C with an osmotic pressure of 959 torr.
Step-by-step explanation:
To calculate the molar concentration of the solution when 4.73 g of nonelectrolyte solute is dissolved in 585 mL (0.585 L) of water, which exerts an osmotic pressure of 959 torr at 23 °C, we can use the formula II = MRT, where II is the osmotic pressure, M is the molarity, R is the ideal gas constant, and T is the temperature in kelvins.
First, convert the osmotic pressure from torr to atm: 959 torr = 959 torr * (1 atm / 760 torr) = 1.262 atm.
Assuming the ideal gas constant R is 0.0821 L·atm/(K·mol), and the temperature is 23 °C or 296 K (23 °C + 273 = 296 K), the molarity M can be found by rearranging the equation to M = II / (RT). Inserting the known values, we get:
M = 1.262 atm / [0.0821 L·atm/(K·mol) * 296 K]
M = 0.0517 mol/L.
To find the number of moles of solute in the solution, multiply the molarity by the volume of the solution in liters:
Moles of solute = 0.0517 mol/L * 0.585 L = 0.0302 mol.
The molar mass of the solute can be calculated by dividing the mass of the solute by the number of moles:
Molar mass = 4.73 g / 0.0302 mol = 156.6 g/mol.
In summary, the molar concentration is 0.0517 M, there are 0.0302 moles of solute in the solution, and the molar mass of the solute is 156.6 g/mol.