The osmotic pressure of a solution containing 7.0 g of a sugar per liter is 23 torr at 25 °C. Assuming ideal solution behavior, what is the molar mass of this sugar?

5650 g/mol

Explanation:

The osmotic pressure (π) is the pressure needed to prevent that the osmose occur in a system. Osmose is the process that a solvent goes through a membrane where the solution is more concentrated.

This property can be calculated by:

π = M*R*T

Where M is the molarity of the solution (mol/L), R is the ideal gas gas constant (62.3 torr. L/mol. K), and T is the temperature (25°C = 298 K), so:

23 = M*62.3*298

M = 1.24x10⁻³ mol/L

So, if the concentration is mass is 7.0 g/L, the molar mass (MM) of the sugar is its concentration is mass divided by the molarity:

MM = 7/1.24x10⁻³

MM = 5650 g/mol