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If 0.459 g of an unknown sugar is dissolved in 100.0 mL of water its osmotic pressure is found to be 0.0824 atm.. If the temperature of the solution was 298 K, what is the molar mass of the sugar (in g/mol)? Give your answer to three sig figs

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The molar mass of the sugar is 1350 g/mol.

What is the osmotic pressure?

We define the osmotic pressure as the pressure that needs to be applied to  effect the movement of the solvent across a semi permeable membrane.

Number of moles of the sugar solution = 0.459 g/MM

Where MM = molar mass

We know that the osmotic pressure is obtained from;

π = icRT

i = Van't Hoff factor

c = concentration

R = molar gas constant

T = temperature

Let us obtain the concentration;

c = π/iRT

c =  0.0824 atm/ 1 * 0.082 * 298

c = 0.0034 M

Now;

Concentration = Number of moles/volume

Volume = 100.0 mL or 0.1 L

0.0034 = 0.459/MM/0.1

0.0034 = 0.459/0.1MM

0.0034 * 0.1MM = 0.459

MM = 0.459/ 0.0034 * 0.1

MM = 1350 g/mol

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