A new non-electrolyte molecule is discovered. When 241 mg of the molecule is dissolved in 250.0 mL of water, it has an osmotic pressure of 0.072 atm at 25 oC. What is the molar mass of the molecule

327.89g/mol

Explanation:

Step 1:

The following data were obtained from the question:

Van 't Hoff factor (i) = 1 (since the molecule is non-electrolyte)

Temperature (T) = 25°C = 25°C + 273 = 298K

Gas constant (R) = 0.0821 atm. L/Kmol

Mass of molecule = 241mg

Volume of water = 250mL

Molarity (M) = ?

Osmotic pressure (Π) = 0.072 atm

Step 2:

Determination of the molarity of the molecule.

This can be obtained as follow:

Π = iMRT

0.072 = 1 x M x 0.0821 x 298

Divide both side by 0.0821 x 298

M = 0.072 / (0.0821 x 298)

M = 2.94*10¯³ mol/L

Step 3:

Determination of the number of mole of the molecule. This can be obtained as follow:

Molarity = 2.94*10¯³ mol/L

Volume of water = 250mL = 250/1000 = 0.25L

Mole of molecule = ... ?

Molarity = mole / Volume

2.94*10¯³ = mole / 0.25

Cross multiply

Mole of molecule = 2.94*10¯³ x 0.25

Mole of molecule = 7.35*10¯⁴ mole.

Step 4:

Determination of the molar mass of the molecule.

Mole of molecule = 7.35*10¯⁴ mole.

Mass of molecule = 241mg = 241*10¯³g

Molar mass of molecule = ... ?

Mole = Mass / Molar Mass

7.35*10¯⁴ = 241*10¯³ / Molar Mass

Cross multiply

7.35*10¯⁴ x molar mass = 241*10¯³

Divide both side by 7.35*10¯⁴

Molar Mass = 241*10¯³/7.35*10¯⁴

Molar Mass = 327.89g/mol

Therefore, the molar mass of the molecule is 327.89g/mol