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In a laboratory experiment, a student found that a 136-mL aqueous solution containing 2.257 g of a compound had an osmotic pressure of 20.7 mm Hg at 298 K. The compound was also found to be nonvolatile and a nonelectrolyte. What is the molar mass of this compound?

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Answer:

14889 g/mol is the molar mass of the compound

Explanation:

Let's apply the colligate property of osmotic pressure to solve this problem

π = M . R . T

First of all, we convert the osmotic pressure from mmHg to atm

20.7 mmHg . 1 atm/760 mmHg = 0.0272 atm

Let's replace the data in the formula to find out the molarity of the compound.

0.0272 atm = M . 0.082L.atm/mol.K . 298K

0.0272 atm / (0.082L.atm/mol.K . 298K) = M

1.11×10⁻³ = M

Molarity is mol/L, and mol is mass (g) / molar mass. Let's make the equation to replace the vaules.

(2.257 g/ X) / 0.136L = 1.11×10⁻³ mol/L

(2.257 g/ X) = 1.11×10⁻³ mol/L  . 0.136L

2.257 g/ X = 1.51×10⁻⁴ mol

2.257 g/ 1.51×10⁻⁴ mol = 14889 g/mol

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