A nonelectrolyte compound with a molar mass of 862 g mol^-1 was dissolved in enough water to make 100 mL of solution at 25 °C and produced an osmotic pressure of 38.4 mbar. Calculate the mass of the compound, in mg, used to make this solution. A) 116 mg B) 185 mg C) 134 mg D) 75.3 mg E) 84.3 mg

Question

Quizplus · Accepted Answer

First, we need to use the van't Hoff equation:

Π = iMRT

Where Π is the osmotic pressure, i is the van't Hoff factor (1 for a nonelectrolyte), M is the molarity, R is the gas constant (0.08206 L · atm · K−1 · mol−1), and T is the temperature in Kelvin.

We can solve for M:

M = Π / iRT

M = (38.4 mbar) / (1 × 0.08206 L · atm · K−1 · mol−1 × 298 K)

M = 1.59 × 10−3 mol · L−1

Next, we can use the definition of molarity to find the number of moles of solute:

M = n / V

n = MV

n = (1.59 × 10−3 mol·L−1)(0.1 L)

n = 1.59 × 10−4 mol

Finally, we can use the molar mass of the compound to find the mass of the solute:

mass = n × Molar Mass

mass = (1.59 × 10−4 mol) × (862 g·mol−1)

mass = 0.137 g

We want the mass in mg, so we can convert:

mass = 137 mg

Therefore, the answer is choice C, 134 mg (the closest answer).

A Nonelectrolyte Compound with a Molar Mass of 862 G