5.00 g of an unknown compound was dissolved in 250.0 mL of water. The unknown compound was found to be a non-electrolyte and the osmotic pressure of the solution was determined to 14.5 atm at 298 K. Calculate the molar mass of the unknown compound (in units of g/mol). R = 0.08206 (L atm) / (mol K)

This unknown compound has a molar mass of 33.74g/mole

Explanation:

Step 1: Given data

The formula for the osmotic pressure is:

π = MRT = 14.5 atm

⇒ with M = Concentration of the solution

⇒ with R = gas constant = 0.08206 L atm / mol K

⇒ with T = absolute temperature (in Kelvin) = 298K

Step 2: Calculate concentration

M = π / RT

M = 14.5 / (0.08206 * 298)

M = 0.593 M this is 0.593 moles per L

Step 3: Calculate number of moles

Since the volume is only 0.250 L, the amount of moles is:

0.593 * 0.250 L = 0.1482 moles

Step 4: Calculate molar mass

The molar mass is : mass / moles

Molar mass of this unknown compund = 5g / 0.1482 moles = 33.74 g/mole

This unknown compound has a molar mass of 33.74g / mole