A 150.0mL sample of an aqueous solution at 25C contains 15.2mg of an unknown nonelectrolyte compound. If the solution has an osmotic pressure of 8.44 torr, what is the molar mass of the unknown compound?

MM = 225.11 g/mol

Explanation:

In this case, let's analyze the data.

We have a 15.2 mg of an unknown electrolyte in 150 mL of solution. The osmotic pressure is 8.44 Torr, and we want the molecular mass of the unknown.

The osmotic pressure can be calculated using the following expression:

π = CRT   (1)    

π: osmotic pressure (8.44 Torr * 1 atm / 760 Torr = 0.011 atm)

C: Concentration of the unknown in the solution

R: universal constant of gases (0.082 L atm / K mol)

T: temperature in Kelvin (25 + 273 = 298 K)

From this expression, we can either solve for C, and then use another expression to calculate the molecular mass, or we can just replace the expressions in the above formula, to get the direct molecular mass. In this case, we'll follow the second method.

Concentration or molarity of a substance can be calculated using:

C = moles / V  (2)

And moles can be calculated using this expression:

moles = m / MM   (3)

Replacing (3) in (2), and then in (1) we have:

C = m / MM * V

π = m * RT / MM * V   (4)

and now, we can solve for MM:

MM = mRT / π V  (5)

Now, we just need to replace the given data into the above expression to get the value of the molecular mass:

MM = (15.2 / 1000) * 0.082 * 298 / 0.011 * 0.150

Hope this helps

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