a 250.0 ml sample of an aqueous solution at 25 degrees celsius contains 35.8 mg of an unknown nonelectrolyte compound. If the solution has an osmotic pressure of 11.25 mmHg, what is the molar mass of the unknown compound?
I know you need to have the answer in g/mol. I have grams (0.358 g), but am having a hard time figuring out how to find mols.
pi = MRT. Substitute and solve for M = molarity. Then n = grams/molar mass. You know grams and mols, solve for molar mass. Note that pressure should be in atm for M to be molarity.
So you invert the equation to M=pi/RTi to solve for Molarity. I plug in the numbers ((0.1480 atm)/(0.08206 L atm/K mol)(298K) (1))
That equals 6.1554*10^-4 mols.
Dont you divide 0.358g/6.1554*10^-4??
To find the molar mass of the unknown compound, we first need to find the number of moles present in the solution.
Given:
Volume of solution (V) = 250.0 ml = 0.250 L
Mass of the compound (m) = 35.8 mg = 0.0358 g
Osmotic pressure (π) = 11.25 mmHg
The osmotic pressure can be related to the molar concentration using the equation:
π = (n/V)RT
Where:
n = number of moles
V = volume of solution (in liters)
R = ideal gas constant (0.0821 L·atm·K^−1·mol^−1)
T = temperature (in Kelvin)
First, let's convert the volume from milliliters to liters:
V = 0.250 L
Next, let's convert the osmotic pressure from mmHg to atm:
π = 11.25 mmHg * (1 atm / 760 mmHg) = 0.0148 atm
The equation can now be rearranged to solve for the number of moles (n):
n = (πV) / (RT)
Substituting the known values:
n = (0.0148 atm * 0.250 L) / (0.0821 L·atm·K^-1·mol^-1 * 25 + 273 K)
Simplifying the equation:
n = (0.0037) / (0.0201 K^-1)
n = 0.184 Moles
Now that we have the number of moles (n), we can calculate the molar mass (M) using the formula:
M = m / n
Substituting the known values:
M = 0.0358 g / 0.184 mol
M = 0.1949 g/mol
Therefore, the molar mass of the unknown compound is approximately 0.195 g/mol.