An aqueous solution of a compound with a very high molar mass was prepared in a concentration of 82.7 g·L-1 at 25 °C. Its osmotic pressure was 0.540 ·102 Pa. Calculate the molar mass of the compound.
Cheers
pi = MRT.
You know pibut change to atm. You know molarity is 82.7/molar mass per L, you know R and T. Solve for molar mass. Post your work if get stuck.
To calculate the molar mass of the compound, we can use the equation for osmotic pressure:
π = MRT
Where:
π = osmotic pressure (in Pa)
M = molar mass of the compound (in kg/mol)
R = ideal gas constant (8.314 J/(K·mol))
T = temperature in kelvin
First, we need to convert the temperature from Celsius to Kelvin. We have:
T = 25 °C + 273.15 = 298.15 K
Next, we need to convert the osmotic pressure from pascals to atmospheres. We have:
π = 0.540 · 10^2 Pa × (1 atm / 101325 Pa) = 0.00532 atm
Now, we have all the values we need to solve the equation for molar mass. Rearranging the equation, we get:
M = (π / RT)
Substituting the values we have:
M = (0.00532 atm) / (0.0821 L·atm/(mol·K) × 298.15 K)
M ≈ 0.00207 mol
Finally, we can calculate the molar mass by dividing the mass of the solute by the number of moles:
Molar mass = Mass / Moles
Since the concentration is given in grams per liter, to calculate the mass, we multiply the concentration by the molar mass (Molar mass = Mass / Concentration):
Molar mass = 82.7 g/L / 0.00207 mol
Molar mass ≈ 39,939 g/mol
Therefore, the molar mass of the compound is approximately 39,939 g/mol.