Phenylalanyl aspartate, Nutrasweet, is an artificial sweetener used in many diet drinks. If a solution prepared by dissolving 6.068 mg of Nutrasweet in 125 milliliters of water exhibited an osmotic pressure at 25ºC of 3.23 mm Hg, what is the molar mass of Nutrasweet?
pi = MRT
Substitute pi(in atmospheres) into the osmotic pressure equation and solve for n = number of moles. Then
n = grams/molar mass.
You know n and grams, solve for molar mass.
Thank you very much!
To find the molar mass of Nutrasweet, we can use the formula for osmotic pressure:
π = (n/V)RT
Where:
π = osmotic pressure
n = number of moles of solute
V = volume of solvent (in liters)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
In this case, we are given the osmotic pressure (π = 3.23 mm Hg), the volume of solvent (V = 125 mL = 0.125 L), and the temperature (T = 25ºC = 25 + 273 = 298 K).
We need to solve for n, the number of moles of solute. Rearranging the formula:
n = (πV) / (RT)
Now we can plug in the values:
n = (3.23 mm Hg * 0.125 L) / (0.0821 L·atm/(mol·K) * 298 K)
Simplifying the equation:
n = 0.40 mmol
Next, we need to convert the mass of Nutrasweet (6.068 mg) to moles. To do this, we use the molar mass.
molar mass = mass / n
Rearranging the formula:
mass = molar mass * n
Now we can solve for the molar mass:
molar mass = mass / n = 6.068 mg / 0.40 mmol
Converting both milligrams and millimoles to grams and moles respectively:
molar mass = (6.068 mg / 1000) / (0.40 mmol / 1000)
molar mass = 15.17 g/mol
Therefore, the molar mass of Nutrasweet is approximately 15.17 g/mol.