Molality is the number of moles dissolved in one kilogram of solvent.
m = n/kg of solvent
n = mass of solute / molar mass of solute
Acetone's chemical formula is C3H6O. Therefore, its molar mass = 12*3 + 6*1 + 1*16 = 58g = 0.058kg
n = mass of solute / 0.058
We have the molality = 0.7500 and the mass of solution = mass of solvent + mass of solute = 450 g = 0.45 kg
Therfore, mass of solvet = 0.45 - mass of solute
0.75 = n / 0.45 - mass of solute
0.75 = (mass of solute / 0.058) / (0.45 - mass of solute)
Let mass of solute = x
0.75 = (x/0.058) / (0.45 - x)
0.3375 - 0.75x = x/0.058
x = 0.019575 - 0.0435x
1.0435x = 0.019575
x = 0.01875 kg
mass of acetone = 0.01875 kg = 18.75 grams
