Answer:
m= 1.84 m
M= 1.79 M
mole fraction (X) =
Xsolute= 0.032
Xsolvent = 0.967
Step-by-step explanation:
1. Find the grams of FeCl3 in the solution: when we have a mass % we assume that there is 100 g of solution so 24% means 24 g of FeCl3 in the solution. The rest 76 g are water.
2. For molality we have the formula m= moles of solute / Kg solvent
so first we pass the grams of FeCl3 to moles of FeCl3:
24 g of FeCl3x(1 mol FeCl3/162.2 g FeCl3) = 0.14 moles FeCl3
If we had 76 g of water we convert it to Kg:
76 g water x(1 Kg of water/1000 g of water) = 0.076 Kg of water
now we divide m = 0.14 moles FeCl3/0.076 Kg of water
m= 1.84 m
3. For molarity we have the formula M= moles of solute /L of solution
the moles we already have 0.14 moles FeCl3
the (L) of solution we need to use the density of the solution to find the volume value. For this purpose we have: 100 g of solution and the density d= 1.280 g/mL
The density formula is d = (m) mass/(V) volume if we clear the unknown value that is the volume we have that (V) volume = m/d
so V = 100 g / 1.280 g/mL = 78.12 mL = 0.078 L
We replace the values in the M formula
M= 0.14 moles of FeCl3/0.078 L
M= 1.79 M
3. Finally the mole fraction (x) has the formula
X(solute) = moles of solute /moles of solution
X(solvent) moles of solvent /moles of solution
X(solute) + X(solvent) = 1
we need to find the moles of the solvent and we add the moles of the solute like this we have the moles of the solution:
76 g of water x(1 mol of water /18 g of water) = 4.2 moles of water
moles of solution = 0.14 moles of FeCl3 + 4.2 moles of water = 4.34 moles of solution
X(solute) = 0.14 moles of FeCl3/4.34 moles of solution = 0.032
1 - X(solute) = 1 - 0.032 = 0.967