Find the molality, mole fraction, and percent by mass of a solution prepared with 500 grams of C12h22O11 in 2000 grams of H20
mols C12H22O11 = grams/molar mass
m = mols/kg
You have mols C12H22O11. Convert 2000 g H2O to mols and find total mols.
Then XC12H22O11 = mols C12H22O11/total mols.
%w/w = [(grams C12H11O11/(2000g H2O + grams C12H22O11)]*(100 = ?
To find the molality, mole fraction, and percent by mass of a solution, we need to calculate the number of moles of solute and solvent.
Let's start by finding the number of moles of C12H22O11:
1. Calculate the molar mass of C12H22O11:
C: 12.01 g/mol x 12 atoms = 144.12 g/mol
H: 1.01 g/mol x 22 atoms = 22.22 g/mol
O: 16.00 g/mol x 11 atoms = 176.00 g/mol
Total molar mass of C12H22O11 = 144.12 + 22.22 + 176.00 = 342.34 g/mol
2. Calculate the moles of C12H22O11:
Moles = Mass / Molar mass
= 500 g / 342.34 g/mol ≈ 1.4606 mol
Now, let's find the number of moles of H2O:
1. Calculate the molar mass of H2O:
H: 1.01 g/mol x 2 atoms = 2.02 g/mol
O: 16.00 g/mol x 1 atom = 16.00 g/mol
Total molar mass of H2O = 2.02 + 16.00 = 18.02 g/mol
2. Calculate the moles of H2O:
Moles = Mass / Molar mass
= 2000 g / 18.02 g/mol ≈ 110.49 mol
Now that we have the moles of solute and solvent, we can calculate the molality, mole fraction, and percent by mass:
1. Molality (m):
Molality = Moles of solute / Mass of solvent in kg
= 1.4606 mol / (2000 g / 1000) kg
= 0.7303 mol/kg
2. Mole Fraction (X):
Mole Fraction of solute (X1) = Moles of solute / Total moles
= 1.4606 mol / (1.4606 mol + 110.49 mol)
≈ 0.013
Mole Fraction of solvent (X2) = Moles of solvent / Total moles
= 110.49 mol / (1.4606 mol + 110.49 mol)
≈ 0.987
3. Percent by Mass (%):
Percent by Mass of solute = (Mass of solute / Mass of solution) x 100%
= (500 g / (500 g + 2000 g)) x 100%
= 20%
Percent by Mass of solvent = (Mass of solvent / Mass of solution) x 100%
= (2000 g / (500 g + 2000 g)) x 100%
= 80%
In summary, the solution prepared with 500 grams of C12H22O11 in 2000 grams of H2O has a molality of 0.7303 mol/kg, a mole fraction of solute (C12H22O11) of approximately 0.013, and mole fraction of solvent (H2O) of approximately 0.987. The percent by mass of C12H22O11 is 20%, and the percent by mass of H2O is 80%.