A solution is prepared by dissolving 3.44 g of sucrose, C12H22O11, in 118 g of water.
a) What is the molality of the resulting solution?
b) What is the mole fraction of water in this solution?
molality=molessugar/kgsolvent
= 3.44/(molmassSucrose*.118)
Mole fraction moles solute/totalmoles
where moles solute=3.44/molmassSucrose
moles water=18/118
and total moles=moles solute+moles water.
Just a slight correction to a typo above.
mols H2O = 118/18
B)
moles of h2o=118g/18(g/mol)=6.5556 mol
moles of c12h22O11= 3.44g/342.3(g/mol)=0.10049 mol
6.5556 mol/(6.5556 mol + 0.10049 mol= 0.984902 mol
A)
M= (0.10049)/(0.00344 kg + 0.118 kg)= 0.82749 m c12h22O11
To find the molality (a) of the resulting solution, we need to first determine the moles of solute (sucrose) and the mass of the solvent (water).
a) Calculate the moles of sucrose:
We will use the formula: Moles = Mass / Molar Mass
The molar mass of sucrose (C12H22O11) can be calculated by summing the atomic masses of the individual elements.
Molar mass of carbon (C) = 12.01 g/mol
Molar mass of hydrogen (H) = 1.01 g/mol
Molar mass of oxygen (O) = 16.00 g/mol
Molar mass of the entire sucrose molecule:
(12.01 g/mol x 12) + (1.01 g/mol x 22) + (16.00 g/mol x 11) = 342.34 g/mol
Now, we can calculate the moles of sucrose:
Moles of sucrose = Mass of sucrose / Molar mass of sucrose
Moles of sucrose = 3.44 g / 342.34 g/mol
Next, we need to determine the mass of the solvent (water) in kilograms:
Mass of water = 118 g
Now, we convert the mass of water from grams to kilograms:
Mass of water in kg = 118 g / 1000 g/kg
Finally, we calculate the molality of the solution:
Molality (a) = Moles of solute / Mass of solvent in kg
Molality (a) = Moles of sucrose / Mass of water in kg
b) The mole fraction (X) of water in the solution can be calculated using the formula:
Mole fraction (X) = Moles of water / (Moles of water + Moles of solute)
To find the moles of water, we need to use the mass of water and its molar mass.
Molar mass of water (H2O) = 1.01 g/mol + 1.01 g/mol + 16.00 g/mol = 18.02 g/mol
Now, calculate the moles of water:
Moles of water = Mass of water / Molar mass of water
With the moles of water and sucrose, we can calculate the mole fraction of water.
Therefore, the answers are:
a) The molality of the resulting solution is calculated using the formula Molality (a) = Moles of sucrose / Mass of water in kg.
b) The mole fraction of water in the solution is calculated using the formula Mole fraction (X) = Moles of water / (Moles of water + Moles of sucrose).