I hae a solution that contains 30 lbs of sugar in 2.5 gallons of water. Calculate the mass percent, molarity, molality and mole fraction.
See your post above.
To calculate the mass percent, molarity, molality, and mole fraction of solution, we need to know the molecular weight of sugar.
The molecular weight of sugar, also known as sucrose, is approximately 342.3 g/mol.
1. Mass Percent:
Mass percent is the mass of the solute (in this case, sugar) divided by the total mass of the solution, multiplied by 100. The total mass of the solution is the sum of the mass of sugar and the mass of water.
Mass of sugar = 30 lbs
Mass of water = 2.5 gallons
First, let's convert the mass to grams for easier calculations:
Mass of sugar = 30 lbs * 454 g/lb = 13620 g
Mass of water = 2.5 gallons * 3.7854 L/gallon * 1000 g/L = 9463.5 g
Total mass of the solution = Mass of sugar + Mass of water = 13620 g + 9463.5 g = 23083.5 g
Mass percent of sugar = (Mass of sugar / Total mass of the solution) * 100
Mass percent of sugar = (13620 g / 23083.5 g) * 100 ≈ 59.05%
Therefore, the mass percent of sugar in the solution is approximately 59.05%.
2. Molarity:
Molarity (M) is the number of moles of solute (sugar) per liter of solution.
Number of moles of sugar = Mass of sugar / Molecular weight of sugar
Number of moles of sugar = 13620 g / 342.3 g/mol = 39.83 mol
Volume of solution = 2.5 gallons * 3.7854 L/gallon = 9.46 L
Molarity of the solution = Number of moles of sugar / Volume of solution
Molarity of the solution = 39.83 mol / 9.46 L ≈ 4.21 M
Therefore, the molarity of the solution is approximately 4.21 M.
3. Molality:
Molality (m) is the number of moles of solute per kilogram of solvent (water, in this case).
Mass of water = 2.5 gallons * 3.7854 L/gallon * 1000 g/L = 9463.5 g = 9.4635 kg
Molality of the solution = Number of moles of sugar / Mass of water
Molality of the solution = 39.83 mol / 9.4635 kg = 4.21 m
Therefore, the molality of the solution is approximately 4.21 m.
4. Mole Fraction:
Mole fraction is the ratio of the number of moles of a component (sugar) to the total number of moles in the solution.
Total number of moles in the solution = Number of moles of sugar (39.83 mol)
Mole fraction of sugar = Number of moles of sugar / Total number of moles in the solution
Mole fraction of sugar = 39.83 mol / 39.83 mol = 1
Therefore, the mole fraction of sugar in the solution is 1.
In summary, the solution contains:
- Mass percent of sugar: approximately 59.05%
- Molarity of the solution: approximately 4.21 M
- Molality of the solution: approximately 4.21 m
- Mole fraction of sugar: 1