A solution of fructose, C6H12O6, a sugar found in many fruits, is made by dissolving 22.0 g of fructose in 1.00 kg of water. What is the molal concentration of fructose the solution? What is the mole fraction of fructose in the solution? What is the mass percent of fructose in the solution? What is the molarity of the fructose solution if the density of the solution is 1.0078 g/mL?

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To find the molal concentration of fructose in the solution, we need to calculate the number of moles of fructose and the mass of water used.

1. Calculate the number of moles of fructose:
The molar mass of fructose (C6H12O6) is calculated as follows:
(6 * atomic mass of carbon) + (12 * atomic mass of hydrogen) + (6 * atomic mass of oxygen)
= (6 * 12.01 g/mol) + (12 * 1.01 g/mol) + (6 * 16.00 g/mol)
= 72.06 g/mol + 12.12 g/mol + 96.00 g/mol
= 180.18 g/mol

Now, we can calculate the number of moles of fructose:
Number of moles = Mass / Molar mass
Number of moles = 22.0 g / 180.18 g/mol
Number of moles ≈ 0.122 mol

2. Calculate the mass of water used:
Mass of water = 1.00 kg = 1000 g

Now that we have the number of moles of fructose and the mass of water, we can calculate the molal concentration:

Molal concentration = Number of moles / Mass of solvent (in kg)
Molal concentration = 0.122 mol / 1.00 kg
Molal concentration = 0.122 mol/kg

To find the mole fraction of fructose in the solution, we need to consider the total number of moles in the solution.

Total moles in the solution = Number of moles of fructose + Number of moles of water
Total moles in the solution = 0.122 mol + (mass of water / molar mass of water)

The molar mass of water (H2O) is 18.02 g/mol.

Total moles in the solution = 0.122 mol + (1000 g / 18.02 g/mol)
Total moles in the solution = 0.122 mol + 55.50 mol
Total moles in the solution = 55.62 mol

Mole fraction of fructose = Number of moles of fructose / Total moles in the solution
Mole fraction of fructose = 0.122 mol / 55.62 mol
Mole fraction of fructose ≈ 0.0022

To find the mass percent of fructose in the solution, we need to calculate the mass of fructose and the total mass of the solution.

Mass of fructose = 22.0 g
Total mass of the solution = Mass of fructose + Mass of water
Total mass of the solution = 22.0 g + 1000 g
Total mass of the solution = 1022.0 g

Mass percent of fructose = (Mass of fructose / Total mass of the solution) * 100
Mass percent of fructose = (22.0 g / 1022.0 g) * 100
Mass percent of fructose ≈ 2.16%

Lastly, to find the molarity of the fructose solution, we need to calculate the number of moles of fructose and divide it by the volume of the solution. We can find the volume using the given density.

Number of moles of fructose is already calculated as 0.122 mol.

Given the density of the solution as 1.0078 g/mL, we can calculate the volume of the solution:

Volume of the solution = Mass of the solution / Density of the solution
Volume of the solution = 1022.0 g / 1.0078 g/mL
Volume of the solution ≈ 1013.9 mL

Now, convert the volume to liters:
Volume of the solution = 1013.9 mL * (1 L / 1000 mL)
Volume of the solution ≈ 1.0139 L

Molarity = Number of moles / Volume (in L)
Molarity = 0.122 mol / 1.0139 L
Molarity ≈ 0.120 M

Therefore, the molal concentration of fructose in the solution is 0.122 mol/kg, the mole fraction of fructose in the solution is approximately 0.0022, the mass percent of fructose in the solution is about 2.16%, and the molarity of the fructose solution is approximately 0.120 M.