Calculate the volume of solution that has a vapour pressure of 25.8 mbar and contains 200.3 g of galactose, C6H12O6, at a temperature of 22.0 °C. The vapour pressure of pure water at 22 °C
is 26.40 mbar, the density of water is 1.00 g mL-1, and assume no change in volume occurs upon dissolution.
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To calculate the volume of the solution, we need to use Raoult's law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent in the solution.
First, let's find the mole fraction of water in the solution. We know the mass of galactose, so we can calculate the mass of water using the total mass of the solution (200.3 g) minus the mass of galactose.
Mass of water = Total mass of the solution - Mass of galactose
Mass of water = 200.3 g - 200.3 g = 0 g
Since the mass of water is 0 g, it means that all of the solution is composed of galactose, and there is no water present. Therefore, the mole fraction of water is 0.
Now, let's calculate the volume of the solution.
Density of water = 1.00 g mL^-1
Mass of water = 0 g
Using the formula:
Volume = Mass / Density
Volume of the solution = Mass of galactose / Density
Volume of the solution = 200.3 g / 1.00 g mL^-1
Volume of the solution = 200.3 mL
To calculate the volume of the solution, we first need to determine the amount of galactose in moles. Then, we can use the density of water to convert the mass of galactose to volume. Lastly, we will take into consideration the molar fraction of galactose in the solution to calculate the total volume.
1. Determine the moles of galactose:
To calculate the number of moles of galactose, we can use the molar mass of galactose, which is 180.16 g/mol.
Number of moles of galactose = mass / molar mass
= 200.3 g / 180.16 g/mol
= 1.11 mol
2. Calculate the volume of galactose:
Since the density of water is 1.00 g/mL, we can assume that 200.3 g of galactose has the same volume.
Volume of galactose = mass of galactose
= 200.3 mL
3. Calculate the mol fraction of galactose:
The molar fraction is the ratio of moles of solute (galactose) to the total moles of solute and solvent (water).
Molar fraction of galactose = moles of galactose / (moles of galactose + moles of water)
The moles of water can be calculated using the molar mass of water, which is 18.02 g/mol:
Moles of water = mass of water / molar mass of water
= 200.3 g / 18.02 g/mol
= 11.11 mol
Molar fraction of galactose = 1.11 mol / (1.11 mol + 11.11 mol)
= 0.0917
4. Calculate the total volume of the solution:
Now, we can calculate the total volume of the solution using the molar fraction of galactose and the volume of galactose:
Total volume of solution = Volume of galactose / Molar fraction of galactose
= 200.3 mL / 0.0917
≈ 2185 mL
Therefore, the volume of the solution is approximately 2185 mL.