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.
I do not understand what steps to take in order to solve this question can you please walk me through this
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To solve this question, we can use Raoult's law, which states that the vapor pressure of a solvent above a solution is directly proportional to the mole fraction of the solvent in the solution.
Step 1: Convert the given density of water to moles.
The density of water is given as 1.00 g mL-1. Since the formula mass of water is approximately 18 g/mol, we can calculate the number of moles using the formula:
moles of water = mass of water / molar mass of water
moles of water = 200.3 g / 18 g/mol
moles of water = 11.1278 mol
Step 2: Calculate the mole fraction of the solvent (water).
The mole fraction (X) of the solvent (water) is calculated by dividing the moles of the solvent by the total number of moles of all components in the solution. Since we are assuming no change in volume upon dissolution, the total moles in the solution only consist of the moles of water.
mole fraction of water (Xwater) = moles of water / moles of water
mole fraction of water (Xwater) = 11.1278 mol / 11.1278 mol
mole fraction of water (Xwater) = 1
Step 3: Calculate the mole fraction of the solute (galactose).
Since we are assuming no change in volume upon dissolution, the moles of the solute remain the same as given, which is 200.3 g of galactose.
mole fraction of galactose (Xgalactose) = moles of galactose / moles of water
mole fraction of galactose (Xgalactose) = (200.3 g / molar mass of galactose) / moles of water
Step 4: Calculate the vapor pressure of the solvent (water) above the solution.
According to Raoult's law, the vapor pressure of the solvent above the solution is directly proportional to its mole fraction. We can calculate the vapor pressure of water above the solution using the equation:
vapor pressure of water above solution = mole fraction of water * vapor pressure of pure water
vapor pressure of water above solution = Xwater * vapor pressure of pure water
vapor pressure of water above solution = 1 * 26.40 mbar
vapor pressure of water above solution = 26.40 mbar
Step 5: Calculate the volume of the solution.
Now that we know the vapor pressure of the solution, we can use the vapor pressure to find the volume of the solution using the equation:
volume of solution = mass of solvent / (density of solvent * vapor pressure of solvent above solution)
volume of solution = moles of water * molar mass of water / (density of water * vapor pressure of water above solution)
Substituting the obtained values:
volume of solution = 11.1278 mol * 18 g/mol / (1.00 g/mL * 26.40 mbar)
Be careful with the units. In this case, we need to convert grams to milliliters and mbar to milliliters by multiplying by the appropriate conversion factors.
Finally, you will have the value for the volume of the solution in milliliters.