Answer :
Final answer:
To calculate the vapor pressure of a solution, we use Raoult's Law, which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent. Using the given information, we can calculate the vapor pressure of the solution as 23.33 torr.
Explanation:
To calculate the vapor pressure of a solution, we can use Raoult's Law which states that the vapor pressure of a solution is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent.
To begin, we need to find the mole fraction of water in the solution. The moles of water can be calculated using the formula moles = mass / molar mass. The molar mass of water is 18.015 g/mol.
Next, we can calculate the mole fraction of water by dividing the moles of water by the total moles in the solution (moles of water + moles of glycerol).
Finally, the vapor pressure of the solution can be calculated by multiplying the mole fraction of water by the vapor pressure of pure water.
Let's proceed with the calculations:
- Find the moles of water using moles = mass / molar mass = 500.0 g / 18.015 g/mol = 27.75 mol
- Find the moles of glycerol using moles = mass / molar mass = 46.5 g / 92.094 g/mol = 0.505 mol
- Calculate the mole fraction of water using mole fraction = moles of water / (moles of water + moles of glycerol) = 27.75 mol / (27.75 mol + 0.505 mol) = 0.9829
- Calculate the vapor pressure of the solution using vapor pressure of solution = mole fraction of water * vapor pressure of pure water = 0.9829 * 23.76 torr = 23.33 torr
Therefore, the vapor pressure of the solution is approximately 23.33 torr.
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