Calculate the vapor pressure of a solution of 33.0 g of gylcerol (C3H8O3) in 500g of water at 25 degrees C. the vapor pressure of water at 25 degrees C is 23.76 torr
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To calculate the vapor pressure of a solution, we need to 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.
First, we need to calculate the mole fraction of water and glycerol in the solution.
1. Calculate the moles of water:
Moles of water = mass of water / molar mass of water
= 500 g / 18.015 g/mol
= 27.76 mol
2. Calculate the moles of glycerol:
Moles of glycerol = mass of glycerol / molar mass of glycerol
= 33.0 g / 92.09 g/mol
= 0.358 mol
3. Calculate the mole fraction of water:
Mole fraction of water = Moles of water / (Moles of water + Moles of glycerol)
= 27.76 mol / (27.76 mol + 0.358 mol)
= 0.987
4. Calculate the mole fraction of glycerol:
Mole fraction of glycerol = Moles of glycerol / (Moles of water + Moles of glycerol)
= 0.358 mol / (27.76 mol + 0.358 mol)
= 0.013
Now we can use Raoult's law to calculate the vapor pressure:
Vapor pressure of solution = mole fraction of water * vapor pressure of water
Vapor pressure of solution = 0.987 * 23.76 Torr
= 23.46 Torr
Therefore, the vapor pressure of the solution of glycerol in water at 25 degrees C is 23.46 Torr.