Glycerin, C3H8O3, is a nonvolatile liquid. What is the vapor pressure of a solution made by adding 164 g of glycerin to 325 mL of H2O at 39.8°C? The vapor pressure of pure water at 39.8°C is 54.74 torr and its density is 0.992 g/cm3.

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Psoln = XH2O*PoH2O

Calculate moles glycerin. moles = grams/molar mass

Calculate moles H2O. Use density to obtain mass, then moles = grams/molar mass.

X = mole fraction H2O = mols H2O/total moles.
Psoln = XH2O*PoH2O

49.958torr

To calculate the vapor pressure of the solution, we need to calculate the mole fraction of glycerin in the solution. The formula for mole fraction (χ) is:

χ = (moles of glycerin) / (moles of glycerin + moles of water)

First, let's calculate the moles of glycerin:
moles of glycerin = (mass of glycerin) / (molar mass of glycerin)

The molar mass of glycerin (C3H8O3) is:
(3 x atomic mass of C) + (8 x atomic mass of H) + (3 x atomic mass of O)
= (3 x 12.01 g/mol) + (8 x 1.01 g/mol) + (3 x 16.00 g/mol)
≈ 92.09 g/mol

So, moles of glycerin = 164 g / 92.09 g/mol

Next, let's calculate the moles of water:
moles of water = (volume of water) / (density of water) x (1 cm3 / 1 mL) x (1 L / 1000 cm3) x (mol of water / 18.02 g)

The volume of water is given as 325 mL, so:
moles of water = 325 mL x (1 L / 1000 mL) / (density of water) x (1 cm3 / 1 mL) x (1 L / 1000 cm3) x (mol of water / 18.02 g)

Substituting the given density of water (0.992 g/cm3) and molar mass of water (18.02 g/mol):
moles of water = 325 mL x (1 L / 1000 mL) / (0.992 g/cm3) x (1 cm3 / 1 mL) x (1 L / 1000 cm3) x (mol of water / 18.02 g)

Now that we have the moles of glycerin and water, we can calculate the mole fraction:
χ = (moles of glycerin) / (moles of glycerin + moles of water)

Next, we can use the equation for Raoult's law to calculate the vapor pressure of the solution:
P_solution = χ * P_water

Here, P_solution is the vapor pressure of the solution and P_water is the vapor pressure of pure water (54.74 torr).

Finally, we substitute the calculated values into the equation to find the vapor pressure of the solution.