A solution is made by mixing 37.0 mL of ethanol, C2H6O, and 63.0 mL of water.?

Assuming ideal behavior, what is the vapor pressure of the solution at 20 °C?

ethanol: 0.789 g/mL 43.9 torr
water : 0.998 g/mL 17.5 torr

.0213

To determine the vapor pressure of the solution, we need to know the mole fraction of each component in the solution. The mole fraction is a measure of the amount of moles of a component compared to the total moles in the solution.

First, let's calculate the number of moles of ethanol and water in the given volumes. We'll use the density and molecular weight of each component to convert from volume to mass to moles.

Given:
Volume of ethanol (V1) = 37.0 mL
Density of ethanol = 0.789 g/mL
Molecular weight of ethanol (M1) = 46.07 g/mol

Number of moles of ethanol (n1) = (Volume of ethanol / Density of ethanol) * (1 / Molecular weight of ethanol)
= (37.0 mL / 0.789 g/mL) * (1 mol / 46.07 g)
= 0.941 mol

Similarly, for water:
Volume of water (V2) = 63.0 mL
Density of water = 0.998 g/mL
Molecular weight of water (M2) = 18.015 g/mol

Number of moles of water (n2) = (Volume of water / Density of water) * (1 / Molecular weight of water)
= (63.0 mL / 0.998 g/mL) * (1 mol / 18.015 g)
= 3.501 mol

Now, we can compute the mole fractions of ethanol (x1) and water (x2):
Mole fraction of ethanol (x1) = n1 / (n1 + n2)
= 0.941 mol / (0.941 mol + 3.501 mol)
= 0.212 (rounded to three decimal places)

Mole fraction of water (x2) = n2 / (n1 + n2)
= 3.501 mol / (0.941 mol + 3.501 mol)
= 0.788 (rounded to three decimal places)

Finally, we can use the vapor pressure of pure ethanol and pure water to calculate the vapor pressure of the solution using Raoult's law. Raoult's law states that the vapor pressure of a component in a solution is equal to the product of its mole fraction and the vapor pressure of the pure component.

Vapor pressure of the solution = x1 * P1 + x2 * P2

Given:
Vapor pressure of pure ethanol (P1) = 43.9 torr
Vapor pressure of pure water (P2) = 17.5 torr

Vapor pressure of the solution = (0.212 * 43.9 torr) + (0.788 * 17.5 torr)
= 9.31 torr + 13.79 torr
= 23.10 torr

Therefore, the vapor pressure of the solution at 20 °C is approximately 23.10 torr.

Use density to convert volume ethanol and volume H2O to grams.

mols ethanol = grams/molar mass
mols H2O = grams/molar mass

Xethanol = nethanol/total mols.
XH2O = nH2O/total mols.

pethanol = Xethanol*Po ethanol
pH2O = XH2O*Po H2O.

Total P solution = pH2O + pethanol.

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