If a solution is made by adding 0.100 mole of ethyl ether to 0.841 mole of ethyl alcohol. If the vapor pressure of ethyl ether and ethyl alcohol at 20oC are 375 torr and 20.0 torr, respectively, the vapor pressure of the solution at 20oC ..is how many torr?
To find the vapor pressure of the 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.
First, let's calculate the mole fraction of the solvent (ethyl alcohol) in the solution:
Mole fraction of ethyl alcohol (X₁) = moles of ethyl alcohol / total moles of solution
X₁ = 0.841 mole / (0.841 mole + 0.100 mole)
X₁ = 0.841 / 0.941
X₁ = 0.894
Next, let's calculate the mole fraction of the solute (ethyl ether) in the solution:
Mole fraction of ethyl ether (X₂) = moles of ethyl ether / total moles of solution
X₂ = 0.100 mole / (0.841 mole + 0.100 mole)
X₂ = 0.100 / 0.941
X₂ = 0.106
Now, we can use Raoult's Law to find the vapor pressure of the solution:
Vapor pressure of solution = X₁ * P₁ + X₂ * P₂
P₁ = vapor pressure of ethyl alcohol = 20.0 torr
P₂ = vapor pressure of ethyl ether = 375 torr
Vapor pressure of solution = (0.894 * 20.0) + (0.106 * 375)
Vapor pressure of solution = 17.88 + 39.75
Vapor pressure of solution = 57.63 torr (rounded to two decimal places)
Therefore, the vapor pressure of the solution at 20oC is approximately 57.63 torr.