Answer:
0.291
Explanation:
Given data
1070 torr × (1 atm/ 760 torr) = 1.41 atm
According to Raoult's law, the vapor pressure of a solvent above a solution is equal to the vapor pressure of the pure solvent at the same temperature scaled by the mole fraction of the solvent present.
Psolution = Psolvent × Χsolvent
Χsolvent = Psolution/Psolvent
Χsolvent = 1.00 atm/1.41 atm
Χsolvent = 0.709
The sum of the mole fraction of the solvent (water) and the solute (ethylene glycol) is 1.
Χsolvent + Χsolute = 1
Χsolute = 1 - Χsolvent = 1 - 0.709
Χsolute = 0.291
Considering the Roult's law, the mole fraction of ethylene glycol in the solution is 0.291
In first place, you know:
On the other side, if a solute has a measurable vapor pressure, the vapor pressure of its solution is always less than that of the pure solvent. Thus, the relationship between the vapor pressure of the solution and the vapor pressure of the solvent depends on the concentration of the solute in the solution.
In other words, Raoult's Law states that the relationship between the vapor pressure of each component in an ideal solution is dependent on the vapor pressure of each individual component and the mole fraction of each component in the solution.
Mathematically, this law expresses that in an ideal solution, the partial pressures of each component in the vapor are directly proportional to their respective molar fractions in the solution. That is, the partial pressure of a solvent on a solution P is given by the vapor pressure of the pure solvent, multiplied by the mole fraction of the solvent in the solution:
P1=x1P1°
where P1 is the partial pressure of a solvent over a solution, x1 is the mole fraction of the solution component, and P1 ° is the vapor pressure of the pure solvent.
In this case, for the solvent, you can calculate the mole fraction as:
Psolvent=xsolventPsolvent°
1 atm=xsolvent1.41 atm
1 atm÷1.41 atm= xsolvent
0.709 atm= xsolvent
The sum of the mole fraction of the solvent (water) and the solute (ethylene glycol) is 1.
xsolvent + xsolute = 1
xsolute = 1 - xsolvent
xsolvent= 1 - 0.709
xsolute = 0.291
Finally, the mole fraction of ethylene glycol in the solution is 0.291
Learn more about Raoul's Law:
