Final answer:
To find the mole fraction of sugar in the solution, divide the vapor pressure of the sugar solution by the total vapor pressure of the solution. Mole fraction of sugar = 0.448
Step-by-step explanation:
To find the mole fraction of sugar in the solution, we need to use the concept of Raoult's law. Raoult's law states that the mole fraction of a component in a solution is equal to the vapor pressure of the component divided by the total vapor pressure of the solution.
In this case, the vapor pressure of the sugar solution is given as 7.84 mm Hg and the total vapor pressure can be assumed to be equal to the vapor pressure of pure water, which is 17.5 mm Hg at 20 °C. Therefore, the mole fraction of sugar (fructose) can be calculated as:
mole fraction of sugar = vapor pressure of sugar solution / total vapor pressure
mole fraction of sugar = 7.84 mm Hg / 17.5 mm Hg
mole fraction of sugar = 0.448