The vapor pressure of water above a sugar water solution at 25.0 degrees C is 21.4 mmHg. What is the mole fraction of sugar in the solution? (assume sugar is a non-electrolyte, non-volatile solute and the vp of pure water at 25 degrees C is 23.8 mmHg)
help, how do i solve this? thanks
delta Psolvent = Xsolute*Posolvent
To solve this problem, you 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.
In this case, the solvent is water and the vapor pressure of pure water at 25 degrees Celsius is given as 23.8 mmHg. The vapor pressure of the water in the solution (P_water solution) is 21.4 mmHg.
Using Raoult's law, we can write the equation as follows:
P_water solution = X_water * P_water
where X_water is the mole fraction of water in the solution.
Knowing that the sugar is a non-volatile solute, we can assume that its vapor pressure is negligible compared to water, and therefore, the mole fraction of sugar (X_sugar) can be considered zero.
Since the total mole fraction of the solution (X_total) should add up to 1, we have:
X_total = X_water + X_sugar
Substituting X_sugar as zero, we find:
X_total = X_water + 0
Therefore,
X_total = X_water
Now, we can rearrange the equation to solve for X_water:
X_water = P_water solution / P_water
Plugging in the given values:
X_water = 21.4 mmHg / 23.8 mmHg
Calculating this:
X_water = 0.8966
Hence, the mole fraction of water in the solution is approximately 0.8966. Since the mole fraction of sugar is assumed to be zero, the mole fraction of sugar in the solution would be (1 - 0.8966) = 0.1034.