Why would [23.8-(.0588)(23.8)] be the proper setup to determine the vapor pressure of a solution at 25 Celsius that has 45g of C6H12O6, glucose (MM=180gxmol^-1), dissolved in 72g of H2O? The vapor pressure of pure water at 25Celsius is 23.8 torr.

vp pure solvent - lowering due to glucose = vp pure solvent - (mole fraction glucose x vp pure solvent) =
Po- XglucosePo

mols glucose = 45/180 = 0.25
mols water = 72/18 = 4
total mols = 4.25
mols fraction glucose = X = 0.25/4.25 = 0.588
Po = 23.8

Note I omitted a zero.
That is 0.25/4.25 = 0.0588

thanks, you're really good at putting this in english

To determine the vapor pressure of the solution, we need to consider the lowering of vapor pressure caused by the presence of glucose in the water. The formula for this calculation is:

vp pure solvent - lowering due to glucose = vp pure solvent - (mole fraction glucose x vp pure solvent)

In this case, the pure solvent is water, which has a vapor pressure of 23.8 torr at 25 degrees Celsius.

To find the mole fraction of glucose, we first need to calculate the number of moles of glucose and water in the solution.

Starting with glucose:
Mass of glucose = 45g
Molar mass of glucose (MM) = 180g/mol

Number of moles of glucose = Mass of glucose / Molar mass of glucose = 45g / 180g/mol = 0.25 mol

Now, let's calculate the number of moles of water:
Mass of water = 72g
Molar mass of water = 18g/mol

Number of moles of water = Mass of water / Molar mass of water = 72g / 18g/mol = 4 mol

To calculate the mole fraction of glucose, divide the moles of glucose by the total moles of the solution:

Mole fraction of glucose (X) = Moles of glucose / Total moles = 0.25 mol / (0.25 mol + 4 mol) = 0.0588

Now we have all the necessary values to calculate the vapor pressure of the solution:

vp solution = vp pure solvent - (mole fraction glucose x vp pure solvent)
= 23.8 torr - (0.0588 x 23.8 torr)
= 23.8 torr - 1.39344 torr
= 22.40656 torr

Therefore, the vapor pressure of the solution at 25 degrees Celsius, with 45g of glucose dissolved in 72g of water, is approximately 22.40656 torr.