The vapor pressure of water at 25.0 oc is 23.8 torr. determine the mass of glucose (molar mass = 180. g/mol) needed to add to 27.78 moles of water to make a solution that has a vapor pressure of 23.1 torr.

According to the formula of vapor pressure:

Pv(solu) = n P°v(water)
when we have Pv(solu) = 23.1 torr & Pv(water) = 23.8 torr so we can get the mole fraction of water (n)
∴ n = Pv(solu) / Pv(water)
      = 23.1 / 23.8 = 0.97 mol
when mole fraction of water = moles of water / (moles of water + moles of glucose)
So by substitution::
0.97 = 27.78 / (27.78+ X)
∴moles of gulcose = 0.85 mol
∴ mass of glucose = no.of moles * molar mass
                                = 0.85 * 180 = 152 g

The answer is 323 g.