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