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
