Saccharin C7H5NO3S MW 1832 gmol is an artificial sweetener

Saccharin, C7H5NO3S, MW = 183.2 g/mol, is an artificial sweetener now known to be carcinogenic. When 19.2 grams of saccharin are added to 172.3 grams of ethanol, 46.08 g/mol, the vapor pressure of the solution at 25°C is measured to be 53.19 mmHg. What is the vapor pressure of ethanol at 25°C in mmHg?

Solution

moles of saccharin = 19.2 g / (183.2 g/mol) = 0.1048 mol

moles of ethanol = 172.3 g / (46.08 g/mol) = 3.73915 mol

now

total moles = moles of saccharin + moles of ethanol

total moles = 0.1048 mol + 3.73915 mol

total moles = 3.84395 mol

now

mole fraction of ethanol = moles of ethanol / total moles

mole fraction of ethanol = 3.73915 mol / 3.84395 mol

mole fraction of ethanol = 0.97273

now

vapor pressure of solution = mole fraction of ethanol x vapor pressure of pure ethanol

53.19 mm Hg = 0.97273 x vapor pressure of ethanol

vapor pressure of ethanol = 54.68 mm Hg