The vapor pressure of ethanol is 54.68 mm Hg at 25 °C. A nonvolatile, nonelectrolyte that dissolves in ethanol is saccharin. Calculate the vapor pressure of the solution at 25 °C when 8.054 grams of saccharin, C7H5NO3S (183.2 g/mol), are dissolved in 163.9 grams of ethanol. ethanol = CH3CH2OH = 46.07 g/mol. VP (solution) = ? mm Hg

The vapor pressure of the solution at 25°C is 54,01 mmHg

Explanation:

Let's solve this with the formula by the colligative property relative lowering of vapour pressure

ΔP = Psv°. X

where ΔP is Pressure sv pure - Pressure of the solution

and X means molar fraction for solute

54,68 mmHg - P sl = 54,68mmHg. X

X (molar fraction for solute) is

moles from solute / moles from solute + moles from solvent

Solute: Saccharin

Solvent: Ethanol

Moles = mass / molar mass

Moles for Saccharin: 8,054 g / 183,2 g/m = 0,0439 moles

Moles for ethanol: 163,9 g / 46,07 g/m = 3,55 moles

X (molar fraction for solute) is 0,0439 moles / 0,0439 moles + 3,55 moles

X = 0,0122

Let's go back - --> 54,68 mmHg - P sl = 54,68mmHg. 0,0122

54,68mmHg - P sl = 0,667 mmHg

54,68mmHg - 0,667 mmHg = P sl

54,01 mmHg = P sl.