Question

Vodka is advertised to be 80 proof, which is 40% by volume of ethanol, C2H5OH. Assuming the density of the solution is 1.0 g/mL and the density of ethanol is 0.789 g/mL. If the solution is at 25oC, what is the vapor pressure of water over the solution?

Please show all work with the correct answer. Thank you!!!!!!!

Answer 1

Find vapor pressure of solution at T = 25°C

Assume a basis of:

100 mL:

calculate volumes of each species:

100 mL *(40%/100%) = 40 mL= --> alcohol

100 mL *(60%/100%) = 60 mL= --> water

Recall that the density formula is:

D = mass/ Volume

so

mass = D*V

so

mass of alcohol = 0.789 g/mL *40 mL = 31.56 g of alcohol

mass of water = 1.0 g/mL *60 mL= 60 g of water

calculate moles:

MW of ethanol = 46.06844 g/mol

mol of alcohol = mass/MW = 31.56/46.06844 = 0.6850

MW of ethanol = 46.06844 g/mol

mol of water = mass/MW = 60/18.00 = 3.333333

x-water = 3.333333 / (3.333333 +0.6850) = 0.8295

x-ethanol = 1-x-water = 1- 0.8295 = 0.171

Vapor pressure of ethanol ( T= 25°C) = 5.95 kPa

Vapor pressure of water ( T= 25°C) = 3.1690 kPa

Apply colligative porperties

x1*P° + x2*P° = Pvapor

0.171*5.95 kPa + 0.8295*3.1690 kPa = Pmix

Pmix = 3.6461 kPa