Question

16) Ethanol, CHsO, is produced by the fermentation of sugars in wine and beer. Given that ethanol has a molecular weight of 46.07 g/mol and a density of 0.789 g/em answer the following questions: a) How many mL of ethanol are consumed in a 12 oz. glass of red wine that contains 13.4 % ABV? Note: ABV stands for alcohol (ethanol) by volume. You must use the following conversion factors in your calculation: 128 oz- 1 gal; 1 gal 3.785 L b) How many molecules of ethanol would be in this glass of wine? c) What is the molarity of ethanol in the 12 oz glass of wine?

Answer 1

a)

Volume of 12oz glass = 12 oz * 1 gal /128 oz * 3.785 L / 1 gal

= 0.35584 L = 355.84 mL

Volume of ethanol = 13.4 * 355.84 / 100

= 47.55 mL

b)

Mass of ethanol = Volume of ethanol * Density of ethanol

= 47.55 mL * 0.789 g /mL

= 37.5 g

Moles of ethanol present = Mass of ethanol / MW of ethanol

= 37.5 g / 46.07 g/mol

= 0.81

Molecules of ethanol = N_A * Moles of ethanol present

= 6.022 x 10²³ * 0.81

= 4.9 x 10²³

c)

Molarity of ethanol = Moles of ethanol / Total Volume (L)

= 0.81 / 0.35584 L

= 2.3 M

d)

Mass of polyphenols = 0.35584 L * 2.568 g / L

= 0.91 g

MW of C₃₄H₂₈O₂₂ = 34 * 12 + 1 * 28 + 16 * 22 = 788 g/mol

Moles of polyphenols = 0.91 / MW of C₃₄H₂₈O₂₂

= 0.00116

Volume of water in wine glass = 355.84 mL - 47.55 mL

= 307.3 mL

Mass of water in wine glass = 307.3 mL * 1 g/mL = 307.3 g

Moles of water in wine glass = 307.3 g / 18 g/mol

= 17.07

Mole fraction of ethanol, X = Moles of ethanol / Total moles of all components

= 0.81 / (0.81 + 0.00116 + 17.07)

= 0.0455

Pure ethanol vapor pressure, P⁰ = 7.869 kPa

Vapor pressure just due to ethanol = P⁰ * X

= 7.869 kPa * 0.0455

= 0.36 kPa