Since October 2004, Jack Daniels Tennessee whisky, produced in Lynchburg, TN, has been bottled at 80 proof (40% alcohol by volume). Given that the density of ethyl alcohol is 0.789 g/cm3, and that of water 1.00 g/cm3, calculate the concentration of the alcohol in (a) percent by weight and (b) molarity (moles per liter).
40% v/v means 40 mL EtOH/100 mL soln.
For EtOH, 40 mL has a mass of 40 mL x 0.789 g/mL = ? grams.
?grams/molar mass EtOH = mols and mols/L = M. The volume is 100 mL which is 0.1 L.
For %w/w you have the conversion of 40 mL EtOH to grams. We want g EtOH/100 g soln. I think you need the density of the solution but you don't show it. We can estimate that 40% v/v means 40 mL EtOH/(40 mL EtOH + 60 mL H2O).
40 mL EtOH = about 31.6g in (31.6g + 60g) soln or (31.6/91.6)*100 = % w/w.
That isn't quite right because it is based on 40 mL EtOH + 60 mL H2O = 100 mL soln and that isn't right. Actually, it occupies only about 96 mL
To calculate the concentration of alcohol in percent by weight and molarity, we first need to determine the mass and volume of alcohol and water in the given solution.
(a) Percent by weight:
1. Calculate the mass of alcohol in the solution:
To find the mass of alcohol, we need to know the total volume of the solution and the density of alcohol.
Given:
Density of ethyl alcohol (ρ alcohol) = 0.789 g/cm³
Density of water (ρ water) = 1.00 g/cm³
We assume that the solution is a mixture of alcohol and water, with no other solutes.
The volume of alcohol (V alcohol) can be determined using the relationship:
V alcohol = V solution × (% alcohol by volume)
Jack Daniels Tennessee whisky is bottled at 80 proof, which means it is 40% alcohol by volume.
Thus, V alcohol = V solution × 0.40
The volume of water (V water) can be determined by subtracting the volume of alcohol from the total volume of the solution:
V water = V solution − V alcohol
2. Calculate the mass of alcohol and water:
The mass of alcohol (m alcohol) is given by:
m alcohol = V alcohol × ρ alcohol
The mass of water (m water) is given by:
m water = V water × ρ water
3. Calculate the percent by weight of alcohol:
Percent by weight = (m alcohol / (m alcohol + m water)) × 100
(b) Molarity:
To calculate the molarity (M) of the alcohol in the solution, we need to find the number of moles of alcohol present.
1. Calculate the moles of alcohol:
Moles of alcohol (n alcohol) = (m alcohol / molar mass of alcohol)
The molar mass of alcohol (C2H5OH) is approximately 46.07 g/mol.
2. Calculate the volume of the solution in liters (V solution):
V solution = V solution / 1000 (since it is given in cm³)
3. Calculate the molarity:
Molarity (M) = n alcohol / V solution
By following these steps, you should be able to calculate both the percent by weight and molarity of alcohol in the Jack Daniels Tennessee whisky.