A company that manufactures wines claim that red wine contains 14.1% by volume of ethanol ( density of ethanol is 0.789g/ cm³) . Calculate the following: molality of ethanol, molarity of ethanol, % by mass of ethanol, ppm and ppb by mass of ethanol.
To calculate the molality of ethanol:
First, we need to convert the volume percent of ethanol to weight percent. Using the density of ethanol, we can convert the volume percent to weight percent:
Volume of ethanol in 100 mL of red wine = 14.1 mL
Mass of ethanol in 100 mL of red wine = 14.1 mL * 0.789 g/mL = 11.109 g
Now, we can calculate the molality of ethanol:
Mass of ethanol = 11.109 g
Molar mass of ethanol = 46.07 g/mol
Mass of solvent (water) = 100 g (since we are assuming the density of water is 1 g/mL)
Molality = (11.109 g / 46.07 g/mol) / 0.1 kg = 0.241 mol/kg
Next, to calculate the molarity of ethanol, we need to consider the volume of the entire solution (not just the ethanol) and calculate the number of moles of ethanol in that volume:
Volume of red wine = 100 mL
Molarity = (11.109 g / 46.07 g/mol) / (100 mL / 1000) L = 0.0241 mol/L
To calculate the % by mass of ethanol in red wine:
% by mass = (11.109 g / 100 g) * 100% = 11.109%
To calculate the ppm by mass of ethanol in red wine:
ppm = (11.109 g / 1000 g) * 10^6 = 11109 ppm
To calculate the ppb by mass of ethanol in red wine:
ppb = (11.109 g / 1000 g) * 10^9 = 11109000 ppb
Therefore, the molality of ethanol in the red wine is 0.241 mol/kg, the molarity is 0.0241 mol/L, the % by mass is 11.109%, the ppm is 11109 ppm, and the ppb is 11109000 ppb.