A bottle of whiskey contains 12% aqueous ethanol by volume. The density of ETHANOL is 0.8 g/cm^3.
Calculate a) Molality b) Molarity c) W/W%
Answers
Answer:
The first thing you need to do is determine exactly how much ethanol your 1-L sample contains.
Since you're dealing with a 50% v/v solution, you'll get 50 mL of ethanol for every 100 mL of solution, which means that you have
%v/v
=
volume of ethanol
volume of solution
⋅
100
%50
=
V
ethanol
1000 mL
⋅
100
⇒
V
ethanol
=
50
⋅
1000 mL
100
=
500 mL
Use the density of ethanol to determine how many grams you have in the 1-L sample
ρ
=
m
V
⇒
m
=
ρ
⋅
V
m
ethanol
=
0.79
g
mL
⋅
500
mL
=
395 g ethanol
Use ethanol's molar mass to determine how many moles you have
395
g
⋅
1 mole
46.068
g
=
8.57 moles ethanol
Since molarity is defined as moles of solute divided by liters of solution, you'll get
C
=
n
V
C
=
8.57 moles
1 L
=
8.6 M
To get the mole fraction of ethanol, you need to determine how many moles of water you have in the 1-L sample.
Since you have 500 mL of ethanol in the 1-L bottle, you'll of course also have 500 mL of water. Use water's density and its molar mass to determine how many moles you have
m
water
=
1
g
mL
⋅
500
mL
=
500 g water
500
g
⋅
1 mole
18.015
g
=
27.8 moles water
The total number of moles present in the solution will be
n
total
=
n
ethanol
+
n
water
n
total
=
8.57
+
27.8
=
36.4 moles
The mole fraction of ethanol will be
χ
ethanol
=
n
ethanol
n
total
=
8.57
moles
36.4
moles
=
0.24
Molality is defined as moles of solute per kilogram of solvent, so you'll get
b
=
n
ethanol
kg of water
b
=
8.57 moles
500
⋅
10
−
3
kg
=
17 molal
Answer:
all the answer with explanation in the image
