Question

Calculate the molarity and molality of 20% of aqueous ethanol (${{C}_{2}}{{H}_{5}}OH$) solution by volume (Density of solution =0.96g/mL)
(A) Molarity = 3.48, Molality = 4.35
(B) Molarity = 4.35, Molality = 3.48
(C) Molarity = 4.48, Molality = 3.35
(D) None of the above

Answer 1

Hint: Morality (M) is defined as the number of moles of solute dissolved in one litre of solution.
Molality (m) is defined as the number of moles of the solute per kilogram of the solvent.

Complete answer:
Given, density of solution = 0.96 g/ml
Density of ethanol (solute) = 0.789 g/ml
20% aqueous ethanol solution by volume,
Hence, 20 mL of ethanol is present in 100 mL solution.
So, the volume of the solution (V) = 100 mL
Volume of ethanol (solute) = 20 mL
Calculation the mass of solution:
Mass of solution = density of solution x volume of the solution
                           m1 = $0.96g/mLX100mL$=96 g ---(1)
Calculation of mass of solute (ethanol):
Mass of solute = density of solute X volume of the solution
          m2= $0.789g/mLX 20mL$= 15.78 g ---(2)
Calculation of mass of solvent:
Mass of solvent = mass of solution – mass of solute
From (1) and (2) , Mass of solvent(m3) = 96-15.78= 80.22 g --(3)
calculation of molarity of solution (M):
Molar mass of solute (mW) ${{C}_{2}}{{H}_{5}}OH$= 46g/mol
Molarity (M) = $\dfrac{15.78gX1000}{46g/molX100mL}$ = $\dfrac{15.78gX 1000}{46g/molX 100mL}$= 3.4304 mol/L -- (4)
Calculation of molality of a solution:
Molality (m) = $\dfrac{15.78X1000}{46X80}=4.288mole/Kg\cong 4.3mole/Kg$
Hence the molarity of 20% aqueous ethanol is = 3.4304 mol/L
The molality of 20% aqueous ethanol solution is = 4.3 moles/Kg

The correct option is A.

Note:
If any problems are these types of solutions, then convert the percentage into volume, for example, 20% aqueous ethanol means 20mL of ethanol solute in 100 mL solution. The relation between molarity and molality is that multiplying the molarity by the volume of the solution to get the number of moles of solute, then dividing by the mass of the solution to get molarity.