Question

Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is 0.040 (assume the density of water to be one).

Answer 1

Calculation of Molarity

• Molarity (M) of a solution is defined as the number of moles of solute per liter of solution.
  $\mathrm{Molarity}=\frac{\mathrm{no}.\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{litres}\mathrm{of}\mathrm{solution}}$

Step 1: Determination of the number of moles of ethanol and water
Moles of Ethanol = 0.04 Mol
Moles of Water = 1 - 0.04
Moles of Water = 0.96Mol

Step 2: Determination of the mass of ethanol and water
Number of moles = $\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Molar}\mathrm{mass}}$
$\mathrm{Mass}=\mathrm{number}\mathrm{of}\mathrm{moles}\times \mathrm{Molar}\mathrm{mass}$
Mass of water = $0.96\times 18$
Mass of water = 17.3 g
Mass of ethanol = $0.04\times 46$
Mass of ethanol = 1.84 g

Step 3: Determination of total mass of soluion
Total mass of the solution = 17.3 + 1.84
Total mass of the solution = 19.1 g

Step 4: Determination of volume
Density = 1g/mL (Assumed)
Density = $\frac{\mathrm{mass}}{\mathrm{volume}}$
Volume = $\frac{\mathrm{mass}}{\mathrm{density}}$
Volume = $\frac{19.1}{1}$
Volume = 19.1 mL
Volume = 0.0191 L

Determination of Molarity
Molarity = $\frac{0.04}{0.0191}$
Molarity = 2.1 M

Hence, the molarity of a solution of ethanol in water is 2.1M