Question

The mole fraction of methanol in an aqueous solution is 0.02 and density is 94g per cm^3. Find the molality

Answer 1

Mole fraction = 0.02 means
To find: Molarity and molality
Solve:
Relation between mole fraction of solute (x_b)and molality is

x_b = (m$\times$MM(solvent)) / (1000 + m$\times$MM(solvent))
Molar mass of solvent = 18 g mol^-1
By putting all the values we get

$$\begin{gathered} 0.02=\frac{m\times 18}{1000+m\times 18} \\ 0.02(1000+m\times 18)=m\times 18 \\ 0.02\times 1000=m\times 18(1-0.02) \\ m=\frac{20}{18\times 0.98} \\ m=1.13 \end{gathered}$$

Molality of solution = 1.13 m

Relation between molality and molarity is given as

Molality = (1000 $\times$ Molarity) / (1000$\times$ density(solute)) - (Molarity $\times$ Molecular Mass (solute))

Molar mass of CH₃OH = 32 g mol^-1
Density of CH₃OH = 0.994 g mL^-1

By putting all the values we get

$$\begin{gathered} 1.13=\frac{1000\times M}{1000\times 0.994-M\times 32} \\ 1.13(1000\times 0.994-M\times 32)=1000\times M \\ 1123.22=1000\times M(36.16+1) \\ M=\frac{1123.22}{37.16\times 1000} \\ M=0.03 \end{gathered}$$

Thus molarity of solution = 0.03 M.