Question

A solid solution is made up of two solids "A" and "B". Mass percentage of "A" is 40% by mass in a solid solution. Find the molar mass of "B" if the mole fraction of "A" $\left(x_A\right)\text{is 0.20}$ and molar mass of "A" is 200 g/mol.

• A. $75g/mol$
• B. $60g/mol$
• C. $80g/mol$
• D. $85g/mol$

Answer 1

The correct option is A $75g/mol$

Taking 100 g of the solid solution,
Mass of A and B present in 100 g solution = 40 g, 60 g respectively.
$\text{Mole fraction of A}\left(x_A\right)=\frac{n_A}{n_A+n_B}=0.2$
By using mass-mole relationship $\to \text{Number of moles}=\frac{mass}{Molarmass}$ we get
$x_A=\frac{\frac{40}{200}}{\frac{40}{200}+\frac{60}{M_B}}=0.2$
$M_B=75g/mol$