Question

Mole fraction of $A$ in $H_2O$ is $0.2.$ The molality of $A$ in $H_2O$ is

• A. $13.9$
• B. $15.5$
• C. $14.5$
• D. $16.8$

Answer 1

Answer: (A)

$13.9$

Answer 2

Mole fraction of $A$ i.e. $X_{A} = \frac{n_{A}}{Total\, moles}$ So $X_{H_2O} = \frac{n_{H_2O}}{Total \,moles}$ Now $\frac{X_{A}}{X_{H_2O}} = \frac{n_{A}}{n_{H_2O}}$ and molality $= \frac{n_{A}\,\times\,1000}{n_{H_2O}\,\times\,18} = \frac{X_{A}\,\times \,1000}{X_{H_2O}\,\times \,18}$ $= \frac{0.2\,\times \,1000}{0.8\,\times \,18} 13.9$