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  4. Mole fraction of A in H2O is 0.2. The molality of A in H2O is

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

Some Basic Concepts of Chemistry

Solution:

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 $= \frac{n_{A}\,\times\,1000}{n_{H_2O}\,\times\,18} = \frac{X_{A}\,\times \,1000}{X_{H_2O}\,\times \,18}$
$= \frac{0.2\,\times \,1000}{0.8\,\times \,18} 13.9$