Question

Water is slightly soluble in liquid nitrogen. At$\mathbf{-}{\mathbf{196}}^{\mathbf{0}}\mathbf{C}$(the boiling point of liquid nitrogen), the mole fraction of water in a saturated solution is$\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}$. Compute the mass of water that can dissolve in 1.00kgof boiling liquid nitrogen.

Short answer

The mass of water that can dissolve in 1.00kg of boiling liquid nitrogen is 0.00642g.

Step-by-step solution

The concept of mole fraction

Calculate the number of moles of nitrogen and water

The no. of moles is calculated as: $n=\frac{Givemass\left(m\right)}{Molarmass\left(M\right)}$

The no. of moles of nitrogen is calculated as:

$\begin{array}{l}n\left(N\right)=\frac{1\times {10}^3}{14.01}\\ n\left(N\right)=71.43\mathrm{g}/\mathrm{mol}\end{array}$

The number of moles of water is calculated as: $nwater=\frac{m}{18.02}$

This m mass of water is to be determined.

Calculate the mass of water 

Determine the actual mass of water that can dissolve in given mass of liquid nitrogen