Mole Fractions, Partial Pressures, and Total Pressure Calculation

Step 1 of 3

a)

The mole fraction of any component in a solution is the number of moles of the component divided by the total number of moles making up a solution. It is denoted by “X”.  

\(\begin{aligned} \text { Mole fraction }(X) & =\frac{\text { Moles of component }}{\text { Total number of moles making up the solution }} \\ X_{\text {Soluie }}+X_{\text {Solvent }} & =1 \end{aligned}\)

From the given,

Moles of hydrogen = 1.5 mol

Moles of nitrogen = 2.5 mol

Let’s calculate the mole fraction of hydrogen;                                    

\(\begin{aligned} X_{H_{2}} & =\frac{\text { Moles of hydrogen }}{\text { Total moles of solution }} \\ & =\frac{1.5 \mathrm{~mol}}{1.5 \mathrm{~mol}+2.5 \mathrm{~mol}}=0.375 \end{aligned}\)

Hence, the mole fraction of hydrogen is 0.375.

Let’s calculate the mole fraction of nitrogen;

\(\begin{array}{l}\text{Mole fraction of Nitrogen }\left(X_{N_2}\right)+\text{ Mole fraction of Nitrogen }\left(X_{H_2}\right)=1\\ \text{Mole fraction of Nitrogen }\left(X_{N_2}\right)=1-\text{ Mole fraction of Hydrogen }\left(X_{H_2}\right)\\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =1-0.375=0.625\end{array}\)

Hence, the mole fraction of nitrogen is 0.625.