Question

A gaseous mixture of ${\mathrm{H}}_2$ and ${\mathrm{NH}}_3$ gas contains 68 mass % of ${\mathrm{NH}}_3$. The vapour density of the mixture is?

Answer 1

Step 1: Calculate the mass of ${\mathrm{H}}_2$

Assuming the mixture is of $100\mathrm{g}$

Given that ${\mathrm{NH}}_3$has 68 mass % $=68\mathrm{g}$

$\therefore$We can write that mass of ${\mathrm{H}}_2$$=100-68=32\mathrm{g}$

Step 2: Calculate the total number of moles

Molecular mass of ${\mathrm{NH}}_3$$=(14+1\times 3)=17$

Number of moles of ${\mathrm{NH}}_3$$=\frac{68}{17}=4$

Number of moles of ${\mathrm{H}}_2$$=\frac{32}{2}=16$

$\therefore$the total number of moles $=16+4=20$

Step 3: Calculate vapour density

We know that Vapour density$=\frac{\mathrm{Molecular}\mathrm{weight}}{2}$

Also the $\mathrm{Molecular}\mathrm{weight}=\frac{\mathrm{Given}\mathrm{mass}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{moles}}$

$\therefore$vapour density of the mixture is$=\frac{\left({\displaystyle \frac{100}{20}}\right)}{2}=\frac{5}{2}=2.5$

Therefore, the vapour density of the mixture is 2.5.