Question

A sample of ethane (${\mathrm{C}}_2{\mathrm{H}}_6$) gas has the same mass as $1.5\times {10}^{20}$ molecules of methane (${\mathrm{CH}}_4$). How many ${\mathrm{C}}_2{\mathrm{H}}_6$molecules does the sample of gas contain?

Answer 1

Step 1: Finding the mass of Methane present:

$1\mathrm{mole}=6.022\times {10}^{23}$ molecules of methane

So, $1.5\times {10}^{20}\mathrm{molecules}\mathrm{of}\mathrm{methane}\mathrm{is}:$$(1.5\times {10}^{20}\times 1)÷(6.02\times {10}^{23})\mathrm{moles}$

Hence, $1.5\times {10}^{20}\mathrm{molecules}\mathrm{of}\mathrm{methane}=2.49\times {10}^{-4}$ moles

As the Molar mass of Methane: $\left({\mathrm{CH}}_4\right):12+1\times 4=16\mathrm{g}$

Hence, the mass of methane:

$\mathrm{Mass}\mathrm{of}\mathrm{methane}=\mathrm{molar}\mathrm{mass}\times \mathrm{Number}\mathrm{of}\mathrm{moles}$ = $16\times 2.49\times {10}^{-4}:3.984\times {10}^{-3}\mathrm{g}(\mathrm{which}\mathrm{is}\mathrm{same}\mathrm{as}\mathrm{the}\mathrm{mass}\mathrm{of}\mathrm{Ethane})$

Step 2: Finding the number of molecules of ${\mathrm{C}}_2{\mathrm{H}}_6$ present in a gas sample:

Molar mass of Ethane = $2\times 12+1\times 6=30\mathrm{g}$.

So, if the $30\mathrm{g}$ of Ethane has $6.02\mathrm{x}{10}^{23}\mathrm{molecules}$

Then, $3.984\times {10}^{-3}\mathrm{g}=(3.984\times {10}^{-3}\times 6.02\times {10}^{23})÷30$

= $8\times {10}^9$ molecules

Therefore, $8\times {10}^9$ molecules of Ethane (${\mathrm{C}}_2{\mathrm{H}}_6$) gas are present.