A sample of ethane (C₂H₆) gas has the same mass as $1.5 \times {10}^{20}$ molecules of methane (CH₄). How many C₂H₆ molecules does the sample of gas contain?

If a sample of ethane (C₂H₆) gas has the same mass as $1.5 \times 10$²⁰ molecules of methane (CH₄), then the number of C₂H₆  molecules present in gas is $8 \times 10$¹⁹.

If 1 mole $= 6.022 \times 10$²³ molecules of methane then $1.5 \times 10$²⁰ molecules of methane will contain,

Moles = Total number of particles/ Avogadro number of particles

$\mathrm{Moles} = \frac{\mathrm{Total} \mathrm{number} \mathrm{of} \mathrm{particles}}{\mathrm{Avogadro} \mathrm{number} \mathrm{of} \mathrm{particles}}$

$= \frac{1.5 \times {10}^{22}}{6.02 \times {20}^{23}} \mathrm{Moles}$

$1.5 \times {10}^{20}$ Molecules of methane $= 2.49 \times {10}^{-4}$ moles

The molar mass of CH_{4 =}16g
⇒$\mathrm{Mass} \mathrm{of} \mathrm{methane} = \mathrm{Molar} \mathrm{mass} \times \mathrm{ }\mathrm{Number} \mathrm{of} \mathrm{moles}$
⇒$\mathrm{Mass} \mathrm{of} \mathrm{methane} =\mathrm{ }16\mathrm{ }\times \mathrm{ }2.49\mathrm{ }\times \mathrm{ }{10}^{-4}\mathrm{ }$
⇒$\mathrm{Mass} \mathrm{of} \mathrm{methane} =\mathrm{ }3.984\mathrm{ }\times \mathrm{ }{10}^{-3}\mathrm{g}$
Mass of C₂H₆ $= 30$
$30$ g or $1$ mole  of ethane contains $6.02 \times {10}^{23}$ molecules
So,
$\Rightarrow \mathrm{Number} \mathrm{of} \mathrm{molecules} \mathrm{of} \mathrm{ethane} =\frac{\mathrm{ }3.984\mathrm{ }\times \mathrm{ }{10}^{-3}\mathrm{ }\times \mathrm{ }6.02\mathrm{ }\times \mathrm{ }{10}^{23}}{30}$
$\Rightarrow \mathrm{Number} \mathrm{of} \mathrm{molecules} \mathrm{of} \mathrm{ethane} =\mathrm{ }8\times {10}^{19}$