A sample of ethane (C2H6) gas has the same mass as 1.5 ×1020 molecules of methane (CH4). How many C2H6 molecules does the sample of gas contain?

6.02 x 10²³ molecules of methane = 1 mole

Hence 1.5 x 10²⁰ molecules of methane = (1.5 x 10²⁰ x 1) ÷ (6.02 x 10²³) moles

= 2.49 x 10 ^-4 moles Molar mass of Methane (CH₄) = 12 + 1x4 = 16 g

Mass of methane = molar mass x no. of moles = 16 x 2.49 x 10 ^-4 = 3.984 x 10^-3 g (This is the same mass as Ethane)

Ethane (C2H6) = 12x2 + 1x6 = 30

If 30 g of Ethane has 6.02 x 10²³ molecules

So 3.984 x 10 ^-3 g = (3.984 x 10^-3 x 6.02 x 10²³) ÷ 30

= 8 x 10¹⁹ molecules of Ethane