Question

. 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?

Answer 1

Molar mass of CH₄ = 12 + 4

= 16 g mol⁻¹ 

1 mole of CH₄ = 16g = 6.022 × 10²³ molecules

Thus, 6.022 × 10²³ molecules of CH₄ have mass = 16g

∴ 1.5 × 10²⁰ molecules of CH₄ will have mass

= `16/(6.022 xx 10^23) xx 1.5 xx 10^20`

= 4 × 10⁻³  g

Molar mass of C₂H₆ = 2 × 12 + 6 

= 30 g mol⁻¹

∴ 1 mole of C₂H₆ = 30g = 6.022 × 10²³ molecules

Thus, 30g of C2H6 have molecules = 6.022 × 10²³ 

∴ 4 × 10⁻³ g of C₂H₆ will have molecules

= `(6.022 xx 10^23)/30 xx 4 xx 10^-3`

= 0.803 × 10²⁰ 

= 8.03 × 10¹⁹