Question

The gases hydrogen, oxygen, carbon dioxide, sulphur dioxide, and chlorine are arranged in order of their increasing relative molecular masses. Given 8 g of each gas at STP, which gas will contain the least number of molecules and which gas the most?

Answer 1

Avogadro's law states that "equal volumes of all gases under similar conditions of temperature and pressure contain the same number of molecules."

∴ 1 mole of each gas contains = 6.02 × 10²³ molecules

Molecular weight of

H2	O2	CO2	SO2	Cl2
(2)	(32)	(44)	(64)	(71)

(1) Now 2 g of hydrogen contains molecules = 6.02 × 10²³

∴ 8 g of hydrogen contains molecules = `8/2 × 6.02 × 10^23`

= 4 × 6.02 × 10²³ 

= 4M molecules

(2) 32 g of oxygen contains molecules = 6.02 × 10²³

∴ 8 g of oxygen contains molecules = `8/32 xx 6.02 xx 10^23`

= `1/4 xx [6.02 xx 10^23]`

= `"M"/4`

(3) 44 g of carbon dioxide contains molecules = 6.02 × 10²³

∴ 8 g of CO₂ contains molecules = `8/4 xx 6.02 xx 10^23`

= `2/11 xx [6.02 xx 10^23]`

= `(2"M")/11`

(4) 64 g of sulphur dioxide contains molecules = 6.02 × 10²³

∴ 8 g of sulphur dioxide contains molecules = `8/64 × 6.02 × 10^23`

= `1/8 xx [6.02 xx 10^23]`

= `"M"/8`

(5) 71 g of chlorine contains molecules = 6.02 × 10²³

∴ 8 g of chlorine contains molecules = `8/71 × [6.02 × 10^23]`

= `(8"M")/71`

Since `(8"M")/71 < "M"/8<(2"M")/11 < "M"/4 < 4"M"`

Thus, Cl₂ < SO₂ < CO₂ < O₂ < H₂

1. Least number of molecules in Cl₂.
2. Most number of molecules in H₂.