Mole Concept | Vapour Density#
Vapour Density#
- Density of a gas relative to hydrogen is called its vapour density. Mathematically, it can be expressed as:
\[Vapour\ Density = {ρ_{gas} \over ρ_{H_2}}\]
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Let us consider that in a container of capacity 'V' litres, we have 'n' moles of H2 gas and in another container of capacity 'V' litres, we have 'n' moles of a gas of molecular mass 'M'.
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Then, the density of H2 gas is given by:
\[ρ_{H_2} = {Mass \over Volume}\]
\[ρ_{H_2} = {n \times 2 \over V}\]
- And, the density of the gas of molecular mass 'M' is given by:
\[ρ_{gas} = {Mass \over Volume}\]
\[ρ_{gas} = {n \times M \over V}\]
- Calculating vapour density of the gas of molecular mass 'M':
\[Vapour\ Density = {ρ_{gas} \over ρ_{H_2}}\]
\[Vapour\ Density = {{n \times M \over V} \over {n \times 2 \over V}}\]
\[∴ Vapour\ Density = {M \over 2}\]
- Vapour Density has no unit. It is a dimensionless quantity.
Relative Density of a gas w.r.t another gas#
- Let us consider that we have two gases, gas1 and gas2 of molecular masses M1 and M2 respectively.. Then, the relative density of gas1 w.r.t gas2 is given by:
\[Relative\ density\ of\ gas1\ w.r.t\ gas2 = {M_1 \over M_2}\]
Examples
- \[Relative\ density\ of\ gas\ of\ molecular\ mass\ M\ w.r.t\ O_2 = {M \over 32}\]
- \[Relative\ density\ of\ gas\ of\ molecular\ mass\ M\ w.r.t\ N_2 = {M \over 28}\]
Relative Density of a gas w.r.t air#
\[Relative\ density\ of\ gas\ of\ molecular\ mass\ M\ w.r.t\ air = {M \over M_{air}}\]
Here, Mair = Average molecular mass of air
- Air consists of approximately 20% oxygen and 80% nitrogen. So, calculating average molecular mass of air:
\[Avg.\ molecular\ mass\ of\ air = {(20 \times 32) + (80 \times 28) \over (20 + 80)}\]
\[∴ Avg.\ molecular\ mass\ of\ air ≈ 29\ a.m.u\]
- Therefore, we can write:
\[Relative\ density\ of\ gas\ of\ molecular\ mass\ M\ w.r.t\ air = {M \over 29}\]
Question#
Density of a gas relative to air is 1.17. Find the molecular mass of the gas. [Mair = 29 g/mole]
\[Relative\ density\ of\ gas\ of\ molecular\ mass\ M\ w.r.t\ air = {M \over M_{air}}\]
\[1.17 = {M \over 29}\]
\[M = 33.95 ≈ 34\ g/mole\]