Which of the following gases have lowest density ?

C O_{2}

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N_{2}

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C H_{4}

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O_{2}

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Solution

The correct option is B $C H_{4}$
Density can be defined as mass per unit volume. If we consider the equal moles of given gases taken in unit volume container then their density will be same as their molecular weight.
$P V = n R T$
$n = (m a s s / m w)$
substitute and rearrange...
$P V = (m a s s / m w) R T$
$m a s s / V = m w x P / (R T)$
and since $d e n s i t y = m a s s / V$
$d e n s i t y = m w x P / (R T)$
So if $P, R,$ and $T$ are the same, the gas with the lowest molar mass will have the lowest density.According to that density of
$C O_{2} = 44 g / l$
$N_{2} = 28 g / l$
$C H_{4} = 16 g / l$
$O_{2} = 32 g / l$
Therefore $C H 4$ has lowest density.

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