Question

❤️❤️❤️Chemistry❤️❤️❤️

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Prove that :
$molar \: mass \: = 2 \times \: vapour \: density$
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Answer 1

$\huge{\boxed{\underline{ \bf{Answer}}}}$


$\boxed{ \bf{Proof} : }$


We know,

$Vapour \: density \: = \: \frac{density \: of \: any \: gas(d_{gas} )}{density \: of \: H_{2} \: \: \: ( d_{H2}) }$

$V.D \: = \: \frac{ d_{gas} }{ d_{{H}_{2}}}$

$V.D \: = \: \frac{ (m_{gas}) \: for \: certain \: 'V' \: L \: volume}{ (m_{{H}_{2}}) \:for \: certain \: 'V' \: L \: volume }$

If N molecules are present in the given volume of gas and hydrogen under similar condition of temperature and pressure, then

$V.D \: = \: \frac{ (m_{gas}) \: of \: N \: molecules \: }{ (m_{{H}_{2}}) \: of \:N \: molecules }$

As, N is common so, by cancelling N we get,

$V.D \: = \: \frac{ (m_{gas}) \: of \: 1\: molecule \: }{ (m_{{H}_{2}}) \: of \:1 \: molecule}$


Now , $\bf{mass \:of \:a\: gas\: of \:1\: molecule}$ is nothing but the $\bf{molar \: mass}$ and We know mass of Hydrogen of 1 molecule is 2.

So, now we get

$V.D \: = \: \frac{Molar \: \: mass}{2}$

$\boxed{ \bf{\therefore \: Molar \: mass \: = \: 2 \: \times \: V.D}}$

where V.D = Vapour Density.


$\boxed{ \bf{HENCE \: \: PROVED}}$