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Gas laws and mole concept - class-X

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A quantity of $2.0\ g$ of a triatomic gaseous element was found to occupy a volume of $448\ ml$ at $76\ cm$ of $Hg$ and $273\ K$.

The mass of its each atom is _______________.

AnswerClick to flip back

$5.53\times 10^{-23}\ g$

💡 Explanation:

Given that

$P=76\ cm$ of $Hg =1\ atm$

$V=448\ ml=0.448\ L$

$T=273\ K$

Now,

$PV=nRT$

$n=\dfrac{PV}{RT}=\dfrac{1\times 0.448}{0.082\times 273}=0.02\ moles$

No. of moles $=\dfrac{mass}{molar\ mass}$

Molar mass $=\dfrac{mass}{mole}$

$3\times$ atomic mass $=\dfrac{2}{0.02}$

Atomic mass $=33.3\ g$

$\therefore$ mass of $1\ atom=\dfrac{33.3}{6.022\times 10^{23}}=5.53\times 10^{-23}\ g$