Question

The vapor density of a mixture of $NO_{2}$ and $N_{2}O_{4}$ is 38.3 at 27°C. Calculate the number of moles of $NO_{2}$ in 100 g of the mixture.

Answer 1

From the given,

Vapour density of a mixture = 38.3

Temperature = 27 ℃

Weight of the mixture of $N{ O }_{ 2 }$ and ${ N }_{ 2 }{ O }_{ 4 } = Density \times 2$

                    $Weight =\quad 38.3\times 2\quad =\quad 76.6$

Let a g of $N{ O }_{ 2 }$ present in 100 g mixture

Molar mass of $N{ O }_{ 2 }$ = 46 g/mol

Molar mass of ${ N }_{ 2 }{ O }_{ 4 }$ = 92 g/mol

                    $Weight\quad of\quad { N }_{ 2 }{ O }_{ 4 }\quad =\quad 100\quad -a$

Therefore,

                    $Mole\quad of\quad N{ O }_{ 2 }\quad =\quad \frac { a }{ 46 }$

                    $mole\quad of\quad { N }_{ 2 }{ O }_{ 4 }\quad =\quad \frac { 100\quad -\quad a }{ 92 }$

                    $Moles\quad of\quad mixture\quad =\quad \frac { 100 }{ 78.6 }$

                    $Mole\quad of\quad N{ O }_{ 2 }\quad +\quad mole\quad of\quad { N }_{ 2 }{ O }_{ 4 }\quad =\quad Mole\quad of\quad mixture$

                    $\frac { a }{ 46 } \quad +\quad \frac { 100\quad -\quad a }{ 92 } \quad =\quad \frac { 100 }{ 78.6 }$

                    $a\quad =\quad 20.10\quad g$

                    $Mole\quad of\quad N{ O }_{ 2 }\quad in\quad mixture\quad =\quad \frac { 20.10 }{ 46 } \quad =\quad 0.437\quad m$

Answer 2

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a=20.10