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(A) The chemical equation for the decomposition of sodium azide is: $2 NaN_{3(s)} \rightarrow 2 Na_{(s)} + 3 N_{2(g)}$.Given mass of $NaN_3 = 130 \ g$

Vedclass · Accepted Answer

$7.38$

Vedclass · Answer

(A) The chemical equation for the decomposition of sodium azide is: $2 NaN_{3(s)} ightarrow 2 Na_{(s)} + 3 N_{2(g)}$.Given mass of $NaN_3 = 130 \ g$. Molar mass of $NaN_3 = 23 + (3 	imes 14) = 65 \ g \ mol^{-1}$.Number of moles of $NaN_3 = \frac{130 \ g}{65 \ g \ mol^{-1}} = 2 \ mol$.According to the stoichiometry,$2 \ mol$ of $NaN_3$ produces $3 \ mol$ of $N_2$ gas.Using the ideal gas equation $PV = nRT$,where $n = 3 \ mol$,$V = 10 \ L$,$T = 300 \ K$,and $R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1}$:$P = \frac{nRT}{V} = \frac{3 	imes 0.082 	imes 300}{10} = \frac{73.8}{10} = 7.38 \ atm$.

$A$ car airbag is inflated by $N_2$ produced during rapid decomposition of $NaN_{3(s)}$. What will be the pressure of the inflated airbag if $130 \ g$ of $NaN_3$ is used (in $atm$)? The volume of the airbag is $10 \ L$ $(T = 300 \ K, R = 0.082 \ L \ atm \ K^{-1} \ mol^{-1})$.

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