$320$ $320$ $g$ $g$ of solid ammonium nitrite, $N H_{4} N O_{2}$ $NH_4NO_2$ , decomposes when heated according to the balanced equation: $N H_{4} N O_{2} \to N_{2} + 2 H_{2} O$ $NH_4NO_2 -> N_2+2H_2O$ . What total volume of gases at $819$ $819$ $K$ $K$ is emitted by this reaction?

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$320$ $320$ $g$ $g$ of solid ammonium nitrite, $N H_{4} N O_{2}$ $NH_4NO_2$ , decomposes when heated according to the balanced equation: $N H_{4} N O_{2} \to N_{2} + 2 H_{2} O$ $NH_4NO_2 -> N_2+2H_2O$ . What total volume of gases at $819$ $819$ $K$ $K$ is emitted by this reaction?

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Answer 1 · 2016-03-21T00:55:48

Each mole of $N H_{4} N O_{2}$ $NH_4NO_2$ produces $3$ $3$ $m o l$ $mol$ of gases total ( $N_{2}$ $N_2$ and $H_{2} O$ $H_2O$ ), and we have $5$ $5$ $m o l$ $mol$ . So $3 \times 5 = 15$ $3xx5 = 15$ $m o l$ $mol$ of gas at STP is $336$ $336$ $L$ $L$ . Converting to $819$ $819$ $K$ $K$ gives a volume of $1008$ $1008$ $L$ $L$ .

Explanation:

The molar mass of $N H_{4} N O_{2}$ $NH_4NO_2$ is $64$ $64$ $g m o l^{- 1}$ $gmol^-1$ (two $N$ $N$ at $14$ $14$ , four $H$ $H$ at $1$ $1$ , two $O$ $O$ at $16$ $16$ ).

Find the number of moles of $N H_{4} N O_{2}$ $NH_4NO_2$ :

$n = \frac{m}{M} = \frac{320}{64} = 5$ $n=m/M=320/64=5$ $m o l$ $mol$

From the balanced equation, each mole of $N H_{4} N O_{2}$ $NH_4NO_2$ yields 1 mole of $N_{2}$ $N_2$ and 2 moles of $H_{2} O$ $H_2O$ (which is definitely a gas at $819$ $819$ $K$ $K$ ), for a total of 3 moles of gas.

For ideal gases (which we can treat these real gases as for our purposes), 1 mole of any gas at STP ( $273$ $273$ $K$ $K$ and $1$ $1$ $a t m$ $atm$ ) occupies $22.4$ $22.4$ $L$ $L$ .

That means we have $3 \times 5 = 15$ $3xx5 = 15$ $m o l$ $mol$ of product gases, and they occupy a volume of $336$ $336$ $L$ $L$ at STP.

We need to change the temperature from $273$ $273$ $K$ $K$ to $819$ $819$ $K$ $K$ , and the pressure stays the same at $1$ $1$ $a t m$ $atm$ , so:

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$ $V_1/T_1=V_2/T_2$

Rearranging:

$V_{2} = V_{1} \frac{T_{2}}{T_{1}} = 336 \times \frac{819}{273} = 1008$ $V_2=V_1T_2/T_1 = 336 xx 819/273 = 1008$ $L$ $L$

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$320$ $320$ $g$ $g$ of solid ammonium nitrite, $N H_{4} N O_{2}$ $NH_4NO_2$ , decomposes when heated according to the balanced equation: $N H_{4} N O_{2} \to N_{2} + 2 H_{2} O$ $NH_4NO_2 -> N_2+2H_2O$ . What total volume of gases at $819$ $819$ $K$ $K$ is emitted by this reaction?

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320320320 ggg of solid ammonium nitrite, NH_4NO_2NH4NO2NH_4NO_2, decomposes when heated according to the balanced equation: NH_4NO_2 -> N_2+2H_2ONH4NO2→N2+2H2ONH_4NO_2 -> N_2+2H_2O. What total volume of gases at 819819819 KKK is emitted by this reaction?

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$320$ $320$ $g$ $g$ of solid ammonium nitrite, $N H_{4} N O_{2}$ $NH_4NO_2$ , decomposes when heated according to the balanced equation: $N H_{4} N O_{2} \to N_{2} + 2 H_{2} O$ $NH_4NO_2 -> N_2+2H_2O$ . What total volume of gases at $819$ $819$ $K$ $K$ is emitted by this reaction?