Question

Automobile air bags inflate during a crash by the rapid generation of nitrogen gas, N2, from sodium azide, NaN3, according to the following equation:
2NaN3 (s) —> 2Na (s) + 3N2 (g)
How many grams of sodium azide are needed to produce enough N2 gas to fill an 8.25 liter air bag to a pressure of 1.37 atmospheres at 25.0 degrees Celsius?

Answer 1

Answer on Question 75490 in General Chemistry

$$V(N_2) = 8.25 \, \text{l}$$ $$P = 1.37 \, \text{atm}$$ $$.t = 25^\circ \text{C}$$ $$2NaN_3(s) = 2Na(s) + 3N_2(g)$$ $$.m(NaN_3) = ?$$

Solution: According to the law of Boyle-Marriott (T=const)

$$p_0 \times V_0 = p_1 \times V_1$$ $$V_0 = \frac{p_1 \times V_1}{p_0} = \frac{1.37 \times 8.25}{1} = 11.3$$

Find the amount of substance of $N_2$

$$.n = \frac{V}{V_m} = \frac{11.3}{22.4} = 0.504 \, \text{mol}$$ $$.n(NaN_3) = \frac{2}{3} n(N_2) = \frac{2}{3} \times 0.504 = 0.336 \, \text{mol}$$ $$M_r(NaN_3) = A_r(Na) + 3 \times A_r(N) = 23 + 3 \times 14 = 65$$ $$.m(NaN_3) = n \times M_r(NaN_3) = 0.336 \times 65 = 21.84 \, \text{g}$$

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