Automobile air bags use the decomposition of sodium azide as their source of gas for rapid inflation: 2NaN₃ (s) → 2Na (s) + 3N₂ (g) .
What mass (g) of NaN₃ is required to provide 40.0 L of N₂ at 25.0 °C and 763 torr?

Question

Quizplus · Accepted Answer

First, convert the volume of $N_2$ gas to moles using the ideal gas law $PV = nRT$, where $P$ is the pressure in atmospheres, $V$ is the volume in liters, $n$ is the number of moles, $R$ is the ideal gas constant (0.0821 L·atm/(mol·K)), and $T$ is the temperature in Kelvin. Convert 763 torr to atm (763 torr / 760 torr/atm = 1.004 atm) and 25.0 °C to Kelvin (25.0 + 273.15 = 298.15 K). Solve for $n$:$$n = \frac{PV}{RT} = \frac{(1.004 \, \text{atm})(40.0 \, \text{L})}{(0.0821 \, \text{L·atm/(mol·K)})(298.15 \, \text{K})} \approx 1.63 \, \text{mol of } N_2$$From the balanced chemical equation, 2 moles of $NaN_3$ produce 3 moles of $N_2$. Therefore, the moles of $NaN_3$ needed are:$$\frac{2}{3} \times 1.63 \, \text{mol} \approx 1.09 \, \text{mol of } NaN_3$$The molar mass of $NaN_3$ is approximately 65 g/mol (23 for Na + 3*14 for N). Thus, the mass of $NaN_3$ required is:$$1.09 \, \text{mol} \times 65 \, \text{g/mol} \approx 70.85 \, \text{g}$$Rounding to the nearest tenth gives approximately 71.1 g, making option D the correct answer.

Automobile Air Bags Use the Decomposition of Sodium Azide as Their