Question

sodium azide (nan₃) is used in some automobile air bags. the impact of a collision triggers the decomposition of nan₃ as follows: 2 nan₃ (s) → 2 na (s) + 3 n₂ (g) the nitrogen gas produced quickly inflates the bag between the driver and the windshield and dashboard. calculate the volume of n₂ generated at 85 °c and 812 mmhg by the decomposition of 50.0 g of nan₃.

Explanation:

Step1: Calculate the number of moles of \( \text{NaN}_3 \)

The molar mass of \( \text{NaN}_3 \) is \( M = 65.01\ \text{g/mol} \).
Using the formula \( n=\frac{m}{M} \), where \( m = 50.0\ \text{g} \)

$$ n_{\text{NaN}_3}=\frac{50.0\ \text{g}}{65.01\ \text{g/mol}} = 0.769\ \text{mol} $$

Step2: Calculate the number of moles of \( \text{N}_2 \)

From the balanced chemical equation \( 2\text{NaN}_3(s)\to2\text{Na}(s)+3\text{N}_2(g) \), the mole ratio of \( \text{NaN}_3 \) to \( \text{N}_2 \) is \( 2:3 \).

$$ n_{\text{N}_2}=\frac{3}{2}n_{\text{NaN}_3}=\frac{3}{2}\times0.769\ \text{mol}=1.154\ \text{mol} $$

Step3: Convert temperature and pressure to appropriate units

Temperature \( T=(85 + 273.15)\ \text{K}=358.15\ \text{K} \)
Pressure \( P=\frac{812}{760}\ \text{atm}=1.068\ \text{atm} \)

Step4: Use the ideal gas law \( PV = nRT \) to find the volume \( V \)

where \( R = 0.0821\ \text{L}\cdot\text{atm/mol}\cdot\text{K} \)

$$ V=\frac{n_{\text{N}_2}RT}{P}=\frac{1.154\ \text{mol}\times0.0821\ \text{L}\cdot\text{atm/mol}\cdot\text{K}\times358.15\ \text{K}}{1.068\ \text{atm}} $$

$$ V = 35.4\ \text{L} $$

Answer:

$$ V = 35.4\ \text{L} $$