Airbags are an important safety feature of today's cars - VCE - SSCE Chemistry - Question 15 - 2011 - Paper 1

Using the Ideal Gas Law: $PV = nRT$ Where:

• P = pressure in Pascals
• V = volume in cubic meters (62.0 L = 0.0620 m³)
• n = number of moles
• R = ideal gas constant (8.314 J/(mol·K))
• T = temperature in Kelvin

Rearranging to find n: n = \frac{PV}{RT}

Substituting: n = \frac{(100,000)(0.0620)}{(8.314)(309.75)} \approx 2.43 ext{ moles}

From the balanced equation, 10 moles of NaN₃ produce 16 moles of nitrogen gas. Thus, ( n_{NaN_3} = \frac{10}{16} n_{N} ) Substituting n(N) from previous step: ( n_{NaN_3} = \frac{10}{16} \times 2.43 \approx 1.52 ext{ moles} )

Now, we can find the mass of sodium azide: ( ext{mass} = n \times \text{molar mass} = 1.52 imes 65.0 \approx 98.8 ext{ g} )

The closest answer option is approximately 97.9 g. Thus, the mass of sodium azide contained in the car's airbag is approximately 97.9 g.