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

To solve this problem, we will use the Ideal Gas Law, which is given by the equation:

$PV = nRT$

where:

• $P$ is the pressure in pascals,
• $V$ is the volume in cubic meters,
• $n$ is the number of moles,
• $R$ is the ideal gas constant (8.314 J/mol·K), and
• $T$ is the temperature in kelvin.

1. Convert the Pressure:
   The pressure of 100 kPa must be converted to pascals: $P = 100,000 ext{ Pa}$

2. Convert the Volume:
   The volume should be converted from liters to cubic meters: $V = 62.0 ext{ L} = 0.0620 ext{ m}^3$

3. Convert the Temperature:
   The temperature must be in kelvin: $T = 36.6 + 273.15 = 309.75 ext{ K}$

4. Plug Values into Ideal Gas Law:
   Now we can plug in the values into the Ideal Gas Law to solve for $n$:

   $n = \frac{PV}{RT} = \frac{100,000 imes 0.0620}{8.314 imes 309.75}$
   $n ≈ 2.39 ext{ moles}$

5. Calculate the Mass of Sodium Azide:
   To find the mass of sodium azide ($m$), we use: $m = n imes M$
   where $M$ is the molar mass of NaN3:

   $m = 2.39 imes 65.0 ext{ g/mol} ≈ 155.35 ext{ g}$

Thus, rounding to three significant figures, the mass of sodium azide in the airbag is approximately 156 g.