Automobile air bags inflate by a rapid decomposition reaction. One typical compound used is guanidinium nitrate, $C(NH_2)_3NO_3$, which decomposes very rapidly to form nitrogen, water vapour and carbon.

$C(NH_2)_3NO_3 (s) → 2N_2 (g) + 3H_2O (g) + C (s)$ 1 mark

1. Calculate the moles of guanidinium nitrate:

2. From the balanced equation, 1 mol of ${C(NH_2)_3NO_3}$ produces 2 mol of ${N_2}$ and 3 mol of ${H_2O}$:

3. Total moles of gas produced = $n({N_2}) + n({H_2O})$ = 0.164 mol + 0.246 mol = 0.410 mol

Award 1 mark for correct substitution of values and 1 mark for the correct final answer.

1. Convert the volume to SI units:

   $$V = 10.0\,\mathrm{dm^3} = 10.0 \times 10^{-3}\,\mathrm{m^3} = 0.010\,\mathrm{m^3}$$

2. Convert the temperature to Kelvin:

   $$T = 127^\circ\mathrm{C} + 273.15 = 400.15\,\mathrm{K}$$

3. Use the ideal gas equation to calculate the pressure:

   $$pV = nRT$$

   Rearranging for $p$:

   $$p = \frac{nRT}{V}$$

   Substituting the values:

   $$p = \frac{(0.4095\,\mathrm{mol})(8.314\,\mathrm{J\,mol^{-1}\,K^{-1}})(400.15\,\mathrm{K})}{0.010\,\mathrm{m^3}}$$ $$p = 1.36 \times 10^5\,\mathrm{Pa} = 136\,\mathrm{kPa}$$

   Award 1 mark for correct substitution of values and 1 mark for the correct final answer