Automobile airbags contain solid sodium azide NaN3 that reac

Automobile airbags contain solid sodium azide, NaN3, that reacts to produce nitrogen gas when heated, thus inflating the bag. 2NaN3(s) 2Na(s) +3N2(g) Calculate the value of work, w, for the following system if 26.9 g of NaN3 reacts completely at 1.00 atm and 22 °C Number w=

Solution

The balanced chemical equation for the reaction is given.

2 NaN₃ (s) -------> 2 Na (s) + 3 N₂ (g)

As per the stoichiometry of the reaction,

2 moles NaN₃ = 3 moles N₂

Molar mass of NaN₃ = (1*22.9897 + 3*14.0067) g/mol = 65.0098 g/mol.

Mole(s) of NaN₃ = (26.9 g)/(65.0098 g/mol) = 0.4138 mole.

Mole(s) of N₂ produced = (0.4138 mole NaN₃)*(3 moles N₂/2 moles NaN₃) = 0.6207 mole.

Assume the N₂ to behave ideally and apply the ideal gas law.

We have

P*V = n*R*T

where P = 1.00 atm; n = 0.6207 mole and T = 22°C = (22 + 273) K = 295 K. Plug in values and obtain

(1.00 atm)*V = (0.6207 mole)*(0.082 L-atm/mol.K)*(295 K)

=====> V = (0.6207 mole)*(0.082 L-atm/mol.K)*(295 K)/(1.00 atm) = 15.0147 L.

The change in volume of the gas = V_f – V_i = (15.0147 L) – (0.0 L) = 15.0147 L (a deflated balloon has zero volume).

The work done, w = -P*V = -(1.00 atm)*(15.0147 L) = -15.0147 L-atm = -(15.0147 L-atm)*(101.33 J/1 L-atm)*(1 kJ/1000 J) = -1.521439551 kJ -1.5214 kJ (ans).