Question

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, ?, for the system if 12.9 g NaN3 reacts completely at 1.00 atm and 22 ∘ C.

Answer 1

Automotive airbags contain solid sodium azide.

Let us calculate the molecular mass first;

Molecular mass of NaN₃ = 65.01 g/mol

Therefore,

12.9 g NaN₃ = 12.9 g/65.01 g/mol = 0.1984 moles

• 0.1984 moles of NaN₃ reacts completely at 1.00 atm and 22°C.

Reaction:

2NaN₃(s) ---> 2Na(s) + 3N₂(g)

• 2 moles NaN3 give 3 moles N₂

Therefore, 0.1984 moles NaN₃ give 0.1984×3/2 moles N₂ = 0.2976 moles N₂

• The volume of 0.2976 moles N₂ at 1 atm and 22°C is V.

T = 22°C = 295 K, p = 1 atm, n = 0.2976 mol

• V = nRT/p (Ideal gas equation)

= (0.2976 mol)×(0.082 atm-L/mol-K)×(295 K)/(1 atm)

= 7.20 L

• Volume expansion work against constant pressure is w.

w = - pV. (Work done)

w = - (1 atm)×(7.20 L) = -7.20 atm-L

(• 1 atm-L = 101.325 J)

w = -7.20×101.325 J = -729.54 J

(Work (w) is -729.54 J)