Question

Automobile airbags contain solid sodium azide, NaN3, that reacts to produce nitrogen gas when heated, thus inflating the bag. Calculate the value of work, w, for the following system if 14.7 g of NaN3 reacts completely at 1.00 atm and 22 °C.

Answer 1

Work for:

m = 14.7 g of NaN3 reacting at P = 1 atm = 101325 Pa, T = 22°C = 22+273 = 295 K

so

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

balance

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

mol of NaN3 = mass/MW = 14.7/65.0099 = 0.226 mol

ratio is 2 mol of NAN3 = 3 mol of N2

0.226 *3/2 = 0.339 mol of N2

so

W = -P*(Vf-Vi)

Vf >> Vi

Vf --> ideal gas law

PV = nRT

V = nRT/P = (0.339)(0.082)(295)/(1) = 8.20041 L = 8.20041*10^-3 m3

W = -P*(Vf)

W = -(101325)(8.20041*10^-3) = 830.906 J

the system will do 830.906 J of work to the usrroundings