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, w, for the following system if 25.6 g of NaN3 reacts completely at 1.00 atm and 22 °C.

Answer 1

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 25.6 g of NaN3 reacts completely at 1.00 atm and 22 °C.

mol of NaN3 = mass/MW = 25.6/65.0099 = 0.39378 mol of NaN3

now, relate mol of NaN3 to mol of gases, N2

2 mol of NAN3 = 3 mol of N2

0.39378mol --> 3/2* 0.39378 = 0.59067 mol of N2

assume this is the only gas

The Work equation

W = -P*dV

W = -P*(Vf-Vi)

Assume:

VF >>> Vi, since gas > solids

so

Vf = Vgas

W = -P*(Vf)

Vf--> apply ideal gas law

PV = nRT

where

P = absolute pressure

V = total volume of gas

n = moles of gas

T = absolute Tmperature

R = ideal gas constant

V = nRT/P

T = 273 + 23 = 296 K

V = (0.59067 )(0.082)(296)/(1)

V = 14.3367 L = 14.3367*10^-3 m3

W = -P*(Vf)

P = 1 atm = 101325 Pa

W = -101325*(14.3367*10^-3) m3Pa

W = -1452.66612 J

W = -1.45 kJ/mol