Question

Automobile airbags contain solid sodium azide, NaN₃, that reacts to produce nitrogen gas when heated, thus inflating the bag.
`2NaN_3(s) \longrightarrow 2Na(s) + 3N_2(g)`Calculate the value of work (w), for the system if 23.3 g NaN₃ reacts completely at 1.00 atm and 22°C.

Answer 1

W = 54.48J

Step-by-step explanation:

Gases do expansion or compression work following the equation:

W = −PΔV

Where P = Pressure

ΔV = Change in Volume

Parameters given in the question:

Pressure = 1atm

Temperature = 22°C + 273 = 295K (Converting to Kelvin Temperature)

Mass of NaN₃ = 23.3g

2NaN₃ --> 2Na + 3N2

From the equation;

2 mol of NaN₃ produces 3 mol of N2 gas

130g (2 * 65g/mol) of NaN₃ produces 3 L ( 3mol * 1mol/L) of N2

23.3 produces x?

130 = 3

23.3 = x

Upon solving for x:

x = (23.3 * 3) / 130

x = 0.5377L

ΔV = Final Volume - Initial Volume

ΔV = 0.5377L - 0

ΔV = 0.5377L

W = −PΔV = - 1 * 0.5377

W = - 0.5377L atm

Note: When the gas does work the volume of a gas increases ΔV>0 and the work done is negative.

1 L atm = 101.325 J.

W = 0.5377L atm * (101.325 J / 1 L atm)

W = 54.48J