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,with,for the system if32.2NaNO3 reacts completely at1.00 atmand22∘C.

Answer 1

Answer : The value of work done for the system is 1.821 kJ

Explanation :

First we have to calculate the moles of
`NaN_3`

`\text{Moles of }NaN_3=\frac{\text{Mass of }NaN_3}{\text{Molar mass of }NaN_3}`

Molar mass of
`NaN_3` = 65.01 g/mole

`\text{Moles of }NaN_3=(32.2g)/(65.01g/mole)=0.495mole`

Now we have to calculate the moles of nitrogen gas.

The balanced chemical reaction is,

`2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)`

From the balanced reaction we conclude that

As, 2 mole of
`NaN_3` react to give 3 mole of
`N_2`

So, 0.495 moles of
`NaN_3` react to give
`(0.495)/(2)* 3=0.7425` moles of
`N_2`

Now we have to calculate the volume of nitrogen gas.

Using ideal gas equation:

`PV=nRT`

where,

P = Pressure of
`N_2` gas = 1.00 atm

V = Volume of
`N_2` gas = ?

n = number of moles
`N_2` = 0.7425 mole

R = Gas constant =
`0.0821L.atm/mol.K`

T = Temperature of
`N_2` gas =
`22^oC=273+22=295K`

Putting values in above equation, we get:

`1.00atm* V=0.7425mole* (0.0821L.atm/mol.K)* 295K`

`V=17.98L`

As initially no nitrogen was present. So,

Volume expanded = Volume of nitrogen evolved

Thus,

Expansion work = Pressure × Volume

Expansion work = 1.00 atm × 17.98 L

Expansion work = 17.98 L.atm

Conversion used : (1 L.atm = 101.3 J)

Expansion work = 17.98 × 101.3 = 1821.374 J = 1.821 kJ

Therefore, the value of work done for the system is, 1.821 kJ