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 w (work) for the following system if 20.2 g of NaN3 reacts completely at 1.00 atm and 22 degrees

Answer 1

Answer : The value of work done for the system is 1144.69 J

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=(20.2g)/(65.01g/mole)=0.311mole`

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, 0.311 moles of
`NaN_3` react to give
`(0.311)/(2)* 3=0.466` 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` = 0.466 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=0.466mole* (0.0821L.atm/mol.K)* 295K`

`V=11.3L`

As initially no nitrogen was present. So,

Volume expanded = Volume of nitrogen evolved

Thus,

Expansion work = Pressure × Volume

Expansion work = 1.00 atm × 11.3 L

Expansion work = 11.3 L.atm

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

Expansion work = 11.3 × 101.3 = 1144.69 J

Therefore, the value of work done for the system is 1144.69 J