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

$\text{Moles of }NaN_3=\frac{32.2g}{65.01g/mole}=0.495mole$

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 $\frac{0.495}{2}\times 3=0.7425$ 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:

$1.00atm\times V=0.7425mole\times (0.0821L.atm/mol.K)\times 295K$

$V=17.98L$

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