Automobile airbags contain solid sodium azide, nan 3 , that reacts to produce nitrogen gas when heated, thus inflating the bag. 2 nan 3 ( s ) ⟶ 2 na ( s ) + 3 n 2 ( g ) calculate the value of work, w , for the system if 16.5 g nan 3 reacts completely at 1.00 atm and 22 ∘ c.

The value of work for the system is -935.23 J

Explanation:

To calculate the number of moles, we use the equation:

Given mass of sodium azide = 16.5 g

Molar mass of sodium azide = 65 g/mol

Putting values in above equation, we get:

The given chemical equation follows:

By Stoichiometry of the reaction:

2 moles of sodium azide produces 3 moles of nitrogen gas

So, 0.254 moles of sodium azide will produce = of nitrogen gas

To calculate volume of the gas given, we use the equation given by ideal gas, which follows:

where,

P = pressure of the gas = 1.00 atm

V = Volume of the gas = ?

T = Temperature of the gas =

R = Gas constant =

n = number of moles of nitrogen gas = 0.381 moles

Putting values in above equation, we get:

To calculate the work done for expansion, we use the equation:

We are given:

P = pressure of the system =     (Conversion factor:  1 atm = 101325 Pa)

= change in volume =     (Conversion factor:   )

Putting values in above equation, we get:

Hence, the value of work for the system is -935.23 J

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml