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Filling Air Bags Automobile air bags produce nitrogen gas from the reaction:


a. If 2.25 g of NaN3 reacts to fill an air bag, how much P–V work will the N2 do against an external pressure of 1.00 atm given that the density of nitrogen is 1.165 g/L at 20°C?


b. If the process releases 2.34 kJ of heat, what is ∆E for the system?

Answer :

Onyebuchinnajigo

(a) The work done by the nitrogen against external pressure is 126.66 J.

(b) The change in the internal energy of the system is -2,466.66 J.

The given parameters:

  • Mass of the compound, = 2.25 g
  • External pressure, P = 1.0 atm = 101325 Pa
  • Density of Nitrogen gas, ρ = 1.165 g/L
  • Temperature of the Nitrogen gas, T = 20⁰C

The molar mass of the given compound is calculated as follows;

NaN₃ = 23+ (14 x 3) = 65 g/mol

65 g -------------- 42

2.25 g ------------- ?

[tex]= \frac{2.25 \times 42}{65} \\\\= 1.45 \ g[/tex]

The volume of the nitrogen gas is calculated as follows;

[tex]\rho = \frac{m}{V} \\\\V = \frac{m}{\rho} \\\\V = \frac{1.45}{1.165} \\\\V = 1.25 \ L[/tex]

[tex]V = 0.00125 \ m^3[/tex]

The work done by the nitrogen against external pressure is calculated as follows;

[tex]W = PV\\\\W = 101325 \times 0.00125\\\\W = 126.66 \ J[/tex]

The change in the internal energy of the system is calculated by applying first law of thermodynamics as follows;

[tex]\Delta E = Q - W\\\\\Delta E = (-2,340) - (126.66)\\\\\Delta E = -2,466.66 \ J[/tex]

Learn more about first law of thermodynamics here: https://brainly.com/question/2965070

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