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First-generation automobile airbags were inflated by the decomposition of sodium azide (M= 65.02): 4. 2 NaN3(s) → 2 Na(s) + 3 N2(g) hat mass of sodium azide would be required to inflate a 16.0 L airbag to a pressure of 1.20 atm at 17 °C? (A) 34.9 g (B) 524 g (C) 78.6 g (D) 157 g

Respuesta :

Answer:

34.94 g

Explanation:

Given:  

Pressure = 1.20 atm

Temperature = 17 °C

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (17 + 273.15) K = 290.15 K  

Volume = 16.0 L

Using ideal gas equation as:

[tex]PV=nRT[/tex]

where,  

P is the pressure

V is the volume

n is the number of moles

T is the temperature  

R is Gas constant having value = 0.0821 L.atm/K.mol

Applying the equation as:

1.20 atm × 16.0 L = n × 0.0821 L.atm/K.mol × 290.15 K  

⇒n = 0.806 moles

Moles of nitrogen gas to be formed = 0.806 moles

Considering the reaction below as:-

[tex]2NaN_3\rightarrow 2Na+3N_2[/tex]

3 moles of gas is produced when 2 moles of sodium azide undergoes decomposition

So,

1 mole of gas is produced when 2/3 moles of sodium azide undergoes decomposition

Also,

0.806 mole of gas is produced when [tex]\frac{2}{3}\times 0.806[/tex] moles of sodium azide undergoes decomposition

Moles of sodium azide = 0.5373 moles

Molar mass of sodium azide = 65.02 g/mol

Mass = Moles*Molar mass = [tex]0.5373\times 65.02\ g[/tex] = 34.94 g

Mass of sodium azide required = 34.94 g

The mass of sodium azide that would be required to inflate will be 34.94 g.

(A) 34.9 g

Given reaction

2 NaN₃(s) → 2 Na(s) + 3 N₂(g)

  • Pressure = 1.20 atm
  • Temperature = 17 °C = 17+273.15= 290.15K
  • Volume = 16.0 L

Ideal gas equation:

[tex]PV=nRT[/tex]

where,  

  • P is the pressure
  • V is the volume
  • n is the number of moles
  • T is the temperature  
  • R is Gas constant having value = 0.0821 L.atm/K.mol

On substituting values in the above formula:

[tex]1.20 atm * 16.0 L = n * 0.0821 L.atm/K.mol * 290.15 K \\\\n = 0.806 moles[/tex]

Moles of nitrogen gas to be formed = 0.806 moles

From given reaction:

2 NaN₃(s) → 2 Na(s) + 3 N₂(g)

3 moles of gas is produced when 2 moles of sodium azide undergoes decomposition

So,

1 mole of gas is produced when 2/3 moles of sodium azide undergoes decomposition

Also,

0.806 mole of gas is produced when  moles of sodium azide undergoes decomposition

Number of Moles of sodium azide = 0.5373 moles

Molar mass of sodium azide = 65.02 g/mol

[tex]\text{ Mass} = \text{ Moles} *\text{ Molar mass} \\\\\text{ Mass} = 34.94 g[/tex]

Mass of sodium azide required = 34.94 g

Thus, correct option is (A).

Find more information about Number of moles here:

brainly.com/question/13314627

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