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At constant pressure, density of gas is inversely proportional to its temperature. This is how hot air balloon is floating in air: burning fuel makes inside air temperature higher and density lower; low density air balloon float on high density regular air. What is the density of air in g/L at 54 degree C if the atmospheric pressure is 1.0 atm? The average molar mass of air is about 29 g/mol. Keep two decimal places for your answer.

Respuesta :

Answer:

1.08 g/L is the density of air.

Explanation:

Pressure of the gas = P (atm)

Volume of the gas = V (L)

Moles of gas = n = [tex]\frac{w(g)}{M(g/mol)}[/tex]

Temperature of the gas = T (K)

[tex]PV=nRt[/tex]

[tex]PV=\frac{w}{M}\times RT[/tex]

[tex]PM=\frac{w}{V}RT=DRT[/tex]

where:

D = density of the gas = [tex]\frac{Mass}{Volume}[/tex]

R = universal gas constant

w = Mass of the gas

M =Molar mass of the gas

Given = P = 1.0 atm , T = 54°C = 327.15 K

Average molar mass of the gas = 29 g/mol

Putting all the given values in above equation.

[tex]1 atm\times 29 g/mol=D\times 0.0821 atm L/mol K\times 327.15 K[/tex]

[tex]D=\frac{1 atm\times 29 g/mol}{0.0821 atm L/mol K\times 327.15 K}[/tex]

D = 1.08 g/L

1.08 g/L is the density of air.

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