Question

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.

Answer 1

1.08 g/L is the density of air.

Step-by-step explanation:

Pressure of the gas = P (atm)

Volume of the gas = V (L)

Moles of gas = n =
`(w(g))/(M(g/mol))`

Temperature of the gas = T (K)

`PV=nRt`

`PV=(w)/(M)* RT`

`PM=(w)/(V)RT=DRT`

where:

D = density of the gas =
`(Mass)/(Volume)`

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.

`1 atm* 29 g/mol=D* 0.0821 atm L/mol K* 327.15 K`

`D=(1 atm* 29 g/mol)/(0.0821 atm L/mol K* 327.15 K)`

D = 1.08 g/L

1.08 g/L is the density of air.