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

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 = $\frac{w(g)}{M(g/mol)}$

Temperature of the gas = T (K)

$PV=nRt$

$PV=\frac{w}{M}\times RT$

$PM=\frac{w}{V}RT=DRT$

where:

D = density of the gas = $\frac{Mass}{Volume}$

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.

$1 atm\times 29 g/mol=D\times 0.0821 atm L/mol K\times 327.15 K$

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

D = 1.08 g/L

1.08 g/L is the density of air.