Calculate the mass in grams of the air

Question

Calculate the mass in grams of the air in a hot-air balloon that has a volume of 4.0 x 105 L when the temperature of the gas is 90.0ºC and the pressure is 750 mm Hg. Assume that the average molecular mass of air is 30.0 g/mole.

Answer 1

The niftiest equation to deal with gas chemistry is this equation.

 

PV = nRT

 

The most popular ideal gas constant is R = 0.0821, but that only works if pressure is in units of "atm," volume is in "liters," and temperature is in "Kelvin." Luckily, a third of the work is done, and the volume is already in liters.

 

However, the pressure and temperature need to be converted. Start by converting the pressure. There is 1 atm per 760 mm Hg.

 

750 mm Hg x (1 atm/760 mm Hg) = 0.987 atm

 

Also, here's the formula to convert Celsius temperatures to Kelvin.

 

K = C + 273.15

K = 90.0 + 273.15

K = 363.15

 

Now we have everything we need. We can use all of these terms to find the number of moles, and then we can use that given molecular mass to convert that into grams. First, plug everything into the ideal gas law to solve for "n," which means moles.

 

PV = nRT

(0.987)(4.0 x 10⁵) = n(0.0821)(363.15)

n = 13242 moles

 

Wow, that's a lot of moles. Anyway, use the molecular mass to convert this into grams.

 

13242 moles x (30.0 g/mole) ≈ 3.97 x 10⁵ grams

 

I hope this helps, and good luck with your other chemistry adventures!