a spherical space colony proposed by Gerald o Neil has a diameter of 1 km . how

Question

a spherical space colony proposed by Gerald o Neil has a diameter of 1 km . how many grams of N2 are needed to fill the interior of the colony at one atmosphere and 20 degrees a spherical space colony proposed by Gerald o Neil has a diameter of 1 km . how many grams of N2 are needed to fill the interior of the colony at one atmosphere and 20 degrees a spherical space colony proposed by Gerald o Neil has a diameter of 1 km . how many grams of N2 are needed to fill the interior of the colony at one atmosphere and 20 degrees

Explanation / Answer

First calculate the volume of colony with its diameter.

Diameter =1 km = 1000 m so radius is 1000/2 = 500 m

V=4/3 r^3

V= 4/3*3.14*(500m)^3

V=523,333,333.3 m^3

1 m^3 = 1000 L

V=523,333,333.3 m^3 = 5.23*10^11L

Now calculate the number of moles of N2 with the use of gas equation as follows:

PV=nRT

n= PV/RT

Here, R= 0.0821 L atm /mol*K, T= 20 degrees or 293 K, P = 1 atm

n= 5.23*10^11L *1atm /0.0821 L atm /mol*K *293 K

n= 2.17*10^10 mol

Now convert the mol to mass of N2 with its molar mass as follows:

molar mass = 28.0 g /mol

2.17*10^10 mol *28.0 g /mol = 60.76 *10^10 g or 60.76 *10^7k g

60.76 *10^10 g grams of N2 are needed to fill the interior of the colony at one atmosphere and 20 degrees.

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