Please show me how to do this chemistry problem, explain your work if you don't mind.

Question

The size of our chemistry classroom is approximately 10 m x 10 m x 3 m.

(a.) What is molar mass of air filling our classroom assuming that air is composed of 20 %

oxygen (O 2 ) and 80 % nitrogen (N 2 ).

(b.) At 27 o C and 1 atm, how many moles of air molecules occupy our classroom?

(c.) What is the mass of air filling our classroom?

Answer 1

(a). The molar mass of air is the mass in grams of 1 mole of air. Since air is composed of 20% O2 and 80% N2, we can find the molar mass as follows:

1 mole O2 = 32 g O2 x 0.20 = 6.4 g

1 mole N2 = 28 g N2 x 0.80 = 22.4 g

1 mole air = 6.4 g + 22.4 g = 28.8 g/mole

(b). Use the ideal gas law, PV = nRT

P = pressure in atm = 1 atm

V = volume in liters = 10 m x 10 m x 3 m = 300 m³ = 300,000 L

n = moles = ?

R = gas constant = 0.0821 Latm/Kmol

Solving for moles (n), we have...

n = PV/RT = (1 atm)(300,000 L) / (0.0821 L)(300K)

n = 12,180 moles of air

T = temperature in K = 27ºC + 273 = 300 K

(c). To find the mass of air, we simply multiply moles of air by the molar mass of air:

12,180 moles x 28.8 g/mol = 350,792 g (not corrected for sig. figs.)