Please check.
Oxygen (O2) is about 20% of our air, with about 80% nitrogen and a bunch of minor components. In Colorado Springs, where I grew up, the elevation is ~ 6500 feet and atmospheric pressure is only around 9 psi (vs. 14.7 psi at sea level). Under those conditions and assuming T = 300 K, calculate the number of moles of oxygen per liter, the number of oxygen molecules per liter, and the density of oxygen in g/L.
A)Calculate the number of moles of oxygen per liter
My work:
n=PV/RT =
(0.612 atm x 0.2 L)/((0.08206 atm x L)/(mol x K)) x 300 K = 0.00497 mol O2
0.00497 mol O2/0.2 L = 0.0249
Is it correct to divide by 0.2 from 20% of O2?
My answer: 0.0249 mol O2/1Liter
B) the number of oxygen molecules per liter
0.00497 mol O2 x (6.02 x 10^23 molecules/1 mol O2)
= 2.99 x 10^21 O2 molecules
(2.99 x 10^21)/0.2 L = 1.50 x 10^22
Is it correct to divide by 0.2 L?
My answer: 1.50 x 10^22 O2 molecules per liter
C) Density of oxygen
d= PM/RT
d= (0.612 atm x 32.00 g/mol)/(0.08206 x 300) = 0.796 g/L
My answer: 0.796 g/L
See above
Your calculations for the number of moles of oxygen per liter and the number of oxygen molecules per liter are correct.
For part A, you correctly used the formula n = PV/RT to calculate the number of moles of oxygen. Since the given percentage of oxygen in air is 20%, you divided the result by 0.2 (equivalent to multiplying by 5) to obtain the number of moles of oxygen per liter.
For part B, you used the Avogadro's number (6.02 x 10^23 molecules/mol) to convert the moles of oxygen into the number of oxygen molecules. Again, you divided the result by 0.2 to get the number of oxygen molecules per liter.
For part C, you correctly used the formula d = PM/RT to calculate the density of oxygen. You plugged in the values for pressure, molar mass of oxygen, gas constant, and temperature to get the answer.
Overall, your answers for all three parts are correct. Well done!