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.

Question

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
Answer This Question

Answer 1

I worked c the same way you did and another way and got the same answer each way. Then I used both ways to to do A and came up with your answer. I assume the others are ok. Here is the OTHER way to do density.

Density at STP is 32/22.4 = about 1.43 g/L. Not convert from STP to the new conditions.
1.43 g/L x (9/14.7) x (273/300) = ?

Then convert to mols O2 in a liter. 0.796/32 = 0.0249

Answer 2

A) Your calculation for the number of moles of oxygen per liter is correct. You correctly used the ideal gas law equation, and dividing by 0.2 L is the appropriate step to convert the moles of oxygen to moles per liter. Your final answer of 0.0249 mol O2/1 Liter is correct.

B) Your calculation for the number of oxygen molecules per liter is also correct. You multiplied the number of moles of oxygen (0.00497 mol O2) by Avogadro's number (6.02 x 10^23 molecules/mol) to get the total number of oxygen molecules. Dividing by the volume of 0.2 L is correct to express the number of oxygen molecules per liter. Your final answer of 1.50 x 10^22 O2 molecules per liter is correct.

C) Your calculation for the density of oxygen is correct. You used the formula d= PM/RT, where P is the pressure, M is the molar mass, R is the ideal gas constant, and T is the temperature. Dividing by 0.08206 (units: atm x L/mol x K) and multiplying by 32.00 g/mol (the molar mass of oxygen) is appropriate. Your final answer of 0.796 g/L is correct.

Overall, your calculations and reasoning are correct. Well done!

Answer 3

To calculate the number of moles of oxygen per liter, you correctly used the ideal gas law equation n = PV/RT, where P is the pressure, V is the volume, R is the ideal gas constant, and T is the temperature.

Given that the pressure is 0.612 atm, the volume is 0.2 L, the gas constant is 0.08206 atm⋅L/(mol⋅K), and the temperature is 300 K, you can substitute these values into the equation:

n = (0.612 atm x 0.2 L) / ((0.08206 atm x L) / (mol x K) x 300 K)

Simplifying the equation, you get:

n = 0.0249 mol O2 / 1L

So, your calculation is correct. The number of moles of oxygen per liter is 0.0249 mol O2/1L.

To calculate the number of oxygen molecules per liter, you need to multiply the moles of oxygen by Avogadro's number (6.02 x 10^23 molecules/mol). This gives you:

0.0249 mol O2 x (6.02 x 10^23 molecules/1 mol O2) = 1.50 x 10^22 O2 molecules

Since you are calculating the number of oxygen molecules per liter, you need to divide this value by the volume:

(1.50 x 10^22 molecules) / (0.2 L) = 7.50 x 10^22 O2 molecules/L

Thus, the correct answer is 7.50 x 10^22 oxygen molecules per liter.

To calculate the density of oxygen, you can use the formula d = PM/RT, where P is the pressure, M is the molar mass, R is the ideal gas constant, and T is the temperature.

Given that the pressure is 0.612 atm, the molar mass of oxygen (O2) is 32.00 g/mol, the gas constant is 0.08206 atm⋅L/(mol⋅K), and the temperature is 300 K, you can substitute these values into the equation:

d = (0.612 atm x 32.00 g/mol) / (0.08206 atm ⋅ L/(mol ⋅ K) x 300 K)

Simplifying the equation, you get:

d = 0.796 g/L

So, your calculation is correct. The density of oxygen in Colorado Springs at an elevation of 6500 feet and atmospheric pressure of around 9 psi, assuming T = 300 K, is 0.796 g/L.