1. 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
A) Yes, it is correct to divide by 0.2 to calculate the number of moles of oxygen per liter. This is because you're assuming that 20% of the air is oxygen, so you need to find the number of moles of oxygen in that fraction of the total volume (1 liter).
B) No, it is not correct to divide by 0.2 when calculating the number of oxygen molecules per liter. In this step, you should multiply the number of moles of oxygen (0.00497 mol O2) by Avogadro's number (6.02 x 10^23 molecules/mol) to find the total number of oxygen molecules.
So, the correct calculation would be: 0.00497 mol O2 x (6.02 x 10^23 molecules/1 mol O2) = 2.99 x 10^21 O2 molecules.
C) Yes, it is correct to use the equation d= PM/RT to calculate the density of oxygen. In this equation, P represents the pressure of the gas, M represents the molar mass, R is the ideal gas constant, and T is the temperature in Kelvin.
Using the given values, you can calculate: d= (0.612 atm x 32.00 g/mol)/(0.08206 x 300 K) = 0.797 g/L.
So, the correct answer is approximately 0.797 g/L for the density of oxygen.
To calculate the number of moles of oxygen per liter, you can use the ideal gas law equation: PV = nRT, where P is the pressure in atm, V is the volume in liters, n is the number of moles, R is the ideal gas constant (0.08206 atm L/mol K), and T is the temperature in Kelvin.
Given that the pressure is 0.612 atm, the volume is 0.2 L, 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 L)/(mol K) x 300 K)
n = 0.00497 mol O2
So the number of moles of oxygen per liter is 0.00497 mol O2/ 1 L.
To determine the number of oxygen molecules per liter, you can use Avogadro's number (6.02 x 10^23 molecules/mol) to convert moles of oxygen to molecules:
0.00497 mol O2 x (6.02 x 10^23 molecules/1 mol O2) = 2.99 x 10^21 O2 molecules
Therefore, there are 2.99 x 10^21 O2 molecules in 1 liter.
Regarding your question about dividing by 0.2 in both parts (A and B), dividing by 0.2 is not necessary because the volume used in the calculations is already 0.2 L.
To calculate the density of oxygen, you can use the formula: density (d) = PM/RT, where P is the pressure in atm, M is the molar mass in g/mol, R is the ideal gas constant (0.08206 atm L/mol K), and T is the temperature in Kelvin.
Given that the pressure is 0.612 atm, the molar mass of oxygen is 32.00 g/mol, 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)
d = 0.796 g/L
So the density of oxygen is 0.796 g/L.
Your answer of 0.796 g/L is correct.