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 12 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.
Start out with PV = nRT, plug in the numbers and solve for n = number of mols of air. Correct for 20% O2 and go from there. Post your work if you get stuck.
To calculate the number of moles of oxygen per liter, we can use the Ideal Gas Law. The formula for the Ideal Gas Law is:
PV = nRT
Where:
P = Pressure (in atm or Pa)
V = Volume (in liters)
n = Number of moles
R = Universal gas constant (0.0821 L•atm/mol•K)
T = Temperature (in Kelvin)
First, we need to convert the atmospheric pressure from psi to atm. Since 1 atm is approximately equal to 14.7 psi, the atmospheric pressure at Colorado Springs (12 psi) can be converted to:
12 psi / 14.7 psi/atm ≈ 0.82 atm
Now, we can substitute the values into the Ideal Gas Law equation, rearranging it to solve for n:
n = PV / RT
Given:
P = 0.82 atm
V = 1 liter
R = 0.0821 L•atm/mol•K
T = 300 K
n = (0.82 atm * 1 L) / (0.0821 L•atm/mol•K * 300 K)
n ≈ 0.033 moles of oxygen per liter
Next, let's calculate the number of oxygen molecules per liter. Avogadro's number states that there are 6.022 x 10^23 molecules per mole. Therefore, the number of oxygen molecules per liter can be obtained by multiplying the number of moles by Avogadro's number:
Number of molecules = n * Avogadro's number
Given:
n = 0.033 moles
Number of molecules = 0.033 moles * 6.022 x 10^23 molecules/mole
Number of molecules ≈ 1.99 x 10^22 oxygen molecules per liter
Finally, let's calculate the density of oxygen in g/L. The molar mass of oxygen (O2) is approximately 32 grams per mole. The density (d) is defined as the mass (m) divided by the volume (V):
d = m / V
Given:
n = 0.033 moles
Molar mass of O2 = 32 g/mol
V = 1 liter
The mass can be calculated as the product of the number of moles and the molar mass:
m = n * Molar mass
m = 0.033 moles * 32 g/mol
m ≈ 1.06 grams
Finally, we can substitute the values into the density equation to find the density of oxygen in g/L:
d = 1.06 grams / 1 liter
d ≈ 1.06 g/L
Therefore, the number of moles of oxygen per liter is approximately 0.033 moles, the number of oxygen molecules per liter is approximately 1.99 x 10^22 oxygen molecules, and the density of oxygen in g/L is approximately 1.06 g/L.