A sample of air contains 78.8% nitrogen, 20.94% oxygen, 0.05% carbon dioxide, and 0.930% argon by volume. How many molecules of each gas are present in 1.00 L of the sample at 35 degrees C and 1.00 atm?
The percentages don't add to 100%. Please check the post for accuracy.
I'm sorry, that should read 78.08% nitrogen
You will have 0.7808 L nitrogen. How many moles is that? PV = nRT
Then n x 6.022 x 10^23 = # molecules.
The others are done the same way.
254.23
To find the number of molecules of each gas in the sample, we will use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature (in Kelvin)
First, we need to convert the given temperature from Celsius to Kelvin:
T(Kelvin) = T(Celsius) + 273.15
T(Kelvin) = 35 + 273.15 = 308.15 K
Next, we need to calculate the number of moles for each gas in the sample. To do this, we will use the percentage composition and molar mass of each gas.
Let's start with nitrogen:
Percent composition of nitrogen = 78.8%
Molar mass of nitrogen (N2) = 28.0134 g/mol
Number of moles of nitrogen (n) = (percent composition / 100) * (Volume / 22.4) * (1 / molar mass)
= (78.8 / 100) * (1.00 / 22.4) * (1 / 28.0134)
= 0.2832 moles
Similarly, we can calculate the number of moles for each gas:
Oxygen:
Percent composition of oxygen = 20.94%
Molar mass of oxygen (O2) = 31.9988 g/mol
Number of moles of oxygen (n) = (percent composition / 100) * (Volume / 22.4) * (1 / molar mass)
= (20.94 / 100) * (1.00 / 22.4) * (1 / 31.9988)
= 0.1496 moles
Carbon Dioxide:
Percent composition of carbon dioxide = 0.05%
Molar mass of carbon dioxide (CO2) = 44.0095 g/mol
Number of moles of carbon dioxide (n) = (percent composition / 100) * (Volume / 22.4) * (1 / molar mass)
= (0.05 / 100) * (1.00 / 22.4) * (1 / 44.0095)
= 0.000125 moles
Argon:
Percent composition of argon = 0.930%
Molar mass of argon = 39.948 g/mol
Number of moles of argon (n) = (percent composition / 100) * (Volume / 22.4) * (1 / molar mass)
= (0.930 / 100) * (1.00 / 22.4) * (1 / 39.948)
= 0.0003693 moles
Now, to find the number of molecules of each gas, we can use Avogadro's number:
Number of molecules = Number of moles * Avogadro's number
= (moles of gas) * (6.02214 × 10^23 molecules/mol)
Let's calculate the number of molecules for each gas:
Number of molecules of nitrogen = (0.2832 moles) * (6.02214 × 10^23 molecules/mol)
≈ 1.70 × 10^23 molecules
Number of molecules of oxygen = (0.1496 moles) * (6.02214 × 10^23 molecules/mol)
≈ 8.99 × 10^22 molecules
Number of molecules of carbon dioxide = (0.000125 moles) * (6.02214 × 10^23 molecules/mol)
≈ 7.53 × 10^19 molecules
Number of molecules of argon = (0.0003693 moles) * (6.02214 × 10^23 molecules/mol)
≈ 2.22 × 10^20 molecules
Therefore, in 1.00 L of the sample, there are approximately:
- 1.70 × 10^23 molecules of nitrogen
- 8.99 × 10^22 molecules of oxygen
- 7.53 × 10^19 molecules of carbon dioxide
- 2.22 × 10^20 molecules of argon.