A sample of air contains 78.08% 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?
Gases to solve for: N2, O2, CO2, and Ar
To determine the number of molecules of each gas present in the sample, we first need to calculate the number of moles for each gas using 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)
Given:
Pressure (P) = 1.00 atm
Volume (V) = 1.00 L
Temperature (T) = 35 degrees C = 35 + 273.15 K = 308.15 K
Let's begin with nitrogen (N2):
Percentage of nitrogen = 78.08%
Calculate the number of moles of nitrogen:
n(N2) = (Percentage of nitrogen / 100) * Volume (V) * Pressure (P) / (R * Temperature (T))
Substituting the given values:
n(N2) = (0.7808 * 1.00 * 1.00) / (0.0821 * 308.15)
Repeat this process for oxygen (O2), carbon dioxide (CO2), and argon (Ar) using their respective percentages.
n(O2) = (0.2094 * 1.00 * 1.00) / (0.0821 * 308.15)
n(CO2) = (0.0005 * 1.00 * 1.00) / (0.0821 * 308.15)
n(Ar) = (0.0093 * 1.00 * 1.00) / (0.0821 * 308.15)
Now that we have the number of moles for each gas, we can calculate the number of molecules for each gas using Avogadro's number (6.022 x 10^23 molecules/mol).
Number of molecules of nitrogen (N2) = n(N2) * Avogadro's number
Number of molecules of oxygen (O2) = n(O2) * Avogadro's number
Number of molecules of carbon dioxide (CO2) = n(CO2) * Avogadro's number
Number of molecules of argon (Ar) = n(Ar) * Avogadro's number
Performing these calculations will give you the number of molecules for each gas present in the 1.00 L sample at 35 degrees C and 1.00 atm.