Dry air near sea level has the following composition by volume: N2, 78.08 percent; O2, 20.94 percent; Ar, 0.93 percent; CO2, 0.05 percent. The atmospheric pressure is 1.00 atm. (Hint: Since volume is proportional to the number of moles present, mole fractions of gases can be expressed as ratios of volumes at the same temperature and pressure.)
(a) Calculate the partial pressure of each gas in atm.
(b) Calculate the concentration of each gas in moles per liter at 0°C.
a. The hint tells you that the mole fraction N2 = 0.7808; therefore the partial pressure of N2 = XN2*Ptotal
b. I would sum the moles and use PV = nRT to calculate volume. Then M = moles/L.
To calculate the partial pressure of each gas, we need to multiply the mole fraction of each gas by the total atmospheric pressure.
Given:
Total pressure (P) = 1.00 atm
(a) Partial pressure of each gas:
- N2 mole fraction = 78.08% = 0.7808
- O2 mole fraction = 20.94% = 0.2094
- Ar mole fraction = 0.93% = 0.0093
- CO2 mole fraction = 0.05% = 0.0005
Partial pressure of N2 = N2 mole fraction * total pressure
= 0.7808 * 1.00 atm = 0.7808 atm
Partial pressure of O2 = O2 mole fraction * total pressure
= 0.2094 * 1.00 atm = 0.2094 atm
Partial pressure of Ar = Ar mole fraction * total pressure
= 0.0093 * 1.00 atm = 0.0093 atm
Partial pressure of CO2 = CO2 mole fraction * total pressure
= 0.0005 * 1.00 atm = 0.0005 atm
(b) To calculate the concentration of each gas in moles per liter at 0°C, we need to use the ideal gas law equation:
PV = nRT
Where:
P = partial pressure of the gas
V = volume in liters (assuming 1 L)
n = number of moles of the gas
R = ideal gas constant (0.0821 L*atm/(mol*K))
T = temperature in Kelvin (0°C = 273.15 K)
Concentration (C) = n/V
Concentration of N2 = n(V) / V = n
Concentration of O2 = n(V) / V = n
Concentration of Ar = n(V) / V = n
Concentration of CO2 = n(V) / V = n
Since the concentration (C) is equal to the number of moles (n), the concentrations will be the same as the number of moles.
Therefore, the concentrations of each gas in moles per liter at 0°C are:
Concentration of N2 = 0.7808 mol/L
Concentration of O2 = 0.2094 mol/L
Concentration of Ar = 0.0093 mol/L
Concentration of CO2 = 0.0005 mol/L
To calculate the partial pressure of each gas in atm, we need to use the mole fraction of each gas along with the total atmospheric pressure.
(a) Partial pressure of a gas can be calculated using the formula:
Partial Pressure = Mole Fraction × Total Pressure
First, let's convert the percentages of each gas into mole fractions.
1. Convert the percentages into decimal fractions:
N2: 78.08% = 0.7808
O2: 20.94% = 0.2094
Ar: 0.93% = 0.0093
CO2: 0.05% = 0.0005
2. Calculate the mole fractions by dividing each decimal fraction by the sum of all decimal fractions:
Total mole fraction = 0.7808 + 0.2094 + 0.0093 + 0.0005 = 1.0000
Mole fraction of N2 = 0.7808 / 1.0000 = 0.7808
Mole fraction of O2 = 0.2094 / 1.0000 = 0.2094
Mole fraction of Ar = 0.0093 / 1.0000 = 0.0093
Mole fraction of CO2 = 0.0005 / 1.0000 = 0.0005
3. Now, we can calculate the partial pressure of each gas:
Partial Pressure of N2 = Mole Fraction of N2 × Total Pressure = 0.7808 × 1.00 atm
Partial Pressure of O2 = Mole Fraction of O2 × Total Pressure = 0.2094 × 1.00 atm
Partial Pressure of Ar = Mole Fraction of Ar × Total Pressure = 0.0093 × 1.00 atm
Partial Pressure of CO2 = Mole Fraction of CO2 × Total Pressure = 0.0005 × 1.00 atm
(b) To calculate the concentration of each gas in moles per liter at 0°C, we need to use the ideal gas law equation:
PV = nRT, where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L · atm/(mol · K))
T = temperature (in Kelvin)
Given that the temperature is 0°C, which is equal to 273.15 K, we can rearrange the equation to solve for n (number of moles) as follows:
n = PV / RT
1. Convert the given atmospheric pressure of 1.00 atm to Pascals (Pa):
1 atm = 101325 Pa
2. Calculate the concentration of each gas in moles per liter:
Concentration (moles/L) = (Partial Pressure of Gas) / (RT / P)
Using the known values for the pressure, gas constant, and temperature of 0°C, we can substitute them into the formula to calculate the concentrations.
I hope this explanation helps you to understand how to calculate the partial pressures and concentrations of gases in the given scenario.