partial pressure, law of partial pressures, or Dalton's law was proposed by the scientist John Dalton, which carried out several meteorological studies and related to the composition of atmospheric air. According to him,
“partial pressure is the force that the molecules of a gas exert on the walls of a container, which is exactly the same as it would exert if it were in a gas mixture.”
Based on this conclusion, Dalton stated that the pressure exerted by a gas mixture (Total pressure, Pt) in the walls of a container is equal to the sum of the individual partial pressures of each of the gases that comprise this Mix.
Pt =PTHE + PB + PÇ
In which,
PTHE = partial pressure of gas A
PB = partial pressure of gas B
PÇ = partial pressure of gas C
For example, if we have a mixture formed by hydrogen gases (H2), oxygen (O2) and carbon dioxide (CO2) inside a container, the pressure of this mixture is the result of the sum of the pressures of each of these gases, thus:
Pt =PH2 + PO2 + PCO2
1- Relation of partial pressure to total pressure
According to John Dalton, the relationship between partial pressure of a certain gas (PTHE) with the total pressure of the gas mixture is always equal to molar fraction (XTHE) of gas, which results in the following formula:
PTHE = XTHE
Pt
It is noteworthy that the molar fraction of a gas is given by the relationship between the number of moles (nA) of this gas by the mole number (nt) of the gaseous mixture (resulting from the sum of the mole number of all the gases that make up the mixture).
XTHE = noTHE
not
Thus, if we substitute the formula for the molar fraction of the gas in the expression of the relationship between partial pressures, we have:
PTHE = noTHE
Pt not
2- Total pressure of a gas mixture
The total pressure of a gas mixture can be found not only by adding the partial pressures of the gases that make it up. It can be calculated using the clapeyron equation:
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Pt.Vt = nt.R.T
This formula can be used to calculate the total pressure, as long as the volume of the container (or the total volume of gases) and the total mol number (n) are used.t), being:
R = general gas constant
T = temperature of the mixture in Kelvin
Note: If the temperature is in degrees Celsius, change it to Kelvin; to do this just add the value provided with 273.
3- Example of application of partial pressure of a gas
Example: (FEI SP) In a 44.8L container, kept at 273K, 4 mol of hydrogen gas and 6 mol of oxygen gas in CNTP were mixed. Partial pressures of H2 it's the2, in atmospheres, are, respectively:
a) 1.0 and 2.0
b) 3.0 and 4.5
c) 0.8 and 1.2
d) 1.0 and 1.5
e) 2.0 and 3.0
Data provided by the exercise:
Temperature = 273 K
System volume = 44.8 L
Number of moles of hydrogen gas = 4 moles
Number of moles of oxygen gas = 6 moles
PH2= ?
PO2= ?
1O Step: Calculate the total mole number
not = nH2 + nO2
not = 4 + 6
not = 10 mol
2O Step: Calculate the total pressure (Pt) of the system using the Clapeyron equation
Pt.Vt = nt.R.T
Pt.44,8 = 10.0,082.273
Pt.44,8 = 223,86
Pt = 223,86
44,8
Pt = 4.996875 atm, then Pt it's about 5 atm
3O Step: Calculate the partial pressure of hydrogen gas
PH2 = noH2
Pt not
PH2 = 4
5 10
PH2.10 = 4.5
PH2.10 = 20
PH2 = 20
10
PH2 = 2 atm
4O Step: Calculate the partial pressure of oxygen gas
As we have only two gases in the mixture and we know the pressure of one of them and the total pressure, to calculate the partial pressure of the oxygen gas, just use the expression of the total pressure of the mixture:
Pt =PH2 + PO2
5 = 2 + PO2
PO2 = 5 – 2
PO2 = 3 atm
By Me. Diogo Lopes Dias
Would you like to reference this text in a school or academic work? Look:
DAYS, Diogo Lopes. "Partial pressure of gases"; Brazil School. Available in: https://brasilescola.uol.com.br/quimica/pressao-parcial-dos-gases.htm. Accessed on June 27, 2021.
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