The partial pressure of a gas increases proportionally with the total pressure of the gas mixture.
Here's a breakdown of why and how:
Understanding Partial Pressure
Partial pressure is the pressure exerted by an individual gas in a mixture of gases. The concept is rooted in Dalton's Law of Partial Pressures, which states that the total pressure of a gas mixture is the sum of the partial pressures of each individual gas.
The Relationship Explained
The key equation that links partial pressure and total pressure is:
*Pi = Xi Ptotal**
Where:
- Pi is the partial pressure of gas i.
- Xi is the mole fraction of gas i (the number of moles of gas i divided by the total number of moles of all gases in the mixture).
- Ptotal is the total pressure of the gas mixture.
This equation clearly shows that if the mole fraction (Xi) of a gas remains constant, then the partial pressure (Pi) of that gas is directly proportional to the total pressure (Ptotal).
Example
Imagine a container with a mixture of nitrogen (N2) and oxygen (O2). Let's say the mole fraction of N2 is 0.7 and the mole fraction of O2 is 0.3.
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If the total pressure in the container is 1 atmosphere (atm), the partial pressure of N2 is 0.7 atm and the partial pressure of O2 is 0.3 atm.
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If the total pressure is increased to 2 atm, the partial pressure of N2 becomes 1.4 atm (0.7 2), and the partial pressure of O2 becomes 0.6 atm (0.3 2).
As you can see, as the total pressure increases, the partial pressures of each gas also increase proportionally.
Constant Mole Fraction
It is crucial to remember that this proportional relationship holds true when the mole fractions of the gases in the mixture remain constant. If you start adding more of one gas to the mixture, the mole fraction of that gas will change, and therefore, while the partial pressure of the gas may increase, it would not be solely due to a change in total pressure. It would be due to both, the change in total pressure and the change in the mole fraction of the gas.
Summary
Partial pressure increases proportionally with total pressure, provided the mole fraction of the gas in the mixture remains constant. The partial pressure of any gas in a mixture is equal to the product of its mole fraction and the total pressure of the mixture.
