Partial pressure, in simple terms, is the pressure exerted by a single gas within a mixture of gases. Here's how to calculate it:
Calculating Partial Pressure
The key formula for finding partial pressure is:
Partial pressure (pi) = Total absolute pressure (P) × Volume fraction of gas component (F)
Where:
- pi is the partial pressure of a specific gas component.
- P is the total absolute pressure of the gas mixture.
- F is the volume fraction of that specific gas component.
Explanation
This formula shows that the partial pressure of a gas is directly proportional to its fraction in the total gas mix. If a gas makes up a larger portion of the mixture, it will contribute more to the total pressure.
How to Use the Formula: A Step-by-Step Guide
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Identify the gas mixture: Determine which gases are present and the specific gas component for which you want to calculate the partial pressure.
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Find the total absolute pressure (P): This is the overall pressure exerted by the entire mixture of gases. You will typically find this value from a pressure gauge or given in the problem statement.
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Determine the volume fraction of the gas component (F): This is the proportion of the specific gas in the total volume of the mixture. This can be expressed as a decimal (e.g., 0.2 for 20%). It's important to note this volume fraction is based on molar fraction, which is equivalent to volume fraction in ideal gases. You can find the fraction if you know:
- The number of moles of your gas and the total moles of the gas mix.
F = moles of the specific gas / total moles of all gases - The volume of your gas and the total volume of the gas mix.
F = volume of the specific gas / total volume of all gases
- The number of moles of your gas and the total moles of the gas mix.
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Multiply: Plug the known values of P and F into the partial pressure equation pi = P × F to get the partial pressure of the specified gas.
Example:
Imagine a container filled with air at a total pressure of 1 atmosphere (atm). Air consists of about 21% oxygen and 78% nitrogen.
- Total pressure (P): 1 atm
- Volume fraction of oxygen (Fo): 0.21
- Volume fraction of nitrogen (Fn): 0.78
Using the formula:
- Partial pressure of oxygen (po): 1 atm × 0.21 = 0.21 atm
- Partial pressure of nitrogen (pn): 1 atm × 0.78 = 0.78 atm
This demonstrates that oxygen contributes about 0.21 atm and nitrogen about 0.78 atm to the total pressure of 1 atm.
Key Takeaways:
- Partial pressure calculations are vital in many areas, especially in chemistry, atmospheric science and diving.
- The total pressure of a gas mixture is equal to the sum of the partial pressures of all the gases present.
- The partial pressure is dependent on the quantity of gas, reflected through volume fraction.
