Partial Pressure Formula: Definition, Steps, Example
Partial Pressure Formula: Partial pressure represents the pressure a single gas would exert if it occupied the entire volume of a gas mixture at the same temperature. It's determined by the gas's mole fraction and the total pressure in the mixture.
Manoj Kumar19 Sept, 2023
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Partial Pressure Formula: The formula for calculating partial pressure is derived from Dalton's law of partial pressure. According to Dalton's law, when you have a mixture of gases that do not react chemically with each other, the total pressure exerted by this mixture is equal to the sum of the individual partial pressures of each gas component within the system.
Also Check - Internal Energy Formula
Partial Pressure Formula Step-by-step Explanation
Partial pressure is a concept applicable to gases within a gas mixture, representing the pressure a gas would exert if it occupied the entire volume of the mixture at the same temperature.
Let's consider a container with volume V containing two gases, nitrogen and oxygen. Applying the ideal gas equation: P t V = (n O2 + n N2 )RT ---Equation (1) According to the definition of partial pressure, we can calculate the partial pressure of oxygen (if it occupied the container alone) using the ideal gas equation: P O2 V = n O2 RT ---Equation (2) Similarly, we can calculate the partial pressure of nitrogen (if it occupied the container alone) using the ideal gas equation: P N2 V = n N2 RT ---Equation (3) By adding equations (2) and (3), we obtain: (P O2 + P N2 )V = (n O2 + n N2 )RT ---Equation (4) Comparing equation (4) with equation (1), we arrive at Dalton's law of partial pressure: P t = P O2 + P N2 This equation is known as Dalton's law of partial pressure. Now, dividing equation (2) by equation (1), we can express the partial pressure of oxygen as a fraction of the total pressure: P O2 /P t = (n O2 /n O2 + n N2 ) This fraction represents the mole fraction of oxygen, denoted as XO2: X O2 = n O2 / (n O2 + n N2 ) Therefore, the partial pressure of oxygen can be expressed as: P O2 = X O2 * P t Similarly, the partial pressure of nitrogen can be calculated by dividing equation (3) by equation (1), yielding: P N2 = X N2 * P tAlso Check - Ionization Energy Formula
Partial Pressure Formula Solved Example
Example 1: Suppose you have a container with a total pressure of 2 atm that contains a mixture of oxygen (O 2 ) and nitrogen (N 2 ). If the mole fraction of oxygen in the mixture is 0.3, what is the partial pressure of oxygen? Solution: We can use the formula for partial pressure derived earlier: P O2 = X O2 * P t Given: Total pressure (Pt) = 2 atm Mole fraction of oxygen (X O2 ) = 0.3 Substitute these values into the formula: P O2 = 0.3 * 2 atm = 0.6 atm So, the partial pressure of oxygen in the mixture is 0.6 atm.Also Check - Molecular Speed Formula
Example 2: In a gas mixture, the partial pressure of nitrogen (PN2) is measured to be 0.8 atm. If the total pressure (Pt) of the mixture is 1.5 atm, what is the mole fraction of nitrogen in the mixture? Solution: We can rearrange the formula for partial pressure to find the mole fraction: X N2 = P N2 / P t Given: Partial pressure of nitrogen (P N2 ) = 0.8 atm Total pressure (P t ) = 1.5 atm Substitute these values into the formula: X N2 = 0.8 atm / 1.5 atm = 0.533 So, the mole fraction of nitrogen in the mixture is approximately 0.533. Example 3: In a gas mixture, the partial pressures of oxygen (P O2 ) and nitrogen (P N2 ) are 0.4 atm and 0.6 atm, respectively. Calculate the total pressure (Pt) of the mixture. Solution: We can use Dalton's law of partial pressure to calculate the total pressure: P t = P O2 + P N2 Given: Partial pressure of oxygen (P O2 ) = 0.4 atm Partial pressure of nitrogen (P N2 ) = 0.6 atm Substitute these values into the formula: P t = 0.4 atm + 0.6 atm = 1.0 atm These examples demonstrate how to use Dalton's law of partial pressure and the derived formulas to calculate partial pressures and mole fractions in gas mixtures.Partial Pressure Formula FAQs
What is Dalton's law of partial pressure?
Dalton's law asserts that when you have a blend of inert gases, the overall pressure is equal to the combined pressures contributed by each individual gas.
How can you calculate the partial pressure of a gas in a mixture?
You can calculate the partial pressure of a gas by multiplying its mole fraction in the mixture by the total pressure.
What is the mole fraction of a gas in a mixture?
The mole fraction of a gas in a mixture is defined as the proportion of the gas's moles to the total moles within the mixture.
Why is Dalton's law applicable only to non-reacting gases?
Dalton's law assumes that gases in a mixture do not chemically react with each other. If they do react, the behavior may not follow this law due to chemical reactions altering the composition and properties of the mixture.
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