Ideal Gas Example Problem Partial Pressure

In any mixture of gases, each component gas exerts a partial pressure that contributes to the total pressure. At ordinary temperatures and pressure, you can apply the ideal gas law to calculate the partial pressure of each gas. What Is Partial Pressure? Lets start by reviewing the concept of partial pressure. In a mixture of gases, the partial pressure of each gas is the pressure that gas would exert if it was the only one occupying that volume of space. If you add up the partial pressure of each gas in a mixture, the value will be the total pressure of the gas. The law used to find partial pressure assumes the temperature of the system is constant and the gas behaves as an ideal gas, following the ideal gas law: PV nRT where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. The total pressure is then the sum of all the partial pressures of component gases. For n components of a gas: Ptotal P1 P2 P3 ... Pn When written this way, this variation of the Ideal Gas Law is called Daltons Law of Partial Pressures. Moving around terms, the law can be rewritten to relate moles of gas and total pressure to partial pressure: Px Ptotal (n / ntotal) Partial Pressure Question A balloon contains 0.1 moles of oxygen and 0.4 moles of nitrogen. If the balloon is at standard temperature and pressure, what is the partial pressure of the nitrogen? Solution Partial pressure is found by Daltons Law: Px PTotal ( nx / nTotal ) wherePx partial pressure of gas xPTotal total pressure of all gasesnx number of moles of gas xnTotal number of moles of all gases Step 1 Find PTotal Although the problem does not explicitly state the pressure, it does tell you the balloon is at standard temperature and pressure. Standard pressure is 1 atm. Step 2 Add up the number of moles of the component gases to find nTotal nTotal noxygen nnitrogennTotal 0.1 mol 0.4 molnTotal 0.5 mol Step 3 Now you have all the information needed to plug the values into the equation and solve for Pnitrogen Pnitrogen PTotal ( nnitrogen / nTotal )Pnitrogen 1 atm ( 0.4 mol / 0.5 mol )Pnitrogen 0.8 atm Answer The partial pressure of the nitrogen is 0.8 atm. Helpful Tip for Performing the Partial Pressure Calculation Be sure to report your units correctly! Typically, when using any form of the ideal gas law, youll be dealing with mass in moles, temperature in Kelvin, volume in liters, and pressure is in atmospheres. If you have temperatures in Celsius or Fahrenheit, convert them to Kelvin before proceeding.Remember real gases are not ideal gases, so although the calculation will have very little error under ordinary conditions, it wont be precisely the true value. For most situations, the error is negligible. Error increases as pressure and temperature of a gas increase because the particles are interacting with each other more often.