GS_Dalton's Law of Partial Pressure Lesson

Dalton's Law of Partial Pressure

John Dalton imageJohn Dalton, when not busy with developing his atomic theory, worked to discover how gas laws work when dealing with mixtures of gases. It is important to note here that the gases involved in these mixtures are not reacting. If the gases react, then an entirely different set of products would appear. But, in nonreacting mixtures, each gas that is present contributes a  partial pressure  to the total pressure of the mixture. This is summarized as Dalton's law of partial pressure, which can be expressed mathematically as:

DALTON'S LAW OF PARTIAL PRESSURE PTotal = PA + PB + Pc...

Example Problem A mixture of oxygen, hydrogen and nitrogen gases exerts a total pressure of 288 kPa. If the partial pressures of the oxygen and the hydrogen are 112 kPa and 83 kPa respectively, what would be the partial pressure exerted by the nitrogen? PTotal Po₂+ PN2 + PH2 = 288 kPa = 112 kPa + PN2 + 83 kPa PN2 288-112-83 PN2 = 93 kPa

Solving problems involving partial pressure aren't all this straight forward. Often they will involve something called mole fraction. Mole fraction is simply the ratio of the number of moles of one chemical to the total moles and is represented by the symbol X. Mole fractions for a mixture must always add up to 1.

MOLE FRACTION ΧΑ = nA/ n₁+ng+ nc+...nz XA = nA/nR

It turns out that mole fraction can also be calculated using pressures, specifically partial pressure. The derivation of this can be found in your book.

MOLE FRACTION XA = PA/ PA+ PB+PC+...Pz XA =PA/ Pr

Example Problem A gas mixture contains CO2, O2, and N2. The mole fraction for CO₂ is 0.02, for O2 is 0.20 and for N2 is 0.78. a) If the total pressure is 750 torr, calculate the partial pressure of the oxygen. Xo=Po₂/PT 0.20= Po/750torr Po=150torr b) If 22 liters of this gas mixture, at 35°C, have to be produced, how many moles of O2 are needed? To calculate number of moles of O2, we can use the ideal gas law and the partial pressure found above. Po2 150 torr (1 atm/760 torr) = 0.197 atm V = 22 L T35+273 308K R= 0.0821 Latm/molK PV = nRT (0.197)(22)=n(0.0821)(308) n = 0.171mol

Often times, it is convenient in a lab to collect a gas over water. If the gas does not react with the water, this is a viable option. To collect gas by water displacement, a collecting tube is filled with water and inverted in an open container of water. Gas is then allowed to rise into the tube, displacing the water. By raising or lowering the collecting tube until the water levels inside and outside the tube are the same, the pressure inside the tube is exactly that of the atmospheric pressure.

However, the gas inside the tube is saturated with water vapor and is said to be a wet gas. So, the pressure inside the tube is a combination of the pressure of the gas collected and the pressure from the water vapor.

To determine the pressure of the gas that has been collected over water, all you have to do is subtract the vapor pressure of the water from the total pressure.

Gas Collection Over Water diagram with the following labelled Gas Pressure, "Wet" Gas, atmospheric pressure, Gas In As the gas bubbles in (it may be attached to a chemical reaction), it is collected in the flask. As the flask fills, it pushes the water down At the same time, atmospheric pressure is pushing down on the water outside the flask. water When the water level inside and outside the container are equal, the pressure inside the container equals the atmospheric pressure outside the container.

GAS COLLECTION BY WATER DISPLACEMENT PTotal = Pgas + Pwater

To find the vapor pressure of water to use in the above equation, you need to know the temperature of the water. Then you can just refer to a chart like the one below. Notice that the vapor pressure increases as temperature increases.

Vapor Pressure Chart with temp versus vapor pressure

Watch this Khan Academy video on partial pressure. Here, a problem is done using several equations to ultimately determine the partial pressures of each gas and ultimately the total pressure in a container. Take notes as you watch. Pause the video as you watch so that you can work the problems as well.

Remember to work on the module practice problems as you complete each section of content.  

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