Dalton's Law: Partial Pressure (Simplified)

partial pressure is the pressure exerted by an individual gas within a mixture. So think of it as the gas is individual pressure, we're going to say in a container of un reacting, gas is total pressure of the container is the sum of partial pressures of each gas. Now this is known as the law of partial pressures. So basically the total pressure inside of a container comes from adding up all the pressures of each individual gas. So total pressure would equal the pressure of gas one plus gas two plus gas three and so on. If there are additional gas, is so just remember, the total pressure that container is experiencing is contributed by each of the individual gasses within it.

here we're told that a sample of neon gas exerts a pressure of 1. atmospheres inside a cylinder. Some nitrogen gas is also present at a pressure of 500 tour. What is the total pressure inside the cylinder? So remember, we just learned about the law off partial pressures, which tells us that the total pressure felt inside of a container, or in this case, a cylinder comes from adding up the partial pressures of each gas present. So in the container, we have neon gas, and we also have nitrogen gas. The total pressure is when you add their partial pressures together. Now the issue is we don't have the same units for these gasses. Neon is in atmospheres, but nitrogen is in tours. Since atmospheres is a standard unit we usually use for pressure. Let's convert the tour into atmospheres. So we're gonna have 500 tour and remember that for everyone atmosphere that's 760 tour. So when we do that, we're gonna get as our atmospheres 0.65789 atmospheres. Take that and plug it in. And when we do that, we're gonna get a total pressure of 2. atmospheres. Within our question, 1.85 has three SIG figs. 500 only has one sick fig here. If we went by 16 fig, this would round up to three, which is a pretty big round there in terms of our value. So it's just better to go. Let's go with the three Sig figs in this 1.85 Again, the question isn't asking for a number of sick fixing. Your final answer. We're doing this as continual, continuous practice in terms of determining Sig Figs again. Better to go with three sig figs. I know it's not the least number of Sig Figs, but going from 2.5 to 33 atmospheres. It's such a big increase better just to go with three sig figs. And then we have 2.51 atmospheres at the end. So now that we've seen this question, let's move on to the next video

So we know at this point that the total pressure felt within a container is a result of adding up. All the partial pressures of the gas is present. Now, if we can focus on one of these gasses and we know it's moles, its temperature and its volume, we could also find its partial pressure. Now we're going to stay here. If you assume that the gasses behave ideally, then their partial pressures can be calculated from the ideal gas law. We're gonna say here that the pressure of that gas that I'm focusing on so let's call a gas one. We confined its partial pressure if we know it's moles. So moles one. Ours are gas, constant times the temperature of the container divided by the volume of the container. So here we're using the ideal gas law to just focus in on one gas and from it determine its partial pressure.

if 12 g of helium and 20 g of oxygen are placed inside a five liter of cylinder at 30 degrees Celsius, what is the partial pressure of the helium gas? All right, so they're giving us information on two gas. Is there giving us information on helium and oxygen, but realize they're only asking for information in terms of partial pressure for the helium. With the healing I have, it's grams. And from that I can determine its moles. I have the volume of the container and I have the temperature of the container. With this information, I can find the partial pressure of helium gas by utilizing the ideal gas law. So we're gonna say here pressure of helium equals moles of helium. Times are times t divided by V. We don't even need to look at the grands of oxygen because the question again is only asking about the partial pressure of helium. All right, so let's take the 12 g of helium We look on the periodic table, you'll see that the atomic massive helium is approximately 4. grands helium for everyone. More of helium grams Here, cancel out and I'll have my moles as 2. Moles of helium. So take that. Plug it into the formula. So 2.9978 moles off helium multiplied by my gas law on my gas. Constant 0.8 to 06 leaders times atmospheres over moles Times K Remember, temperature must be in Kelvin. So the 30 degrees Celsius I'm gonna add to 73. to it and that gives me 303. 15 Kelvin. Then we take the volume, which is five leaders, and we just plug it in. Look at the units leaders cancel with leaders. Kelvin's cancel out with Calvin's moles cancel with moles And at the end, what we have left is atmospheres. So we plugged that in and we'll get 14.9149 atmospheres If we look at the sig Figs within our question, we have three sig figs, three sig figs to sig figs and one sigfig here. If we wanted 16 figure around down to 10 atmospheres again, that's such a big deviation from our actual number. So let's go with a number that makes more sense because we don't want around so much we're gonna say our answer here is 14.9 atmospheres again. We're constantly trying toe Remember, significant figures play a role in a lot of our questions here. We're not being asked to directly, but when applicable, we should apply it here. It wouldn't make sense to apply it because it would round our answer toe a number that doesn't quite fit. Going from 14.9 to 10 is such a big difference. So here we're just gonna go with 366 14.9 atmospheres is more reasonable. It's not a big deviation from our original answer. So just remember, if we have the moles, the temperature and the volume, we confined the partial pressure of a gas by using the ideal gas law formula.

Now, when the percent composition of a gas is given, first determine its fractional composition. Now by fractional composition, we mean that it represents the percent composition of a gas divided by total percent. So here we have our fractional composition formula. So here we're going to say fractional composition, which we're gonna use em As a stand in Ford's variable equals the percentage of your particular gas. You're looking at divided by the total percent, which is 100%. Then we're going to say that we can calculate the partial pressure of the gas using its fractional composition and the total pressure. So that feeds into Dalton's Law. And Dalton's Law says that the partial pressure of a gas, let's say, call it gas A equals the fractional composition of gas a times the pressure total. Right? So, using fractional composition allows us to step into Dalton's Law to help us figure out the partial pressure of gases within any given container.

A cylinder of a gas mixture used for calibration of blood gas analyzers in medical laboratories contains 5% carbon dioxide, 12% oxygen and the remainder nitrogen at a total pressure of 146 atmospheres. What is the partial pressure of each component of this gas? All right. So We're going to say we have 5% co two We have 12% oxygen and if we did 100% minus the 5% and 12% That would give us the percentage of our nitrogen gas. So that will come out to 83% nitrogen gas. Now that we know each other percentages, we can figure out their fractional compositions and by extension or partial pressures. So for C. 02 so pressure of C. 02 equals its fractional composition, which is 5% divided by 100% Times the total pressure of 1 46 atmospheres. This tells me that the partial pressure of co two is about 7. atmospheres for that B 12%. So pressure of 02 equals 12% divided by 100% times the total pressure, So that will come out to 17.5 atmospheres. And then finally we have nitrogen gas. So that would be pressure of nitrogen gas equals 83%, divided by 100 Times 1 Atmospheres. So this comes out to approximately one 21.2 Atmospheres. So this will be the partial pressure of each gas component within the gas mixture of this cylinder.