Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 °C, calculate the number of moles of CO₂ exhaled.

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Hey there, welcome back. So we have this mixture of gasses that was collected and 21 liters still tank. So this is going to be a total volume of this tank or this container until the pressure reaches 861.4 tours at 58 degrees Celsius. Alright, so here we have a total pressure and then of course the temperature. Now we have two questions. We need to calculate the moles of gas collected. So the total moles, right, for all three of these different gasses and then for part B was the partial pressure and tours of S. 02 if its concentration and the mixture is this much in parts per million, um per volume. So this is a volume of component over volume of mixture times 10 to the six. Alright, so let's go ahead and take a look at the first part eight. So in order to calculate the moles of gas collected, the total moles, we just need the ideal gas law equation PV equals NRT. And everything else here is basically given to us except for n moles. Right? So we're going to solve for moles by dividing both sides by RT So P V over R. T. Now we do need to make sure that all of the variables that we have are in the correct units because not all of them are for example, pressure has to be in atmospheres. It isn't tourist volume has to be in leaders. It is an leaders. So that is correct. Are we always have and temperature has to be in Celsius, I'm sorry, in Calvin. And it's in Celsius. So let's go ahead and actually Convert the C into Calvin. So all we need to do is add to 73.15 to the Celsius and that will give us 331.15 Calvin. All right. So we have the temperature in the correct unit. Now we have this tour. So we have 861.4 tour. Let's go ahead and convert that into atmospheres. So tour will go on the bottom atmosphere on top and then one atmosphere There are 760 tours. Alright, so this cancels the tour and that will give us 1.133 atmospheres. So even though for part B they want the partial pressure of CO two gas and tourists doesn't really matter. We still needed to do this because we are using the ideal gas law equation. Right? So for n For the moles of gas collective for part a. Let's go ahead and plug in the numbers. So pressure is 1.133 atmospheres vol is incorrect. It is 21 l divided by R. T two R. S point oh 8206206 Leaders Times Atmospheres over more times Calvin. It's very useful to memorize all of the units of the gas constant because it will tell you exactly which units everything else has to be in. And then temperatures 3 31. Calvin. Alright. So as you can see atmospheres cancel out, leaders cancel out Calvin, cancel out and now we're going to have more as the unit that's left over. Uh and that's because we're solving for moles. Alright, so for part a once you multiply and divide these numbers, you're going to get .876 moles. Alright, so that is the total moles collected for that mixture from part A. So that includes moles of C. 02, S. So two and H two. Well, Alright, so now for part B. So for part B is a little bit trickier. We want the partial pressure and what we're given here is parts per million and volume. So we're gonna go ahead and take a look at the equation that is going to solve for partial pressure of a gas. So the gas here is S. 02 and it is going to equal to the mole fraction of that gas Plus the total pressure of the mixture. So the total pressure we actually have it is 861.4 tours or 1.133 atmospheres. So this we have um this is what we're trying to solve for the pressure a vessel to and the mole fraction, we don't have but we can actually figure it out from the concentration that's given to us. Okay, so the concentration here is dealing with volume and X here is mole fraction, but we can actually go ahead and say that the mole fraction is going to be the same as the volume fraction because it's just the ratio, so the ratio is going to be the same. So we're going to say that um X of S Instead of having moles of S 02 divided by the total number of moles were going to say it is volume of OSO two divided by the total volume. Okay, so even though we have the total moles, we actually don't have the moles of S 02 and we're just going to go ahead and say that it's in the volume. Right? So we have Total volume but we don't have the volume of S. 02. We can figure that out again from the concentration is given to us. So this 1.83 times 10 to the third, let's see what it's going to equal to. So we're told that it's going to be volume of the components divided by the volume of the mixture, times 10 to the sixth. So volume of S. 02 goes on the top, Right, this is what we actually don't know, but we do have the volume of the mixture, Right? We have that as 21 leaders. So we're going to put that in. So that's 20 one leaders and then all of this Times 10 to the six will give us this answer. So this is the only unknown. So we're going to go ahead. And Of course put these numbers in parentheses. So we're gonna divide both sides by 10 to the six and then multiply both sides by 21. And because these two numbers don't have a unit only this one, we're going to have volume with a liter unit, so volume of S. 02 is going to equal two 0384 liters. Right? So we just divided both sides by 10 to the six and multiply both sides by 21 in order to solve for the volume of S. 02. And that's it. Of course we don't want the volume, we want the pressure but we just found a way to find our mole fraction of S. 02 or volume fraction vessel to. Right. So now we know how many moles of S. 02 we have. It is . Leaders divided by the total. It's still 21 leaders. Okay, And that will give us a mole fraction or no one actually did not calculate the number. I actually put that all in here. So let's go ahead and move this over here. So s. 0. 2. So X of S. 02 is just going to be equal to this. Right? So .03 84 L divided by 21 L. of course, leaders canceled out. Leaders cancel out and then plus the partial the total pressure, which is I'm sorry, did I say? Plus that is supposed to be a Multiplication. So we're multiplying this fraction of S. 02 by the total pressure. I'm so sorry. Times the total pressure, which we said was 861.4 tours now realize that because they want the partial pressure for B um and tours, we are going to use this tour and we're not using um ideal gas law here. So we are allowed to use other Units other than atmospheres. Right? So we're not going to use the atmosphere unit. We're going to use the tour units. So 8 61.4. So as you can see the leaders here canceled out. And we're just going to have towards as the answer. So partial pressure of Co two. Once you divide and multiply is going to be 1.58, it's worse. Okay, so that is going to be the final answer for part B. So I know the second part was a little bit more confusing than the first one. The first one was easy. It's just ideal gas law and you're solving for and using the total pressure of the mixture of gasses for the second one, we wanted the partial pressure of S. 02 but we don't know the partial pressure of partial pressures of any other of the gasses. So we can't subtract from the total to find the partial pressure of CO two. We had to use this equation Right here and it is usually mole fraction of that gas plus the total pressure will give us the partial pressure of the gas. But we don't have moles of S. 02. We can't find the actual mole fraction. But again because moles and volume are going to be directly proportional, we were able to find basically the volume fraction of S. 02 and substituted into this equation by using the concentration that they gave us, Which was an volume of component or volume of s. 0. 2 divided by the total volume and then of course, times 10 to the six because it's parts per million. Okay, so we're able to find volume of S. O. To plug it into here to find the volume fraction and then just multiplied by the total pressure. So it looks a little complicated but it's actually pretty simple. If you think about it. If you have any questions let us know and we'll see you the next problem

Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 °C, calculate the number of moles of CO₂ exhaled.

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Verified Solution

Key Concepts

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Composition of Air

Assume that an exhaled breath of air consists of 74.8% N2, 15.3% O2, 3.7% CO2, and 6.2% water vapor. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 °C, calculate the number of moles of CO2 exhaled.

Recommended similar problem, with video answer:

Verified Solution

Key Concepts

Ideal Gas Law

Molar Volume of a Gas

Composition of Air

Assume that an exhaled breath of air consists of 74.8% N₂, 15.3% O₂, 3.7% CO₂, and 6.2% water vapor. (b) If the volume of the exhaled gas is 455 mL and its temperature is 37 °C, calculate the number of moles of CO₂ exhaled.