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A balloon inflated with three breaths of air has a volume of 1.7 L. At the same temperature and pressure, what is the volume of the balloon if five more same-sized breaths are added to the balloon?
4.53 $\mathrm{L}$
00:48
Aadit S.
01:21
Charotte M.
Chemistry 101
Chapter 9
Gases
Rice University
Drexel University
University of Maryland - University College
University of Kentucky
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So if you blow into something like a balloon and you assume that the breaths that you take, you take the same breath every time, it's not like you take a deep breath in a shallow breath, we take the same size breath each time. That means that the number of breaths that you take is directly proportional. That's what this little alpha sign says to the volume of the breaths. So why is that important? Well, because what that means is mathematically we're going to set up a proportion to be able to solve this. So we're gonna say the if we have three breaths And we know that those three breaths take up 17 L. Well what if we use more breaths and if we add five more breaths, five more than three is eight breaths. I don't know what the volume will be in leaders but we can solve that. We can uh solve for X and cross multiply and divide so without the units, just the numbers in the X. we can take three times X is equal to eight Times 1.7. And then to get X by itself will divide both sides by three. And so if we go ahead and do that math, that's going to tell us the volume of eight breaths and the volume of eight breaths is four 0.5 liters. Now your calculator may give you more decimal places. 4.53333333 leaders. But we are constrained by two significant figures. Three breaths is an infinite number. Eight breaths is an infinite number because it's exactly three breaths for eight breaths, 1.7 liters is measured, so we only have two significant figures. So eight breaths, 4.5 L.
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