The air in a bicycle tire is bubbled through water and collected at 25 °C. If the total volume of gas collected is 5.45 L at a temperature of 25 °C and a pressure of 745 torr, how many moles of gas were in the bicycle tire?

Video transcript

Hello. Everyone in this video. We're going to be dealing with partial pressures as well as the ideal guest Law equation. So first I want to go ahead and write down all the information I've gathered just by reading the problem. So information that I'm given First, it's going to be that we have 135 ml. We have football. We have a temperature at 28°C. We have a pressure of 742 tour And we're trying to find here is going to be my moles of beauty. So first thing to notice is that the sample of beating gasses collected over water at a certain temperature. So we have a partial pressure situation going on here And how we deal with that. Let's spread the question 1st. So a total pressure. It goes through the partial pressure of our beauty plus our pressure pressure from the water. So we want to find the pressure of our beauty. So I'm gonna go ahead and subtract each side by the pressure pressure of the water. Leaving us with the pressure of Beauty two equals two. The total pressure minus the pressure of our water. She just spread out H 20. So that's going to be equal to. They're given Pressure of 7 tour. And the pressure of the water at 28°C is actually going to be something that I have found in my textbook or can be given to you from our textbook or a professor and that's going to be that the pressure is 28 0. Tour. And then that will be equaling to put that into my calculator. I'll get a value of 7 13.6 four. Now my ideal gas law equation is PV equals N R. T. With our being my gas law constant which is 0.8206. The units at ATM times leader all over kelvin times mold. And because this is a constant, any values in which I'm going to plug in here into my gas line equation must have the same units as what we're trying to have here in my constant. So here we see we want the volume and leaders but we have here that's going to be milliliters. So we need to go ahead and convert that. We want to pressure at ATM but we have tour, we want the temperature to be in kelvin's but we have Celsius. So we do have a little bit of calculation work to do before we can plug in anything. Alright, so I can go ahead and start off bye converting my volume which were given to be 135 ml when I convert that into L. So every leader has 1000 ml. You can see here that the male layers will cancel out nicely Putting that into my calculator. I'll get 0.135 L. Next go ahead and convert my temperature. So we're given the 28°C. How convert that into Calvin's is by adding to 73.15. Putting that into my calculator. I would get the value of 300 a month 0. kelvin's. Next is my pressure that we solved for here. I can actually go ahead and continue the conversion on this side so we can save a little space. So how can I convert tour into A. T. M. Every ATM Consist of 7 tour. You can see here now that the tour will cancel out nicely, resulting in a value of 0.9389 A. T. M. Now that everything is converted, we go ahead and finally utilize our guest law equation here. So again we have PV equals N. R. T. To make our lives a little bit easier. We're going to go ahead. Isolate what we're solving for which is our end by defining each side by R. T. You see here now aren't you? A council isolating us but just the end. So scrolling down we have N. It goes P. V over R. T. Alright so I want to go ahead and plug in my numerical values now. So we have the pressure that we just calculated for being at 0.9389 And then we have a volume of 0.135 L. And that's going to be defied by our gas law constant which is 0.8206 units. Again 80 M times leaders Calvin per mole. And that's going to be multiplied by our temperature, which is 301 0.15 kelvin's. You can see here how nice you have thin counsels regarding units. So a t. M. Leaders and Calvin's. So final answer. Once I go ahead and put that into my calculator Is going to be 0.00 most. Just to clean this up a little bit. I want to go ahead and write that into in scientific notation. So the end value is going to be 5. Times 10 to the -3 moles of butane. And there's going to be my final answer for this problem. Thank you so much for watching.