A small cylinder of helium gas used for filling balloons has a volume of 2.30 L and a pressure of 13,800 kPa at 25 °C. How many balloons can you fill if each one has a volume of 1.5 L and a pressure of 1.25 atm at 25 °C?

Video transcript

Hello everyone today. We are working with the falling problem, a tank of experimental gas with 3.5 liter volume and 14,500. Killer pascal's pressure at 26 degrees Celsius was used to fill up balloons. How many balloons can be filled if each balloon has 2l volume and 1.13 atmospheres pressure at 26°C. So we see that we have a bunch of variables. And so we need to organize these. The first thing that we want to do is we want to convert our pressure from Killer pascal's two atmospheres because atmospheres is the standard unit for pressure. So we're gonna say pressure is equal to our 14,500 killer Pascal's. And we're gonna use we're gonna convert from Killer pascal's to pascal's and then from pascal's two atmospheres. And so to do that we're gonna use a conversion factor that for every one Killer pascal we have 1000 pascal's. We can then take the conversion or the unit conversion factor that one atmosphere is equal to 101,325 pascal's Our units for Pascal's and killer Pascal's will cancel out and we will be left with 143 0.0 atmospheres. We're gonna save that number for later in this problem, it was noted that our number of moles and our temperature were kept constant. So our temperatures stayed the same and thus are the number of moles did not change. And so the second thing we must use, you must recall Boyle's law. And so what is Boyle's law? States Boyle's law states that the initial volume or the initial pressure times the initial volume is equal to the final pressure times the final volume. And so when we rearrange this equation to solve for our final volume, we get our final volume is equal to our initial pressure times our initial volume divided by our final pressure. We can go ahead and plug in our units here for our initial pressure. We had 143.1 atmospheres that we solved for And our volume, our initial volume was 3.5 L. And then our final pressure was 1. atmospheres. When our units canceled out, we're left with 443.24 L. And so we're going to use that for the next part of this problem. And that is to calculate the number of balloons that the question is asking for. And so we know that We have our volume here which was 443.24 L. And we also know from the question that one balloon occupies two leaders volume. And so when our units of leaders cancel that were simply left with units of our balloons, which will give us 221.62 And rounded to the nearest whole number will be 221 balloons as our final answer. And with that we have answered the question overall. I hope that this helped until next time.