A compressed air tank carried by scuba divers has a volume of 8.0 L and a pressure of 140 atm at 20 °C. What is the volume of air in the tank in liters at STP?

Video transcript

Hello everyone today. We're being given the following problem at 15 degrees Celsius, a gas occupies a volume of 35.0. Leaders has a pressure of 136 atmospheres, calculate the volume it occupies at S. T. P. Or standard temperature and pressure. So the very first thing you want to do is you want to realize about variables we're working with here. We see we have volume, we have pressure and we have temperature. So this should tell us that we are working with our combined gas law which puts all these variables together. And that says that our initial pressure times our initial volume gets divided by our initial temperature and that is going to be equal to our final pressure, final volume and divided by our final temperature. And so we have to figure out what variables we're working with here. So we see that we have our temperature but we notice that it is in Celsius and it must be converted into kelvin. So we have to convert our Celsius into kelvin. And so for our first temperature, our initial temperature, we have 15°C To convert that to Kelvin. We simply added to 73.15 and we get to 0.15 kelvin. We will use that number later. Now for our final temperature it was noted that it's going to be at standard temperature and pressure and so this just indicates that that is going to be at 273.15 Kelvin automatically. What's also important to note that at standard temperature pressure our pressure is going to be one atmospheres. So our final pressure will be one atmosphere And so now we have all of our variables and values that we need to calculate for our final Volume. So solve for V two. So we have our combined gas law and step one And we are simply going to rearrange it to solve for our final volume which will be as follows. Our final volume will be equal to our initial pressure times our initial volume, times our final temperature over our final pressure times our initial temperature. And so we can go ahead and plug our values and that we sold for our initial pressure as stated in the question was 136 atmospheres And our initial volume was 35 L. And our our Final temperature which was at standard temperature pressure we said was 273. Kelvin. And this was all going to be divided by our final pressure which was one atmospheres which is what it is at standard temperature and pressure times our initial temperature which was converted from 15°C to 288.15 Kelvin. And so our units of atmospheres and kelvin will cancel out and we will be left with As our for our final volume. We will be left with 4.51 times 10 to the third leaders as our final answer. And with that we have answered our question overall. I hope that this helped until next time.