A 48.3-mL sample of gas in a cylinder is warmed from 22 °C to 87 °C. What is its volume at the final temperature?

Video transcript

Welcome back everybody. Our next problem says a 48.3 mL sample of gas in a cylinder is warmed from 22 °C to 87 °C. What is its volume at the final temperature? A 60.9 mL, B 45.7 mL C 58.9 mL or D 50.7 mL. So we're looking here at the relationship between volume and temperature. So we're gonna be looking at variations of that natural gas law so that basic form of its being PV equals N RT. And here we're looking at varying volume and temperature but constant pressure. So if we rearrange this equation to say that V over T equals NR over P and if pressure is constant, then this right side of the equation is a constant value. And so in that case, volume, one over temperature, one must equal volume, two over temperature two. So we have this ratio here and we can easily solve because we have our initial volume, our initial temperature and our final temperature, we can easily solve for our final volume. So in that case to solve for V two, that's going to equal V one multiplied by T two over T one. So pretty straightforward, the only complication is, of course, we need to think about units now, volumes in milliliters, which is not our si unit, but we're just solving for another volume. We see our answers are expressed in milliliters as well. We don't need to worry about changing that, but we do need to change our temperatures into Kelvin from Celsius. So to go from Kelvin to Celsius, we need to add 273.15. So our T one is equal to 22 °C plus 273.15 is going to equal 295.15. Kelvin and then T two which is equal to 87 °C plus 273.15 will then equal 360.15. Kelvin. So we converted our temperatures. We've got volume one. So V two equals. Now we have volume 1 48.3 mL multiplied by temperature to 360.15. Kelvin divided by our temperature one which is 295.15. Kelvin. So just plug those numbers into the calculator, rounding off to three significant figures and we have 58.9 mL as our final volume. So when we go to our answer, choices, choice C is that answer we received 58.9 mL. See you in the next video.