A piece of dry ice (solid carbon dioxide) with a mass of 28.8 g sublimes (converts from solid to gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon, what is the volume of the balloon at 22 °C and a pressure of 742 mmHg?

Video transcript

Hello. Everyone in this video, we're going to go ahead and do some problems on gas laws. So there's several different gas laws, but the one you want to keep in mind will be the ideal gas law because it's the most universal and diverse. So let's start off by separating our information from the problem. I'll go ahead and have a section for my given information. And of course what we're trying to find as well. So where were given? You can see that we have a mass of 36.4 g. That's useful information. Let's go ahead, write that down Then. If you re further, we have a temperature of 84 Degrees C and a pressure of 765. M M H G. Alright. And what we saw in far is the volume. So the question is, can we use the ideal gas law equation? So pivot, can we use this? Let's see here. So the first piece of information we're given, we have our potential and value. So you do some dimensional analysis to go from grams to moles. So yes, we have our end then of course we have our temperature and then we have our pressure. What we're trying to solve for is our volume. You can see here in the equation we have our value as well. The R value is our gas law constant. Since it's named a constant, we can never change its values or its units. The R will be 0. times A T. M times L. All over Calvin's times more highlight said the units will never change. And because we have these specific units, we want to cancel out and find whatever we need to find in their case will be volume. So every given a piece of information that we're plugging it into this equation will need to match up with these units as well. So like I said, we have our 36.4 g. We need to go ahead and convert this to the M.olds. So as you see on top were given a compound. Let's go ahead and find the molar mass. So first we have 10 carbons. Each adam weighs in at 12 0.1 g that we're gonna go ahead and add the mass of our hydrogen atoms who have eight hydrogen atoms and each atom weighs in that one g. Now putting that into my calculator, I get some of 128.1 grams per moles. And this is going to be my conversion factor from going from the given mass into my moles. So let's start off the dimension analysis with 36.4 g. Then using the conversion factor, the Mueller mass I just used, We'll put as its nominator 128.1 g on the top will be one mole of my compound. Now I can see that the grams unit will cancel out leaving us the answer of moles, which is what we need. So putting that into my calculator. I get 0.2842 Mnolds. Now. Moving on, so finished that. Just a little check mark for me to know. And let's see we have the 84.0°C, we want the units to be in Kelvin's that can easily be converted. So we have starting 84.0°C. Let's go ahead and add to 73. to convert our Celsius or degree Celsius into kelvin's And put that in my calculator. I get a sum of 357 0. healthy. Alright again, little trademark for me to keep tabs. Last piece of information, we need to do some conversion will be our pressure. So starting off We have the value of 765 MMHG. And the coverage factor into the A. T. M unit is as my denominator 60 M M H G zero and two on top of the A. T. M. So this is again a converted factor and you can see that this unit will cancel out and our and the answer will have A. T. M. Being our units And plugging that into my calculator. I get 1.066 A. T. M. So we are ready to basically put everything in to our equation here. So let me just go ahead and draw a little arrow here. Alright, so I had said that we are going to be solving for our volume. So first again, let me rewrite my equation. Okay and we are sovereign for V. So let's go ahead and divide each side by P. You see that the people cancel out here and the equation will be using actually is now volume equals the end times R times t. All over our pressure. So plugging in our values so we have this this this and of course our gas law constant on blue over here, we'll go ahead and plug everything in. So volume because our more value which we calculated to be 0.2842 more. Then our constant is 0. units, A. T. M. Times Leader all over kelvin times. Then our temperature that would calculate it is 357.15 Kelvin's and this is all going to be over Our pressure which we calculated to be 1.06680 M. You see that the units will cancel out nicely. Malls, malls, A T M. With A T M. And lassie, kelvin and kelvin leaving us the leader units as our unit for our final answer. So once I put all this into my calculator, my final volume or my answer is going to be eight point 27 liters. And that is going to be my final answer for this problem