A 2.85-g sample of an unknown chlorofluorocarbon decomposes and produces 564 mL of chlorine gas at a pressure of 752 mmHg and a temperature of 298 K. What is the percent chlorine (by mass) in the unknown chlorofluorocarbon?

Video transcript

Hello. Everyone in this video, we're going to be working with mass percent. As well as the ideal gas law equation. So mass percent. Who's going to be equal to the mass of our chemical all over the total mass of our compound. Of course, multiplied by 100. And as for our ideal gas law occasion, that's going to be PV. Because N. R. T. And our our value is our guest law constant. And we know that to be 0.08206. And the units of A. T. M. Times later all over kelvin's times more. So let's first identify what information we're given just by reading the problem. So we can see here that we know we have a 1.67 g sample. So let's table that the sample. All right. And we know that we have 407 millions of chlorine gas and we also are given a temperature of 300 Kelvin's And we have a pressure of 746. M M H G. So we can see here from the pivot that we have a volume, we have a temperature and we have a pressure. We know what our value is, but we don't know what our and values. So manipulating my equation a little bit, we divide each side by R. T. So that my end can be isolated and that will give us and equaling two PV equals R. T. So one thing to keep in mind is that because we have this constant. Any information we want to go ahead insert into our equation must have the same units as our constant. Let's see here. So we have the pressure being an M M A G. But we want a T. M. So let's do that conversion first. So we have given 7 M. M H G. And we want to convert that into A. T. M. So on team nominator we have 760 mm H. G. On Top 1 80 M. And we can see their unit will cancel leaving us the answer of 80 M. And we want that. So 0.9816 is the value I get once I put that into my calculator. Alright moving on. Let's see we have Calvin says temperature, Calvin as temperature. And then we have milliliters but we need leaders. So again let's do some dimension analysis. Were given the ml of a corn gas. But we want leaders. So 1000 ml in one leader, the Millers will cancel out And that will give us a value of 0.407 L. Now we can go ahead and plug in to this equation. Yes, scrolling down just a bit. Okay, so we have our moles equaling to pressure of seven. What we saw for us. 0.9816 A. T. M. Times the volume which would also just calculated for 0.407 L. That's all going to be divided. Our first, our gas law constant. So 0.8206 units being A. T. M. Times leaders over Calvin's times more. And our temperature, we said there's 300 Kelvin's. You can see here that the A. T. M. Will cancel. Leader will cancel as well as the kelvin leaving us with just a moles. So I'm going to put that into my calculator and I'll get a value Of 0.016 - three. Most Of that cl two or chlorine gas. All right. So because we have that in moles actually want to convert that into grams. Because when we use our massive percent, we want the mass of our chemical which is our chlorine gas. And that needs to be in grounds. So, submission analysis. So, how we want to convert the moles into grams is molar mass. So let's first calculate the molar mass. First the moller mass of cl two. So we know that we have two chlorine atoms and each chlorine atom has a mass of 35. g. So two times 35.45. It's 70.9. And the unit is going to be g per mole of the chlorine gas. Alright, so again, bring this value down and starting our dimensional analysis with a different color. So zero point 01623 malls of chlorine. And using the molar mass that we just calculated for you guys scroll down. So on denominator, we will have one more of cl two On top will be 70.9 g of that seal. I can see here that the malls will cancel leaving us with the gramps as we wanted. So 29 to make a calculator. I'll get 1. 707g of cl Now we can go ahead and use this value and plug it into our mass percent. So, the massive or chemical, it's very calculated for So mass percent. So 1.150707 grams of the chlorine gas. And we have as a denominator, It's going to be the total Maciver compound which was given to us in the beginning as 1.67 g of our sample. So scrolling back down, we'll plug in that 1.67 Grimm's Times 100%. And what we get here is that the mass percent. I'm just pulling that into my calculator. I'll get Percentage of 0.9%. And that is going to be my final answer for this problem. Thank you so much for watching