A cylinder contains nitrogen gas. A piston compresses the gas to half its initial volume. Afterward, a. Has the mass density of the gas changed? If so, by what factor? If not, why not?

Video transcript

Hey, everyone in this problem, a cylindrical container filled with chlorine gas is closed using a tight quark. The quark is used to reduce the volume of the gas to 3/5 of the original volume. When we're asked to find the new mass density of the chlorine gas, we're given six answer choices here. Option A Rona, no change. Option B 1.7 Rono, option C 0.6 Rono, option D 0.4 Rono, option E 2.8 Rono and option F 0.51 Rona. So let's recall it when we're talking about a mass density row, we can write this as the mass M divided by the volume B. So when we're talking about this new mass density, which we're gonna call row F the final mass density, this is going to be equal to the final mass MF. And we're just gonna call the M, the mass hasn't changed. OK. This is closed using a tight quark. And so there's gonna be no change in mass. So we just have M divided by the final volume. VF All right, now, we don't know exactly the mass. We don't know exactly the final volume, but we do know a relationship between the final volume and the original volume. And so we can write that row F is going to be equal to the mass and divided by 3/5 V. No, OK? Because that volume is reduced by 3/5 or sorry, 2, 3/5 of the original. OK. So VF is 3/5 V knot. OK. Now we can rewrite this, OK? We have three fi in the denominator. So we can write this as five thirds multiplied by the mass and divided by the volume up. That's our final density. Now M divided by V not. What's that? Well, we've written that our density is M divided by V. And so our initial density row not is going to be M divided by V. No. And that's exactly what we have on the right hand side of our equation say that M divided by V knot term. And so what we have here is that row F, our final mass density or the new mass density is going to be five thirds multiplied by row knot, the initial mass density. OK. So this is five thirds. If we round that to one decimal place, we get that. This is approximately 1.7 multiplied by Rona. So comparing this to our answer choices, we can see that answer B is the correct option. Thanks everyone for watching. I hope this video helped see you in the next one.