Suppose you are given two flasks at the same temperature, one of volume 2 L and the other of volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is x kPa. The 3-L flask contains 0.36 g of gas, and the gas pressure is 0.1x. Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

Video transcript

hey everyone for this problem, it says assume you have two flasks at the same temperature. One of the flasks has a volume of four liters and the other has a volume of five liters, the four liter flask contains 6.3 g of gas and the pressure is X 80 M and r five liter flask contains 50.66 g of gas and the pressure is 0.6 X. And we need to decide do the two gasses have the same moller mask, and if not, which flask would contain the gas with the higher molar mass. So we need our ideal gas law for this equation because we're dealing with pressure. So we know that pressure times volume equals N. R. T. And here they tell us that our temperature is the same. So we can go ahead and cross out this variable and r r r gas constant is constant. So we can ignore it as well. So we're left with pressure, volume and moles. And we need to solve for molar mass. So we know that molar mass is equal to grams over moles. And if we rearrange this so that we're solving for moles, we get moles is equal to grams over molar mass. So we can substitute that in for N. In this equation so that we can solve for molar mass. And what that looks like is this, we get P V equals N, which is our moles. So that's going to equal grams over molar mass. And we want to move everything to one side because we're dealing with two sets of equations, so we need to set them equal to each other. And when we move it over to one side we get p times V times molar mass over grams. And I'll change that variable for grams to little M. For mass. So we have P one times V one times molar mass one over mass one is equal to P two times V two times molar mass too over mass too. So we want to solve for molar mass one and moller mass too and we can go ahead now and plug in what we know based off what's given in the problem. So our first pressure, so we have the four liter flask and the five liter foss. So for the first one we have a pressure Of X 80 M. And the volume for that is the four liter flask. And we have M. M one r moller mass one. And that's all over Our mass which is given 6.3 gramps. And that's equal to our five liter flask. The information for our five liter flasks. So we're told that our pressure is 0.6 X Our volume is five l and we have a molar mass two And that's all over our mass of 0.66 g. Okay, So remember we're solving here for molar mass one and moller mass too. So we want to go ahead and get are Equation set up so that we have molar mass one and two on opposite sides of the equation. So let's start off by multiplying both of our equations by 0.66. Or let's start off by multiplying both sides by 6.3. So we'll multiply both sides by 6.3 g. And when we do this cancels here and we're left with molar mass one is equal to 0.6 X times five. Leaders Times 6. g times molar mass too. Over 0.66 grams times X A T. M times for leaders. Now our X's cancel so we can cross that out. Our X's cancel here and we'll do the math. And when we do that we'll get 18. Molar Mass one is equal to 18.9 times molar mass too. All over 2. and We'll get molar mass one. We'll divide molar mass one is equal to 18.9 divided by 2. or two. Yes, 2.64 is 7.16 times molar mass too. And this is what we're looking for here to compare the two. So we don't have the same moller mass for both of our flasks. So we see that in order for molar mass to to equal molar mass one we need to multiply our molar mass two by 7.16. So that means molar mass two is 7.16 times smaller Than Molar Mass one. And so our final answer for this problem Is moller mass one is larger. Now that's the end of this problem, I hope this was clear.