What are the molecular weights of the gases with the following densities: (a) 1.342 g/L at STP

Video transcript

Hello everyone today, we got the following problem calculate the molar mass of a gas if its density at standard temperature and pressure is 1.827 g per liter. So the first thing in this probably want to do is you want to assume that are gas occupies one leader in our sample. And so we essentially need to find a mass from this density because molar masses in units of grams per mold. And so to find our mass, We simply take our one leader and we multiply by the density which is 1.827 g/l. Our units of leaders will cancel out and it will be left with 1.827 g. And we'll use that value later. Next, we must make note of what standard temperature and pressure indicates. This simply indicates that our that our temperature Is going to be at 273.15 Kelvin and our pressure is going to be at one atmospheres. We'll make note of that for later. The third thing that we want to do is you want to write out our ideal gas law and then we're gonna rearrange that gas law. So the original gas law says that our pressure times our volume is equal to the number of moles. We have times r gas constant r times r temperature T. So we we arranged that to solve for moles and we get that moles are in is equal to our pressure times are volume over our gas constant times our temperature. So plugging in the values that we have, we can solve for moles. We have one atmospheres for our pressure for our volume. We have one leader For a gas constant. This is going to be 0.08206 leaders times atmospheres over moles, Times Kelvin. And then lastly we're going to multiply by our temperature which at standard temperature and pressure was 2 73.15 Kelvin. And so essentially our units are going to cancel out, except for moles. We're going to be left with 0. moles. We're going to use that in our next step. So our next and final step is going to be to solve for our moller mass. And so our molar mass is in units of g per mole. And so our grams that we have is our 1.827g. And our moles that we saw it for is 0.04461 moles. And that leaves us with the molar mass of 41 grams per mole as our final answer. And with that we have answered the question overall. I hope that has helped. And until next time