Rank the following gases from least dense to most dense at 101.33 kPa and 298 K: O2, Ar, NH3, HCl.

Video transcript

everyone in this example, we're told that at 1.5 a t. M. S. And 300 kelvin's to arrange the given gasses, hydrogen gas, neon gas and methane gas by decreasing density. So we're listing them in descending order. We want to recall our ideal gas equation, pressure times well equal to the molds of our gas times, the gas constant R times temperature, which we can also recall that we can re interpret this as pressure times volume equal to the mass of our gas times, the gas constant R. Times temperature and divided by the molar mass of our gas. Because this question focuses on density. We can recognize that we can replace our PV portion of our ideal gas equation with the symbol for row, which stands for density. And we're going to set this equal to the pressure times polarity of our gas and then divided by the gas constant R times temperature. And writing this relationship out, we would recognize that there's a direct relationship with density and molar mass of our gas because they're both in the numerator. And so that would mean that we can assume as our molar mass is increasing in value. That would therefore also increase our density value for our given gas. So what we're going to do is make note of our solar masses for each of our gasses. So, for H. Two from the periodic table, we see it has a molar mass of two point oh two g per mole For our neon gas from the periodic table. We see it has a molar mass of 20.18 g per mole. And then for methane gas, we see that it has a molar mass equal to a value of 30.08. And sorry, let's just scoot this over. So it has a value of 30.08 g per mole as a smaller mass from the periodic table. And so because we want to list by decreasing density, we're going to start off with the gas that has the highest moller mass because we know that that corresponds to the highest density value. And so that would correspond to our ethane gas, which had the highest molar mass at 30.8 g per mole. And so therefore our methane gas has the highest density. So we want to list by decreasing density. So we're going to list out our second highest density gas next. And that's going to correspond to the second highest molar mass, which comes from our adam neon At 20.18 g from also will this neon next. And then that leaves us with H2 gas as the gas with the lowest density because it also had the lowest molar mass. And so, to complete this example, our final answer is going to be the ranking here that we've outlined which lists our given gasses in order of decreasing density