What is the density in g/L of a gas mixture that contains 27.0% F2 and 73.0% He by volume at 714 mm Hg and 27.5 °C?

Video transcript

Hi everyone for this problem it reads calculate the density and g per liter of a gas mixture at 37.5°C and 654 mm of mercury, composed of 62% Krypton gas and 38% chlorine gas by volume. So our goal here is to calculate the density of a gas and grams per leader. Alright, so because we're dealing with gasses here, let's start with the ideal gas formula. And that formula is pressure, times volume is equal to the number of moles times gas constant. R times temperature. Okay. And here if we solve the equation for a volume, we get volume is equal to N. R. T over P. Okay, so we know everything. We need to find the volume except the number of moles of gas to find this, remember the relationship between number of moles and mass. And that relationship is N equals M over molar mass. Okay, where N equals the number of moles of gas, M is the mass of gas, and M M is the molecular mass of the gas. This is helpful since we needed to find the mass and we know the molecular mass of krypton gas and chlorine gas, we can calculate this if we substitute for N. In the first equation we're going to get volume is equal to M R. T over M M P. Okay, and what we're gonna do is we're gonna divide both sides by em. Alright, so when we divide both sides by em, what we get is V over M is equal to R. T over M M P. Okay, but look at the left side. V over. Em density is equal to mass over volume, not volume over mass. So we are going to flip the equation over so that we get mass over volume is equal to M M P over R. T. This is the equation that we're going to use to solve for density because remember density is equal to mass over volume. So we see here that M over V equals MMP over R T. This is what we're going to use to get our density and grams per leader. So let's go ahead and write down what we know we need the molar mass M m to calculate the average molar mass. What we're going to do is we need to recall that percent volume is equal to percent mole or mole percent. Okay, so what we can do is we're going to take our mole fraction for both of our gas is our mole fraction. For krypton gas is going to equal are more percent but we're gonna Right this in its decimal form. So our mole fraction is going to be 0.6204 Krypton and for our chlorine gas It's going to equal 0.480. So the way we're going to calculate our average molar mass. So we're going to write average molar mass is going to equal the more percent. Okay, so our mole fraction, let's just write that, it's gonna equal our mole fraction times molar mass. It's going to equal the sum for both. So let's go ahead and write down our molar mass for both. Our molar mass for krypton, using our periodic table is 83.8 g per mole. And our molar mass for chlorine gas is we have two moles of chlorine. So we're going to take it 35.45 g per mole times two. Okay, and that is going to give us a molar mass of chlorine gas equal to 70.9 grams per mole. So we're going to take the average molar mass. Okay, so we're going to take the sum of both of these. So let's go ahead and write. So we said it's going to be the mole fraction times the molar mass. So let's start off with our krypton gas. The molar mass. So we'll write average moller mass. So the mole fraction for krypton gas is 0.6 to zero Times a smaller mass, 83 point eight g per mole. And this is going to be plus the chlorine gas. So we're going to take our mole fraction for chlorine gas, which is 0.480 and multiply that by its molar mass, which is 70.9 grams per mole mhm. Okay, so Let's just clean that up a little bit 70.9. Okay, so that means our average molar mass is going to equal 78.898 g per mole. So that's the number. We're going to plug in for our molar mass. Okay, so let's go ahead and do that. Let's go ahead and write this in a different color. So it's going to be our molar mass we just calculated is 78.898 g per mole. And this is going to be times pressure. Okay, We're told that the pressure Is 654 mm of mercury. So we're going to convert that mm of mercury to atmospheres. Okay, so we have 654 millimeters of mercury. And we want to go from millimeters of mercury to atmospheres in one atmosphere, there is 760 millimeters of mercury. Making sure our units cancel millimeters of mercury cancel. And we have 0.8605 atmospheres. So this is the value, we're going to plug in four pressure. So 0.8605 atmospheres. And this is over r r gas constant R is 0.8 206L atmosphere over Mole Kelvin. And this is times temperature. So our temperature We're told is 37.5°C. And we need this in Kelvin. So we're going to add 273.15. So we're going to get a temperature of 310.65 Kelvin. So let's go ahead and plug that in 310.65 Kelvin. So let's go ahead and do this calculation. And when we do this calculation, we're going to get density is equal to 2.66 g per liter. Okay, So we're going to make sure our units canceled properly. So moles cancels, kelvin Cancell, atmospheres, cancels. And as you can see, we have g per leader. So our final answer is density, which we said is mass over volume is equal to 2.66 g per leader. And this is going to be our final answer for this problem. That's it. I hope this was helpful.