A gas mixture composed of helium and argon has a density of 0.670 g>L at a 755 mmHg and 298 K. What is the composition of the mixture by volume?

Video transcript

Hi everyone here we have a question telling us at 663 millimeters of mercury and 315 kelvin. The density of the gas mixture of nitrogen and oxygen is 0.976 g per liter. And our goal is to calculate the composition of the mixture by volume. So first we want to calculate our total mass. So our mass mixture Equals 0. g per leader. And we're going to assume a volume of 22.4 L. So we're going to multiply that by 22. l And our leaders here are going to cancel out. And that's going to equal 21.86-4 g. So now we need to calculate the total moles and we're going to do that using the formula PV equals N R. T. So let's look at the information, we know our pressure Equals 663 mm of Mercury and we want to change that to atmosphere. So we're going to multiply by one atmosphere over 760 of Mercury And our mm of mercury are going to cancel out. And that's going to equal 0. atmospheres. Next we know that our volume Is 22. l and we know that our temperature Is 315 Kelvin. So our total moles or our in is going to equal PV over R. T, which equals 0.6. 7-4 atmospheres times 22 0.4 leaders divided by Our gas constant, which is 0. leaders, times atmosphere over moles, times killed. Then Times 315 Kelvin And that equals 0. moles. Now we can calculate the mass of each component. So we're going to let X equal are moles of nitrogen and it is a di atomic atom so into. And that means that 0. minus X is going to equal our moles of oxygen, which is also die atomic so molds of 02. So x times 28.02 g per mole Plus 0.7560 -1 Times 32 g per mole. That is the molar mass of two. Oxygen's equals 21.86 to g. So x times 28. Plus 24. -32 x equals 21.86 - four g. So 32 x -28. x equals 24. -21.86 - four. So when we subtract that, we get 3.98 x Equals 2.3296. So x equals 0.5853. So our moles of nitrogen equal, 0.5853 and our moles of oxygen equals 0. moles. Because that is our total number of moles -0. equals zero .1707. Now, lastly, we can calculate the percent, so the percent of nitrogen Equals 0. moles Divided by our total number of moles. So 0. times Equals 77.42%,, and our percentage of oxygen equals -77. Equals 22.58%. And those are our final answers. Thank you for watching. Bye.