Calculate the density of (a) a mixture of 21% O2 and 79% N2 and (b) one in which He is at 760 torr and 0.0C. Will the ratio of densities be different at 100 ATM and 6.0 C?

Consider 100 mL of gas. You will have 21 mL O2 and 78mL N2. Ratio of volume is the same as the ratio of moles.
So equivalent (in a larger volume) to 21 moles O2 and 78 moles N2
If a mole of O2 has a mass of 32g and N2= 28g, find the masses of these moles.
Find the volume occupied by 100 mole of the mixture using PV=nRT. Add the masses calculated together and divide combined mass by the volume occupied by 100 mole of the gas mixture

For He, 22.4 L at stp = 1 mole = approx 4g (use your data) So He is at stp anyway. So density = mass/volume

If you compress gases, the density increases as volume decreases. At a slightly higher temperature, the volume is slightly greater. According to Avogadro's law equal volumes of different gases under the same conditions of T and P have the same number of moles. The mass of the gases will not change on compressing the gas, just the volume. As the volumes of all gases should change by the same extent, I expect densities to increase by the same proportion.

Consider 100 mL of gas. You will have 21 mL O2 and 78mL N2. Ratio of volume is the same as the ratio of moles.

So equivalent (in a larger volume) to 21 moles O2 and 78 moles N2

If a mole of O2 has a mass of 32g and N2= 28g, find the masses of these moles.

Find the volume occupied by 100 mole of the mixture using PV=nRT. Add the masses calculated together and divide combined mass by the volume occupied by 100 mole of the gas mixture

For He, 22.4 L at stp = 1 mole = approx 4g (use your data) So He is at stp anyway. So density = mass/volume

If you compress gases, the density increases as volume decreases. At a slightly higher temperature, the volume is slightly greater. According to Avogadro's law equal volumes of different gases under the same conditions of T and P have the same number of moles. The mass of the gases will not change on compressing the gas, just the volume. As the volumes of all gases should change by the same extent, I expect densities to increase by the same proportion.

Thanks, I think I have a better understanding now.