What is the molar volume of He gas under the conditions of temperature and pressure where its density is 0.142 g/L?

Answer 1

The "molar volume" of the gas is how much volume is occupied by one mole of the gas at the designated conditions of Temperature and Pressure. The units of "molar volume" are Liters, not moles per liter (that's molarity!)

At STP, one mole of an ideal gas occupies approximately 22.4 L. You can find that by plugging into the ideal gas equation PV = nRT, using STP values (T = 273.15 K, P = 1.00 atm) and using 1.00 moles of gas for n. Solving for V, you will find V = 22.4 L under these conditions.

You can find the density of a gas at STP easily by taking the molar mass (molecular weight) in grams per mole of that substance, and dividing that mass by the volume it would occupy at STP (which is 22.4 L!). So for He, the density would be 4.00 g / 22.4 L = 0.179 g/L at STP.

However, this problem states that the He gas is NOT at STP. The density is actually lower than what would expect at STP. And we are given the density, we aren't looking for density! We are asked for molar volume. So the real question is "what is the volume of one mole of this gas" under these conditions?

The gas is He, so we know that 1 mole of He weighs 4.00 g (from the periodic table). The density is given as 0.142 g / L.

1.00 mol He x (4.00 g He / mol He) x (1 L / 0.142 g He) = 28.16901408 L (from the calculator)

Round to 3 sig figs = 28.2 L

This should make sense with the density value being *lower* than it is at STP, because the volume is higher! 1 mole of a gas in 22.4 L (at STP) would have a higher density than 1 mole of the same gas in a larger volume, 28.2 L (not at STP). Hope that helps, let me know if you need more help!