Question #1cb83

1 Answer
Feb 15, 2018

Here's what I got.

Explanation:

The trick here is to realize that under STP conditions, which are currently defined as a pressure of "100 kPa"100 kPa and a temperature of 0^@"C"0C, 11 mole of any ideal gas occupies "22.723 L"22.723 L--this is known as the molar volume of agas at STP.

Now, you know that at STP, this gas has a density of "1.7824 g L"^(-1)1.7824 g L1. This tells you that at a pressure of "100 kPa"100 kPa and a temperature of 0^@"C"0C, "1.7824 g"1.7824 g of this gas occupies exactly "1 L"1 L.

Use the molar volume of a gas at STP to find the number of moles present in the sample

1 color(red)(cancel(color(black)("L"))) * "1 mole gas"/(22.723color(red)(cancel(color(black)("L")))) = "0.0440083 moles gas"

To find the molar mass of the gas, you need to find the mass of exaftly 1 mole. Since you know that 0.0440083 moles have a mass of "1.7824 g", you can say that

1 color(red)(cancel(color(black)("mole"))) * "1.7824 g"/(0.0440083color(red)(cancel(color(black)("moles")))) = "40.501 g"

Therefore, you can say that the molar mass of the gas is equal to

color(darkgreen)(ul(color(black)("molar mass = 40.501 g mol"^(-1))))

The answer is rounded to five sig figs, the number of sig figs you have for the density of the gas at STP.

color(white)(a)
SIDE NOTE More often than not, the molar volume of a gas at STP is given as "22.414 mol L"^(-1), the value that corresponds to a pressure of "1 atm" and a temperature of 0^@"C".

If that's the value given to you, make sure to redo the calculations using "22.414 L mol"^(-1) instead of "22.723 mol L"^(-1).