Question

The density of a Gas is 1.43 g/mol at STP. What is the gas?

1)Cl2
2)S
3)O2
4)Ne

I know the correct answer should be 3) O2 because of it molarity is 32.032g, but I don't get it why is not 2)Sulfur? it also has the molarity of 32.066?

Answer 1

The answer is indeed oxygen gas.

Explanation:

For starters, you don't have the right units for the density of the gas.

The density of a substance is supposed to tell you the mass you have per unit of volume of that substance, not per mole like you have there.

So instead of `"1.43 g/mol"`, you should have `"1.43 g/L"`, i.e. `"1 L"` of this gas has a mass of `"1.43 g"` at STP conditions.

Now, you were probably taught that `1` mole of any ideal gas occupies `"22.4 L"` at STP conditions, which back in the day were defined as a temperature of `0^@"C"` and a pressure of `"1 atm"`.

In order to be able to identify your unknown gas, you must figure out its molar mass, i.e. the mass of exactly `1` mole of that gas.

Since you know that `"1 L"` of gas has a mass of `"1.43 g"` at STP and that `1` mole of any ideal gas occupies `"22.4 L"` under these conditions for pressure and temperature, you can say that `1` mole of this gas will have a mass of

`overbrace(22.4 color(red)(cancel(color(black)("L gas"))))^(color(blue)("= 1 mole at STP")) * overbrace("1.43 g"/(1color(red)(cancel(color(black)("L gas")))))^(color(blue)("the density at STP")) = "32.032 g"`

So if `1` mole of this gas has a mass of `"32.032 g"`, you can say that its molar mass is equal to

`color(darkgreen)(ul(color(black)("molar mass = 32.0 g/mol")))`

The answer must be rounded to three sig figs, the number of sig figs you have for the density of the gas at STP.

Now, the answer is indeed oxygen gas, `"O"_2`, because that's the closest match in terms of the molar mass.

`M_ ("M O"_2) = "31.9988 g/mol"`

Sulfur has a molar mass of

`M_ ("M S") = "32.065 g/mol"`

but it cannot be a match here because sulfur is not a gas at STP conditions `->` see here for info on the boiling point of sulfur at a pressure of `"1 atm"`.