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

Md Ariful Islam

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Md Ariful Islam

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For starters, you don't have the right units for the 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 , 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 for info on the boiling point of sulfur at a pressure of $"1 atm"$.

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