# An unknown element #"X"# with oxygen forms a gas compound #"X"_2"O"# whose density at #-120^@"C"# and a pressure of #"320 mmHg"# is #"1.809 g/L"#. What is element #"X"#?

##### 1 Answer

Here's what I got.

#### Explanation:

Your starting point here will be to use the **ideal gas law equation** and the **density** of this compound to find its **molar mass**.

#color(blue)(ul(color(black)(PV = nRT)))#

Here

#P# is the initial pressure of the gas#V# is the volume it occupies#n# is the number of moles of gas present in the mixture#R# is theuniversal gas constant, equal to#0.0821("atm L")/("mol K")# #T# is theabsolute temperatureof the gas

Now, you know that when kept at a temperature of

To make the calculations easier, let's assume that we have exactly **moles** of gas present in this sample

#PV = nRT implies n = (PV)/(RT)#

Plug in your values to find--**do not** forget to convert the temperature of the gas to *Kelvin* and its pressure to *atmospheres*!

#n = (320/760 color(red)(cancel(color(black)("atm"))) * 1 color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + (-120)) color(red)(cancel(color(black)("K"))))#

#n = "0.03349 moles"#

Now, this sample has a mass of **moles** of **molar mass** of the compound, i.e. the mass of exactly **mole** of

#M_ ("M X"_2"O") = "1.809 g"/"0.03349 moles" = "54.16 g mol"^(-1)#

Notice that the chemical formula of the compound suggests that **every** **mole** of

#2# molesof element#"X"# ,#2 xx "X"# #1# moleof oxygen,#1 xx "O"#

Since elemental oxygen gas a molar mass of about **mole** of

#"mass X" = "54.16 g " - " 16.0 g"#

#"mass X"# #=# #"38.16 g"#

This is the mass of exactly **moles** of element **molar mass** of

#M_ ("M X") = "38.16 g"/"2 moles" = "19.08 g mol"^(-1)#

Rounded to two **sig figs**, the molar mass of element

#M_ ("M X") = "19 g mol"^(-1)#

The closest match that you have for the identity of element *fluorine*,

#M_ ("M F") = "18.998 g mol"^(-1)#

This would make the unknown compound *oxygen difluoride*,