# A sample of a compound of xenon and fluorine contains molecules of a single type; #XeF_n#, where #n# is a whole number. If #9.03 * 10^20# of these #XeF_n#, molecules have a mass of 0.311 g, what is the value of #n#?

##### 1 Answer

#### Explanation:

The idea here is that you need to use the number of molecules to determine how many *moles* you have, then use that and the mass of the sample to figure out the compound's **molar mass**.

So, you know that **one mole** of any substance contains exactly *Avogadro's number*.

You can thus use Avogadro's number to determine how many moles you have in that sample

#9.03 * 10^(20)color(red)(cancel(color(black)("molecules XeF"_n))) * overbrace(("1 mole XeF"_n)/(6.022 * 10^(23)color(red)(cancel(color(black)("molecules XeF"_n)))))^(color(blue)("Avogadro's number")) = 1.4995 * 10^(-3)"moles XeF"_n#

The **molar mass** of a substance tells what the exact mass of **one mole** of that substance is. In your case, the molar mass of the compound will be

#color(blue)(M_"M" = m/n)#

#M_"M" = "0.311 g"/(1.4995 * 10^(-3)"moles") = "207.4 g/mol"#

Now, the molar mass of a compound can also be found by adding the molar masses of **each** atom that's part of that compound's molecule or formula unit.

In your case, you know that one molecule of the compound contains

#1# atom of xenon,#"Xe"# #color(blue)(n)# atoms of fluorine,#"F"#

The molar masses of these two elements are

#"Xe: " "131.293 g/mol"# #"F: " "18.9984 g/mol"#

This means that you can write

#1 xx M_"M Xe" + color(blue)(n) xx M_"M F" = "207.4 g/mol"#

#1 xx 131.293 color(red)(cancel(color(black)("g/mol"))) + color(blue)(n) xx 18.9984 color(red)(cancel(color(black)("g/mol"))) = 207.4 color(red)(cancel(color(black)("g/mol")))#

The value of

#color(blue)(n) = (207.4 - 131.293)/18.9984 = 4.006 ~~ color(green)(4)#

The compound is *xenon tetrafluoride*