Question #8da8d

1 Answer
May 22, 2016

Answer:

#"C"_4"H"_8"O"_2#

Explanation:

A compound's empirical formula tells you the smallest whole number ratio that exists between the elements that make up a compound.

In your case, the unknown compound has an empirical formula of #"C"_2"H"_4"O"#, which means that it contains carbon, #"C"#, hydrogen, #"H"#, and oxygen, #"O"#, in a #2:4:1# ratio.

In other words, one mole of this compound will contain carbon, hydrogen, and oxygen in a #2:4:1# mole ratio.

All you have to do now is determine the mass of the empirical formula and compare it with the molar mass of the compound. You will have

#2 xx "12.011 g mol"^(-1) + 4 xx "1.00794 g mol"^(-1) + 1 xx "15.9994 g mol"^(-1) = "44.053 g mol"^(-1)#

The molar mass of the compound essentially tells you the mass of one mole of the compound. This means that you will have

#44.053 color(red)(cancel(color(black)("g mol"^(-1)))) xx color(blue)(n) = 88color(red)(cancel(color(black)("g mol"^(-1))))#

Rearrange to get

#color(blue)(n) = 88/44.053 = 1.9976 ~~ 2#

Therefore, the molecular formula of the compound, which tells you the exact number of atoms of each element present in one molecule of the compound, will be

#("C"_2"H"_4"O")_color(blue)(2) = color(green)(|bar(ul(color(white)(a/a)"C"_4"H"_8"O"_2color(white)(a/a)|)))#