Question #e7817

1 Answer
Jan 9, 2018

Answer:

#x = 2#

Explanation:

Your unknown compound has #"C"_7"H"_8"O"_x# as the molecular formula, so you know for a fact that #1# mole of this compound contains

  • #7# moles of carbon, #7 xx "C"#
  • #8# moles of hydrogen, #8 xx "H"#
  • #x# moles of oxygen, #x xx "O"#

This means that the molar mass of the compound can be calculated like this

#M_"M" = overbrace(7 xx "12.011 g mol"^(-1))^(color(blue)("7 moles C")) + overbrace(8 xx "1.00794 g mol"^(-1))^(color(blue)("8 moles H")) + overbrace(x xx "15.9994 g mol"^(-1))^(color(blue)(x quad "moles O"))#

#M_"M" = (94.14052 + 15.9994 * x)quad "g mol"^(-1)#

Now, you know that this compound contains #26.2%# oxygen by mass. This means that if you take the mass of #1# mole of this compound, you can say that you have

#( 15.9994 * x color(red)(cancel(color(black)("g mol"^(-1)))))/((94.14052 + 15.9994 * x)color(red)(cancel(color(black)("g mol"^(-1))))) xx 100% = 26.2%#

This basically means that if you take the mass of oxygen present in #1# mole of this compound, divide it by the total mass of #1# mole of the compound, and multiply the result by #100%#, you will end up with #26.2%#, the percent concentration by mass of oxygen.

You will thus have

# (15.9994 * x)/((94.14052 + 15.9994 * x)) xx 100 color(red)(cancel(color(black)(%))) = 26.2color(red)(cancel(color(black)(%)))#

Rearrange to solve for #x#

#15.9994 * 100 * x = 26.2 * 94.14052 + 26.2 * 15.9994 * x#

#x * 15.9994 * (100 - 26.2) = 26.2 * 94.14052#

You will end up with

#x = (26.2 * 94.14052)/(15.9994 * (100 - 26.2)) = 2.089 ~~ 2#

You can thus say that you have #x = 2#, which implies that the molecular formula of the compound is #"C"_7"H"_8"O"_2#.