Question

Question #e7817

Answer 1

`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`.