Question

How can you determine the molecular formula of a substance from its percent composition?

Answer 1

The percent composition gives you only the empirical formula.

Explanation:

To get the molecular formula, you must either know the molecular mass or do an experiment to find it.

Example

An unknown compound contains `"85.63 % C"` and `"14.37 % H"`. Its experimental molar mass is `"56 g/mol"`. What is its molecular formula?

Solution

Assume we have `"100 g"` of the compound. Then we have `"85.63 g of C"` and `"14.37 g of H"`.

`"Moles of C" = 85.63 color(red)(cancel(color(black)("g C"))) × "1 mol C"/(12.01color(red)(cancel(color(black)("g C")))) = "7.130 mol C"`

`"Moles of H" = 14.37 color(red)(cancel(color(black)("g H"))) × "1 mol H"/(1.008 color(red)(cancel(color(black)("g H")))) = "14.26 mol H"`

`"Moles of C"/"Moles of H" = (7.130 color(red)(cancel(color(black)("mol"))))/(14.26 color(red)(cancel(color(black)("mol")))) = 1/2.000 ≈ 1/2`

The empirical formula is `"CH"_2`.

The empirical formula is the simplest formula of a compound.

The actual formula is an integral multiple of the empirical formula.

If the empirical formula is `"CH"_2`, the actual formula is `("CH"_2)_n` or `C_nH_(2n)`, where `n = 1, 2, 3, …` .

Our job is to determine the value of `n`.

The empirical formula mass of `"CH"_2` is `"14.03 u"`. The molecular mass of `"56 u"` must be some multiple of this number.

`n = (56 color(red)(cancel(color(black)("u"))))/(14.03 color(red)(cancel(color(black)("u")))) = 4.0 ≈ 4`

∴ The molecular formula is `C_nH_(2n) = "C"_4"H"_8`.