Question

What is the empirical formula of a compound that is 26.58% K, 35.35% Cr, and 38.07% O?

Answer 1

The empirical formula is `"K"_2"Cr"_2"O"_7"`.

Explanation:

The empirical formula represents the lowest whole number ratios of elements in a compound. You must first determine the number of moles of each element, then determine the mole ratios. The mole ratios, or a multiple of the mole ratios, will be the subscripts for the elements in the empirical formula.

Determine moles.

Since the percentages add up to `100%`, we can make a direct conversion of the percentages to grams.

Divide the given number of grams for each element by its molar mass (atomic weight on the periodic table in grams/mole). Since molar mass `("g"/"mol")` is a fraction, we can divide by multiplying by the reciprocal of the molar mass `("mol"/"g")`.

`"mol K":` `26.58color(red)cancel(color(black)("g K"))xx(1"mol K")/(39.09826.58color(red)cancel(color(black)("g K")))="0.6798 mol K"`

`"mol Cr":` `35.3526.58color(red)cancel(color(black)("g Cr"))xx(1"mol Cr")/(51.99626.58color(red)cancel(color(black)("g Cr")))="0.6833 mol Cr"`

`"mol O":` `38.0726.58color(red)cancel(color(black)("g O"))xx(1"mol O")/(15.99926.58color(red)cancel(color(black)("g O")))="2.380 mol O"`

Determine mole ratios.

The mole ratios are determined by dividing the number of moles for each element by the least number of moles. If they all come out to whole numbers, then the mole ratios are the subscripts for the empirical formula. If they do not come out to whole numbers, they must be multiplied by a number that will result in whole number.

`"K":` `(0.679826.58color(red)cancel(color(black)("mol")))/(0.679826.58color(red)cancel(color(black)("mol")))=1.000`

`"Cr":` `(0.683326.58color(red)cancel(color(black)("mol")))/(0.679826.58color(red)cancel(color(black)("mol")))=1.005~~1`

`"O":` `(2.38026.58color(red)cancel(color(black)("mol")))/(0.679826.58color(red)cancel(color(black)("mol")))=3.5`

Since the mole ratio for oxygen is `3.5`, it must be multiplied by `2` to get the whole number `7`. The mol ratios for potassium and chromium must also be multiplied by `2`.

Empirical Formula: `"K"_2"Cr"_2"O"_7`

This represents the formula unit for the ionic compound potassium dichromate.