Question

Calculate the empirical formula of a sample of compound in which the mass percentage of potassium, chromium and oxygen are 26.6%, 35.4% and 38.1% respectively?

Answer 1

Hint: The empirical formula of a chemical compound is expressed as the simplest positive integer ratio between the numbers of atoms of different elements present in a molecule of the compound.

Complete step by step answer:
-There are students who get confused while writing the empirical formulas of any given compounds. To make it clear, let's take an example which would make this concept clearer:
A simple example is that the empirical formula of sulfur monoxide would simply be SO, as is the formula of disulfuric dioxide $S_2{O}_2$. Thus, sulfur monoxide and disulfuric dioxide, both are the compounds of Sulphur and oxygen, and have the same empirical formula. However, their molecular formulas, which express the number of atoms in each molecule of a compound, are not the same. An empirical formula makes no mention for the arrangement or number of atoms. It is standard for many ionic compounds, like calcium chloride ($CaC{l}_2$), and for some macromolecules like silicon dioxide ($Si{O}_2$).
-Now, let's have a look one the steps for determining an empirical formula:
- Start with the number of grams of each element of the compound given in the problem (If percentages are given, assume that the total mass is 100 grams so that the mass of each element will be equal to the percentage given)
- Convert the mass of each element into moles using the molar mass of the respective elements from the periodic table.
- Divide the value of each mole by the smallest number of moles calculated.
- Round to the nearest whole number. This is the mole ratio of the elements and is represented by subscripts in the empirical formula.
- If the number is too far to round up, then multiply each solution by the same factor to get the lowest possible whole number multiple.
Now, with reference to the above discussion, let's find out the empirical formula of the given sample of compound: Let us assume that the mass of the compound is 100gm.
So, we have: -
K=26.6g
Cr=35.4g
O=38.1g
Now convert each of them in terms of moles: -
Moles of K= ${\displaystyle \frac{26.6}{39}}=0.68$ moles
Moles of Cr=${\displaystyle \frac{35.4}{52}}=0.68$ moles
Moles of O=${\displaystyle \frac{38.1}{16}}=2.38$ moles
Now, divide all of them with the minimum mole (which in this case is 0.68) and convert them in nearest whole numbers by multiplying with a suitable factor:
K=${\displaystyle \frac{0.68}{0.68}}=1\times 2=2$
Cr=${\displaystyle \frac{0.68}{0.68}}=1\times 2=2$
O=${\displaystyle \frac{2.38}{0.68}}=3.5\times 2=7$

So the empirical formula is $K_{2}C{r}_2{O}_7$.

Note: Don't get confused between molecular formula and empirical formula. Empirical formulas show the simplest whole-number ratio of atoms in a compound whereas molecular formulas show the number of each type of atom in a molecule.