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What is the empirical formula of C2H4O2?
The empirical formula tells you what the smallest integer ratio between the atoms that make up a substance is.
In essence, the empirical formula can be thought of as the building block of a substance. The molecular formula will thus tell you how many building blocks are needed to form that substance.
So, for a given molecule, the empirical formula will tell you what is the minimum number of atoms of each element needed to form the building block for the molecular formula.
In your case, the molecular formula is given to be ##"C"_2"H"_4"O"_2##. What that tells you is that the molecule contains
- two atoms of carbon
- four atoms of hydrogen
- two atoms of oxygen
But what is the minimum number of atoms of each element that you need in order to be able to start building the molecule?
The minimum number of atoms an element can contriubte to a building block is ##1##, since you can't have half an atom or one atom and a half as whole numbers.
With this in mind, notice that if you divide all these values by ##2##, you will get
- one atom of carbon
- two atoms of hydrogen
- one atom of oxygen
This tells you that the building block for this particular molecule is ##"CH"_2"O"##. This will thus be the compound's empirical formula.
In other words, if you take two such building blocks, ##"CH"_2"O"##. you can build the molecule ##"C"_2"H"_4"O"_2##.