One way to separate the different kinds of matter in a mixture is through A. filteration
B. decomposition
C. electrolysis
D. chemical reactions

The answer is filtration (A).

Creating a mixture is a physical process; as such, the substances that make up a true mixture do not undergo any chemical reactions with one another. It follows, then, that to separate substances that are mixed together, the process to use would be physical, not chemical. Filtration fits that bill: Solutes that do not dissolve in the solvent can be trapped, for example, by a fine mesh whose openings are large enough for the solvent to pass through but too small for the undissolved solute(s) to do so.

Choices B, C, and D are all chemical processes.

Decomposition (B) is the breakdown of a substance into chemically distinct fragments. For example, hydrogen peroxide in a mixture (solution) with water decomposes in the presence of an appropriate catalyst—the products you are left with are water and oxygen gas, which bubbles out of the mixture. But you haven’t separated the hydrogen peroxide from the water—through decomposition, the hydrogen peroxide molecules are broken up and the atoms rearranged to form different molecules. There’s no hydrogen peroxide left to separate anymore. So, decomposition doesn’t separate different substances in a mixture—it transforms them.

Electrolysis (C) is a chemical process that uses an electric current to drive the movement of charged particles (electrons and ions) through a conductive medium. Suffice it to say that this will almost certainly change the chemistry of a mixture. For example, assume you’ve got a mixture of some inert, insoluble solute in water. If you run a very strong electric current through water, you’ll end up decomposing the water molecules themselves into oxygen and hydrogen gases. Again, you haven’t technically separated the solute from the mixture because separation implies that you have the separated substances still around. In this example, you’ve “separated” your solute by chemically transforming your solvent into two different gases; one part of your mixture no longer exists. (Side note: electrolysis of pure water takes quite a bit of energy; on the other hand, tap water, which contains dissolved electrolytes, can be readily decomposed via electrolysis using the current delivered by a standard alkaline battery.)

As a rule of thumb, the suffix (–lysis) usually indicates chemical decomposition, and the stem that precedes the suffix usually indicates what the decomposition process involves. Examples include electrolysis (as we just discussed), hydrolysis (breaking a chemical bond using water), glycolysis (the biochemical process of breaking down glucose into smaller molecules to harness the energy released), and radiolysis (splitting a bond within atoms comprising a molecule using ionizing radiation).

Finally, as should be clear by this point, chemical reactions are not the way to go about separating mixtures. Again, the chemical substances in a mixture retain their chemical identities. Separating the constituents of a mixture essentially entails isolating these substances. Filtration can and does isolate solutes from solvents without altering their chemical identities (assuming the filter itself is chemically inert). A chemical reaction changes a substances chemical identity, and so could not properly be regarded as a method of separation, and only separation.