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From Chemguide:

The difference in the colours is going to be a combination of the effect of the change of ligand, and the change of the number of ligands.

Is this comma justified? Wouldn't it be better to use no comma in the coordination?

The difference in the colours is going to be a combination of the effect of the change of ligand and the change of the number of ligands.

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It is really a matter of style. Different style books or websites may give their rules. But no one has to follow them, unless they are writing for a publication who insists on their use.

The use of commas, semicolons, dashes, etc., even whether the relative pronoun that can follow a comma, changes over time.

One should use punctuation to assist the reader. And imho, one should not use too many commas. The one in your sentence allows the reader to pause and assists him in processing the information in the preceding clause before throwing additional information at him. It's neither necessary or unnecessary. And only a martinet married to certain rules of punctuation will insist his way is the right way. (Note: no reference or allusion to anyone on ELU is meant.)

To me this issue is akin to that of such ones as ending a sentence with a preposition, using 'whom' versus 'who', using 'different from' versus 'different than'.

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The No. 7 of the linked Commas: Quick Rules by Purdue University states:

Use a comma near the end of a sentence to separate contrasted coordinate elements or to indicate a distinct pause or shift.

Your example sentence boils down to:

The difference in the colours is going to be a combination of the effect and the change.

The effect is modified by a prepositional phrase, "of the change of ligand" and the change is by "of the number of ligands".

The problem with the sentence is there are too many of's, a total of 5. It is not easy to tell which is modifying which at first glance without pausing somewhere. All of them modify the noun right before them.

The comma helps a reader (1) to pause for a moment and identify more clearly what the combination consists of (effect and change) as the comma is placed before "and" and (2) to get less confused about the structure of the sentence.

The biggest risk a sentence without the comma runs is it could be read the combination is of the two effect(s), (1) "of the change of ligand" and (2) "the change of the number of ligands" as there are two change's used in the sentence. Under the circumstances where there are one preposition (of) used multiple times and the same noun (change) used in the middle twice, I think it is better to use the comma.

Using punctuation (except for very obvious ones like a period and question mark, etc.) largely depends on your style and preference and the manual you or your editor use. I don't think not using the comma makes the sentence far more unclear, but my principle is use a comma when it looks more clear and better (when used) and don't use a comma when it doesn't do anything to help the sentence. I think the comma helps the sentence and it could be justified.

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You are correct. Commas should be used before and when you have 2 independent clauses, or a list of 3 or more things. Neither of those applies here.

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