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I find that both usages are abundantly used on the internet and am confused as to which is the correct version.

Example:

Only a small amount of product is necessary since our formula is highly concentrated in active ingredients.

vs.

Only a small amount of product is necessary since our formula is highly concentrated with active ingredients.

  • books.google.com/ngrams/… – user180089 Jul 14 '16 at 12:43
  • @V0ight I'm afraid that the ngram is probably looking at things like Sally concentrated in British Literature while studying abroad... – USER_8675309 Jul 14 '16 at 12:54
  • @USER_8675309 ~ no, did you look at the sources at the bottom? – user180089 Jul 14 '16 at 12:55
  • @V0ight "workers concentrated in kitchens" is analogous to "ingredients concentrated in formula," not "formula concentrated in ingredients." Which of the sources do you see using it the way the question does? – jejorda2 Jul 14 '16 at 13:00
  • @V0ight I stand corrected -- although it seems that many of these are not sentences, rather they are titles of articles. – USER_8675309 Jul 14 '16 at 13:00
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Both of these are wrong.

Here are some other ways to phrase your message:

The formula has a high concentration of the active ingredients.

Our product is a concentrated formula of the active ingredient.

The active ingredients have been concentrated in our formula.

All of these are based on Oxford's 3rd definition of concentrate, which requires an object:

[with object] Increase the strength or proportion of (a substance or solution) by removing or reducing the other diluting agent or by selective accumulation of atoms or molecules: ‘plants and micro-organisms can concentrate metals from the environment’

  • You're wrong; concentrated is acting as an adjective in OP's sentence, not as a verb. oxforddictionaries.com/definition/english/concentrated – user180089 Jul 14 '16 at 12:51
  • @V0ight Using the prepositional phrase to modify the adjective is awkward and unclear, so the sentences should be re-written to use a verb instead of an adjective. I've provided some examples of how this can be done. The answer to "which preposition should modify the adjective" is "neither- don't use the adjective like that." – jejorda2 Jul 14 '16 at 12:55
  • what makes it awkward and unclear? @jejorda2 – user180089 Jul 14 '16 at 13:15
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I think the problem here is that "concentrate" is a transitive verb and thus needs a direct object. Here, in your examples

. . . since our formula is highly concentrated in/with active ingredients.

the problem is that whether you consider "concentrated" to be a verb or an adjective, it has a passive meaning. That is, the object of the action needs to be the grammatical subject. In this case, it appears that "the active ingredients" is the object of the action, and so should be the grammmatical subject.

That's what @jejorda2 has done in these examples:

The formula has a high concentration of the active ingredients.

Our product is a concentrated formula of the active ingredient.

The active ingredients have been concentrated in our formula.

as well as @USER_8675309 here:

Only a small amount of product is necessary since our formula has a high concentration of active ingredients.

So, neither "in active ingredients" nor "with active ingredients" is appropriate because the prepositions (in, with) prevent "active ingredients" from being the object of the verb "concentrate", which is true whether you decide to use it in the passive voice or not.

Here then is my solution:

Only a small amount of product is necessary since the active ingredients are highly concentrated in our formula.

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To elaborate on jejorda2's answer:

I don't think both of these are wrong, but they don't exactly roll off the tongue. I believe, in your example, that

Only a small amount of product is necessary since our formula is highly concentrated with active ingredients.

would be an acceptable use here, although a smoother way to write this sentence could be

Only a small amount of product is necessary since our formula has a high concentration of active ingredients.

But this is an opinion.

Consider this:

I cannot concentrate (in/on) class because of all the noise coming from the hallway.

Here concentrate is being used as a verb, with on being the subject of the concentration and in being the location of the person who is doing the concentrating.

As V0ight has helpfully offered, the use of concentrated in seems to be the preferred method:

Danielle's product is highly concentrated in active ingredients

The majority of low income citizens are concentrated in an area just north of the river.

Consider this:

The cities population boom has been largely concentrated around the area north of the river.

That being said, when using concentrate as a verb, there are plenty of cases where the word with could follow:

I concentrated with a group of my peers to come up with the correct formula.

The formula was concentrated with a large amount of active ingredients.

I will say, at the end of this I have perhaps confused myself more on the subject of concentration

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