This is how the person’s credentials would naturally be presented in an English-language text (in the US, and I believe anywhere else in the English-speaking world as well).

If there is a university department anywhere in the English-speaking world that has “Exact Sciences” as part of its name, this would be a very rare exception. The main division in the sciences is between the “natural sciences” and the “social sciences,” with chemistry squarely falling into the former category.

See the following for a simple explanation of this division:

https://www.quora.com/What-is-the-difference-between-social-...

See also:
https://en.m.wikipedia.org/wiki/Natural_science

The only Google hits for “Department of Exact Sciences” that I can see on the first couple of pages of results are (questionable) translations from other languages. It is certainly possible that a more exhaustive search could reveal the use of “Department of Exact Sciences” by some institution of higher learning somewhere in the English-speaking world but -again - this would be exceptional rather than usual.



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Note added at 2 hrs (2018-03-19 19:09:22 GMT)
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Upon further reflection, I thin you need to make sure that the degree in question is the equivalent of a “Ph.D.” (rather than being a lesser degree, e.g., the equivalent of a Master’s degree). Even if such is the case, it might be prudent not to use “Ph.D.” in the translation, but instead to translate the Spanish of the diploma (or other documentation at your disposal) literally.

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Note added at 2 hrs (2018-03-19 19:18:19 GMT)
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Erratum:

I thinK you need to...