You can generally patent an improvement on something else, even if it relies on another patent. The combined use of other patents could qualify.
The new combination, though, must not be "obvious" to those in the field, or it is not novel.
Mr. Hawkins' answer correctly hits the key legal point: your ability to get a patent depends on the combination being both "novel" and "non-obvious". Each of those is a 'term of art' in the field of patent prosecution -- which means the answer depends on the specific facts and requires skilled interpretation of both the case law, and thorough (preferably, exhaustive) knowledge of the technical field(s). You will definitely want to consult with qualified patent counsel -- and most probably, one with chemical engineering, chemistry, or chemical processing background knowledge and experience. (My technical background is in computer science, so I am recusing myself as not being sufficiently skilled in those areas.)
However, be sure to ask the practitioner to help you evaluate whether there may be other aspects of your invention which may be patentable -- such as, for example, the process(es) you use to effect the 'mixture'. Even if the resulting chemical structure is identical to one already disclosed, if you have a way to produce it that is novel, non-obvious, and useful, you may have a patentable invention there. This can be true in many fields and is an area where nano-engineering is going to have an increasing impact in the years ahead.
However, you must also consider whether you may need to license another person's patent(s) to practise your invention. If one of the ingredients is protected, then your ability to produce your product depends on their selling the right to use theirs, to you. They may not wish to do so, or may demand a price which makes your invention uneconomical -- until their protection is gone. So a final step before proceeding with filing any application should be considering, carefully, the economic aspects and assumptions you must take on or make about turning your idea into a marketed product.
I do recommend that you find a good patent attorney or patent agent with the technical background and business expertise to help you answer those further questions. Good luck!
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Short Answer: Perhaps! You can get a patent on your mixture as long as your mixture has some new property that is considered "non-obvious" over what has been done before under the U.S. patent laws. your patent attorney can run a prior art (what has been done before) search and tell you if your mixture is sufficiently different for patentablility.
Keep in mind, however, that if any of the "off the shelf" products you refer to have patents of their own, you (or the eventual owner) will need consent of those patent owners to practice your invention. Good Luck.