"Why am I investigating this reaction?"" --> it's a bit awkward. Change to something more colloquial.
"For science!
Why go to the moon?
[...]
Who knows what real world applications the oscillating reaction might have in the future?"
I think it'd be better if you combined these paragraphs into one...
"Interested in developing and applying theoretical concepts in our real world, I have been inspired by Dr. Fenn's story to further my interest in research..." --> The phrase is a bit awkward. Maybe change it to "After learning about Dr. Fenn, I am inspired to do the same. I want to discover, develop, apply theoretical concepts, just as Dr. Fenn did..."
"To be able to study engineering at Yale is unique in many ways" Consider revising it to "Studying to become an engineer at Yale is a unique opportunity that provides an incredible amount of resources." then go on to talk about how one such resource is the 1:1 faculty to student ratio.
I really like your last paragraph. However, I have to agree with krcheng that the "Amongst a group of fun and brilliant hoodie-wearing students" portion seems...too common. You can find a group of fun and brilliant hoodie-wearing students at any good college...Perhaps change this to a different description.
Now, about your intro. I have a sense that you want the intro to be a little comical... compared to the common language, the elaborate description of the chemical reaction is bizarre and throws the reader off balance, which is a great way to catch his or her attention. But right now, I feel there is something lacking in this paragraph. Try to describe more.
--> "It was a normal day in the chemistry lab. I was studying the effect of change in concentration of potassium iodate on the rate of reaction of the Briggs-Rauscher oscillating reaction for a research paper. I watched the clear solution in the beaker change colors, from blue to yellow, then yellow to blue. Nothing else happened. This went on for a couple of minutes; that's when I turned to my chemistry teacher and asked her, "What's the point of looking at this reaction? It's just changing colors."
That was a rather crude and rough substitution, but you get the idea.
Nice essay, overall!