[CRuffinside]

THIS IS NOT A QUESTION. This is about a formula I created from discovering a pattern in my homework!

Here is what I found ON 9/17/2009

My Initials are CAR. Don't want to give my full name....but still want credit!

I was working on homework and I noticed a pattern in the answers while trying to determine how many Isomers are formed when you have two substituents on a STRAIGHT carbon chain.

I noticed that the pattern was true for any straight carbon chain that I worked out by hand. I tried to make things more simple by creating a formula to help with larger carbon chains that took too long to work out by hand. And this is what I found.

TRY THIS, it holds true for any sized straight carbon chain with two substituents. But pay attention to the number of carbons, the formula is different for an odd numbered chain than for an even numbered chain...but that makes sense.

n = # of Carbons in the straight carbon chain with two substituents

Take any straight EVEN carbon chain with any 2 substituents, let's say C4 and Chlorine...C4H8CL2
The EVEN # formula is [(1/2n) (1/2n+1)] = the number of isomers for that butane molecule is 6 possible Isomers.

Take any straight ODD carbon chain with any 2 substituents, let's say C5 and Chlorine...C5H10Cl2
The formula is [{1/2n) + .5]^2 = the number of isomers for that pentane molecule is 9 possible Isomers.

Check this for yourself. Use a low number chain, and work it by hand. then apply the CORRECT formula (odd and even is different), you will get the same number. try a larger chain, work it by hand, then apply the formula. It still holds true...BUT KEEP 2 Substituent's and apply the formulas correctly. I have begun trying to figure out a formula for a straight chain with 3 substituents, but as you know the number of isomers resulting explodes with increasing substituents!

I promise you, it is no where else online, I did not "steal" it and I advise you don't either...honor is hard to find these days! It is also not in any text book. I have put it online because I am proud and wanted to share it with others that appreciate Organic Chemistry.

If YOU WANT TO KNOW THE PATTERN i discovered leading to the creation to this formula. Just ask and I will be happy to oblige.

I know this isn't ground breaking or worthy of a Journal publication, but all in all I think it's pretty neat.

caruffin@hotmail.com

[KritikalMass]

Your even number formula can be simplified to [n(n+2)]/4

[KritikalMass]

And your odd number formula can be simplified to (n+1)²/4

[CRuffinside]

HEY THANKS...I didn't think to try that. That's brilliant. I agree that is much more simple!

[KritikalMass]

HEY THANKS...I didn't think to try that. That's brilliant. I agree that is much more simple!

No problem, and congrats on discovering the formulas, good job 

[CRuffinside]

you simplified it in what....2 minutes? Bravo