alkanes

How many different alkanes are there with n carbon atoms.

Alkane: a collection carbon atoms, with the property that a carbon atom is connected with at least one and up to four other carbon atoms and has no cykels.

Originally posted by Fiathahel
How many different alkanes are there with n carbon atoms.

Alkane: a collection carbon atoms, with the property that a carbon atom is connected with at least one and up to four other carbon atoms and has no cykels.

According to Wikipedia (http://en.wikipedia.org/wiki/Alkane), the generic formula for acyclic alkanes is C(n)H(2n+2).

According to the definition, there can only be exactly one alkane (by definition) for each n, so I would conclude that the answer to your question is 1.

-Ray.

Originally posted by rgoudie
According to Wikipedia (http://en.wikipedia.org/wiki/Alkane), the generic formula for acyclic alkanes is C(n)H(2n+2).

According to the definition, there can only be exactly one alkane (by definition) for each n, so I would conclude that the answer to your question is 1.

-Ray.

I do no know what you mean with C(n)H(2n+2)

Their are more than one alkanes possible with n C-atoms. for example with n = 4:

C-C-C-C

and

C
|
C-C
|
C

Originally posted by Fiathahel
I do no know what you mean with C(n)H(2n+2)

Their are more than one alkanes possible with n C-atoms. for example with n = 4:

C-C-C-C

and

C
|
C-C
|
C

Is

//////C///
//C///C///
C C C C C
//C///C///
//C///////

different from


//C///C///
C C C C C
//C///C///
//C///C///

? (The slashes are for spacing purposes)

Originally posted by Acolyte
Is

//////C///
//C///C///
C C C C C
//C///C///
//C///////

different from


//C///C///
C C C C C
//C///C///
//C///C///

? (The slashes are for spacing purposes)

No, that is the same.

It is difficult to draw them here, but If you mean that there are 4 C's in the 2nd column and 4 in the 4th it is also the same as

//C///C///
C C C C C C
//C///C///
//C///////

You should see them as a 3D object that can twist in every direction.

Originally posted by Fiathahel
I do no know what you mean with C(n)H(2n+2)

Their are more than one alkanes possible with n C-atoms. for example with n = 4:

C-C-C-C

and

C
|
C-C
|
C

C subscript(n) H subscript(2n+2)

-Ray.

Originally posted by Fiathahel
No, that is the same.

It is difficult to draw them here, but If you mean that there are 4 C's in the 2nd column and 4 in the 4th it is also the same as

//C///C///
C C C C C C
//C///C///
//C///////

You should see them as a 3D object that can twist in every direction.

Ah, that makes things easier. It means you can see an n-alkane as a relation ~ on the set {1,...,n} with the following properties:

~ is symmetric and antireflexive

The 'edges' (x,y) where x~y form a tree connecting the whole set

Given any x, the number of y for which x~y is <5

Two relations are equivalent iff they can be mapped to each other by permutation of the set.

Originally posted by Fiathahel
You should see them as a 3D object that can twist in every direction.

although


- - - c - - - -
c c c c c c c c
- - - c - - - -
- - - c - - - -

is different from

- - c - - - -
c c c c c c c
- - c - - - -
- - c - - - -
- - c - - - -

Originally posted by iamatiger
although


- - - c - - - -
c c c c c c c c
- - - c - - - -
- - - c - - - -

is different from

- - c - - - -
c c c c c c c
- - c - - - -
- - c - - - -
- - c - - - -

Not in the light of Fiathahel's example. If you picture the molecule as balls connected by sticks, both the balls and the sticks can be twisted as much as you like.

Another example, to make sure you know whats possible:

c c c c c c c
- c - c - c -
- - c c c - -
- - - c - - -

is also allowed

Originally posted by Acolyte
Not in the light of Fiathahel's example. If you picture the molecule as balls connected by sticks, both the balls and the sticks can be twisted as much as you like.

I don't think that's always true. Some molecules, known as "chiral" molecules or "stereoisomers" can have different properties than their mirror image.
(i.e.:
/////D
/////|
A---C---B
/////|
/////E

is different than:
/////E
/////|
A---C---B
/////|
/////D)

Originally posted by richjohnson
I don't think that's always true. Some molecules, known as "chiral" molecules or "stereoisomers" can have different properties than their mirror image.
(i.e.:
/////D
/////|
A---C---B
/////|
/////E

is different than:
/////E
/////|
A---C---B
/////|
/////D)

That's why I asked. I think for the purposes of this puzzle we are to ignore chirality.

Originally posted by Acolyte
Not in the light of Fiathahel's example. If you picture the molecule as balls connected by sticks, both the balls and the sticks can be twisted as much as you like.

I think it's impssible to twist balls and sticks to make those two the same!

Originally posted by iamatiger
I think it's impssible to twist balls and sticks to make those two the same!

Those balls are very twisty. It doesn't matter where the sticks are connected with the ball, but only that they are connected.

We can draw any alkane from ethane upwards like this:

...../P'
C-C-Q'
.....\R'

where the Cs are carbon atoms, and P', Q' and R' are collections of carbon atoms (possibly empty) such that P = C-P', Q = C-Q' and R = C-R' are alkanes. Let P, Q and R be p-,q- and r-alkanes respectively. Then p+q+r = n+1, where n is the number of carbon atoms in the whole thing. The way I've done things p,q and r could be 1,2,3,4,5...., but given n we must have p between 1 and n-1, q between 1 and n-p and r = n+1-p-q.

Two porblems arise with trying to do an induction on this basis. Firstly we don't care about the order of p,q and r, but that's easily fixed; more seriously, given an alkane, the choice of start atom (the C on the left of the diagram) is arbitrary, aside from the insistence that it only connects to one other carbon atom (such an atom must exist for ethane or bigger, as alkanes have no cycles), and the same alkane could have representations which look different from each other by choosing a different start atom. Can anyone think of a better representation that deals with this second issue?