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Posers and Puzzles

Posers and Puzzles

  1. Standard member Fiathahel
    Artist in Drawing
    10 Feb '04 15:47
    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.
  2. 10 Feb '04 19:09
    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.
  3. Standard member Fiathahel
    Artist in Drawing
    11 Feb '04 08:43
    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
  4. Donation Acolyte
    Now With Added BA
    11 Feb '04 11:24 / 1 edit
    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)
  5. Standard member Fiathahel
    Artist in Drawing
    11 Feb '04 12:52
    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.
  6. 11 Feb '04 19:04
    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.
  7. Donation Acolyte
    Now With Added BA
    13 Feb '04 11:30
    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.
  8. 13 Feb '04 14:57
    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 - - - -

  9. Donation Acolyte
    Now With Added BA
    14 Feb '04 01:12
    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.
  10. Standard member Fiathahel
    Artist in Drawing
    16 Feb '04 11:47
    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
  11. Donation richjohnson
    TANSTAAFL
    16 Feb '04 20:50
    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)
  12. Donation Acolyte
    Now With Added BA
    17 Feb '04 11:16
    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.
  13. 17 Feb '04 18:35
    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!
  14. Standard member Fiathahel
    Artist in Drawing
    18 Feb '04 11:46
    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.
  15. Donation Acolyte
    Now With Added BA
    18 Feb '04 18:26 / 1 edit
    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?