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Posers and Puzzles

Posers and Puzzles

  1. Subscriber joe shmo On Vacation
    Strange Egg
    31 Oct '07 22:31
    The chemical equation C3H8 +O2 = CO2 +H2O is not balanced

    I know what coefficients are needed. Im Interested in the math to find them.

    Baisically im looking for something to this effect

    x(C3 + H8) + y(O2) = a(C + O2) + b(H2 + O )

    Just using brainpower and guess and checking is obviously eisier, but im curious what the mathamatics would look like.

    I set it up the way I did because it looked the most promising

    I asked my algebra prof. she said something about matrices for a possible solution
  2. 01 Nov '07 01:24 / 3 edits
    Matrices aren't necessary. Also, guess and check is still easier. Here's to algebra:

    Basically, you have 4 variables and several equations, namely:
    3x=a
    8x=2b
    2y=2a+b

    We only need to find the "smallest" set of a,b,x, and y, which makes this question possible. Otherwise, we would need 4 equations.

    Using the first two equations, we can form a relation between a and b:
    24x=8a
    24x=6b
    0=8a-6b
    8a=6b
    4a=3b

    The smallest integer solution is a=3 and b=4. That means x=1. Now we solve for y.
    2y=2a+b
    2y=6+4
    2y=10
    y=5.

    In conclusion, a=3, b=4, x=1, and y=5. Note this is possible only because we took the smallest integer solution for 4a=3b. Otherwise, at best, we would have the coefficients in terms of one variable.

    Thanks to Joe Shmo for pointing out an error.
  3. Subscriber joe shmo On Vacation
    Strange Egg
    01 Nov '07 01:58
    Originally posted by twilight2007
    Matrices aren't necessary. Also, guess and check is still easier. Here's to algebra:

    Basically, you have 4 variables and several equations, namely:
    3x=a
    8x=4b
    2y=2a+b

    We only need to find the "smallest" set of a,b,x, and y, which makes this question possible. Otherwise, we would need 4 equations.

    Using the first two equations, we can form a ...[text shortened]... tion for 2a=3b. Otherwise, at best, we would have the coefficients in terms of one variable.
    First I thank you for showing me, I had an inkling of an idea, but not enough education.

    only the answers you provided don't balance the equation.

    On your second equation down If I have got the logic correct you have

    8x=4b and believe it should be 8x=2b

    could that be where your mistake is, I would check it myself but I'm not sure how exactly to solve this yet.
  4. 01 Nov '07 02:01
    Oops, I'll edit my post. Thanks for finding the error.
  5. Subscriber joe shmo On Vacation
    Strange Egg
    01 Nov '07 02:09
    Originally posted by twilight2007
    Oops, I'll edit my post. Thanks for finding the error.
    no,...... thank you twilight for helping out........now I just have to figure out how to do every thing else....haha

    thanks, Eric
  6. Standard member wolfgang59
    Infidel
    01 Nov '07 18:49
    I'd basically do the same as Twilight only I would set x=1 right away and solve for 3 variables with 3 equations.

    If you get non-integer solutions just multiply up.

    In other words

    (Carbon) ...... 3 = a
    (Hydrogen) ... 8 = 2b
    (Oxygen) ......2y = 2a + 2b
  7. Standard member TheMaster37
    Kupikupopo!
    02 Nov '07 07:06
    What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method
  8. Subscriber joe shmo On Vacation
    Strange Egg
    02 Nov '07 12:09
    Originally posted by TheMaster37
    What Twilight2007 does can be done a bit faster using matrices. The method used by him/her is by far the most enlightening method
    Whats cool about it, is that i can actually reproduce the results.....thanks in no small part to those here at RHP

    I just had a hunch, but boy is it sweet when they turn out to be correct