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Simple Question: Units and volume of DNA - Can't get formula correct?

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  1. May 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Deoxyribonucleic acid (DNA) is thought to be the chemical compound
    responsible for the process of heredity. A sample of DNA was found to have
    density 1.10 g/cm3 and its molecular weight was estimated to be
    3.04 × 108 g. What is the average volume occupied by one DNA molecule?


    2. Relevant equations



    3. The attempt at a solution

    I am stuck here. I know V = mass/density

    Would I go something like:

    3.04 x 10^8 g per mol x (1 mol / 6.022x10^23 molecules) x ( 1 cm^3 / 1.10 g)

    No thats not right...dammit

    Any help would be great. I know its a simple question, but I need to know exactly how to get the answer.

    Thanks all!!!
     
  2. jcsd
  3. May 9, 2012 #2

    tms

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    Ignore.
     
    Last edited: May 9, 2012
  4. May 9, 2012 #3
    I thought the correct units for molecular weight is g/mol, and since we are finding the volume of one DNA molecule, I thought I had to do a few conversion factors.
     
  5. May 9, 2012 #4
    If I do it that way 3.04 x 10^8 / 1.1 I get... 2.76364 x 10^8 cm^3

    which is impossible for just one DNA molecule to occupy that space.
     
  6. May 9, 2012 #5

    gneill

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    Staff: Mentor

    Your method looks okay. Why do think it's not right? Are having difficulty with the unit conversions for grams or cubic centimeters?
     
  7. May 9, 2012 #6
    The molecular weight defines how much mass of something is in a mole, i.e. 6.02(10^23) molecules. You need to normalize the volume to one molecule. Your answer should be correct. Just make sure you put your answer in the units that the answer called for.
     
  8. May 9, 2012 #7

    tms

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    Forget what I said; I was answering the wrong question.
     
  9. May 9, 2012 #8
    Is there a better way to do this. Can you maybe explain?

    When you look at this question, what steps are you thinking to do?

    Yes, having little issue with last part (1 cm^3 / 1.10g)

    So, when I see something like 1.10g/cm^3, if I want to get rid of the g, i would just go...1cm^3 / 1.10 g

    Slightly confused :(
     
  10. May 9, 2012 #9

    tms

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    DNA molecules are huge (although not that huge; I didn't realize you were still looking at my first stupid answer). Compare its molecular weight with that of a more typical molecule.
     
    Last edited: May 9, 2012
  11. May 9, 2012 #10
    lol, yea its true. They are pretty big.
     
  12. May 9, 2012 #11

    gneill

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    Staff: Mentor

    The method that you used is the standard approach, so no need to tinker there.
    Same as you did!
    The grams will cancel with another grams earlier in the expression chain. In fact the first item in the chain was the molecular weight given as grams/mol. So the grams in its numerator cancel the grams in the denominator of the density, even though they are separated by other links in the calculation chain.
     
  13. May 9, 2012 #12
    Great, thanks. Much better understanding now!
     
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