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Ratio problem

  1. Jul 12, 2007 #1
    In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol?

    -- I know that the first thing you should do is try to find the mass of alcohol in both the 8-gram and the 12-gram solution. However, to find the amount of alcohol in the 8-gram solution why would you multiply it by 1/4 and not 1/3? Its just confusing how the ratios can be written like 1:3 and then 1/4?
     
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  3. Jul 12, 2007 #2

    bel

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    The mass of the alcohol to water is 1:3, but the mass of the alcohol to the original 8 grammes solution is 1:4, hence multiply by 1/(3+1), hope this clears up the confusion.
     
  4. Jul 12, 2007 #3
    Lol, I still don't get it. I know that for every 1 gram of alcohol there are 3 grams of water. I can solve it by doing it that way. But I can't seem to get why it changes when you find the amount of alcohol in the 8-gram solution. Mabye I'm dumb or something. I just suck at ratios.
     
  5. Jul 13, 2007 #4

    HallsofIvy

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    Do you understand the difference between

    "The ratio of alchohol to water is 1:3" and
    "The ratio of alchohol to solution is 1:4"?
     
  6. Jul 14, 2007 #5
    Well kind of. Solution would be the water + alcohol right? So you just add the msas of alcohol and the mass of water to get 4. Am I doing it correct?
     
  7. Jul 14, 2007 #6

    uart

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    Yes. Why don't you imagine a really simple example. Say you added one gram of alcohol to 3 grams of water. You now have a total of 4 grams solution of which one gram is alcohol. It's not exactly rocket science as they say. :)
     
  8. Jul 14, 2007 #7
    I see! Thanks! :smile:
     
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