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Do I have enough information to solve this density problem?

  1. Jan 29, 2015 #1
    1. The problem statement, all variables and given/known data
    "If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 degrees Celsius, what volume does the ice occupy? Water has a density of 0.997 g/cm^3 at 25 degrees Celsius; ice has a density of 0.917 g/cm^3 at -10 degrees Celsius."

    2. Relevant equations
    D = m/V
    D = m/1500 mL
    m = x(0.997) + y(0.917)
    x + y = 1500 mL
    x = 1500 - y

    3. The attempt at a solution
    m = (1500 - y)(0.997) + y(0.917)
    m = 1495.5 - y0.997 + y0.917
    m = 1495.5 - y0.08

    I feel like I would need the mass of the bottle's contents or its density in order to proceed. Am I plugging in my numbers wrong?
     
    Last edited: Jan 29, 2015
  2. jcsd
  3. Jan 29, 2015 #2

    Borek

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    Question is rather lousy if you ask me. I guess they want you to assume bottle is either elastic enough to expand, or it simply breaks (and all water is converted to ice).
     
  4. Jan 29, 2015 #3
    I agree; my chemistry professor doesn't seem to know what she's talking about.

    But do I have enough information to solve for the volume of the ice?
     
  5. Jan 29, 2015 #4

    Borek

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    Yes. Mass of water doesn't change.
     
  6. Jan 29, 2015 #5
    But I don't know what the mass of the water is...
     
  7. Jan 29, 2015 #6

    Borek

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    You have enough data to calculate it.
     
  8. Jan 29, 2015 #7

    SteamKing

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    Re-read the problem statement carefully:

    "If a soft-drink bottle whose volume is 1.50 L is completely filled with water and then frozen to -10 degrees Celsius, what volume does the ice occupy? Water has a density of 0.997 g/cm^3 at 25 degrees Celsius; ice has a density of 0.917 g/cm^3 at 10 degrees Celsius."

    Some problems will not spoon-feed you all the data you need for solution. You have to do a little work to find it.

    It's not clear how the ice exists at a temperature of 10 degrees Celsius, unless this is a typo which occurred when copying the problem statement.
     
  9. Jan 29, 2015 #8
    If that's the case, then wouldn't the ice take up the whole bottle since it can't be two different temperatures?
     
  10. Jan 29, 2015 #9

    SteamKing

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    That wasn't the point I was trying to make, but now that you asked it ...

    What happens to ice when the temperature is greater than 0 degrees Celsius?

    (Hint: What is the freezing point of water?)
     
  11. Jan 29, 2015 #10
    The freezing point of water is 0 degrees Celsius, isn't it?

    If it's greater, then it starts to melt?
     
  12. Jan 29, 2015 #11

    SteamKing

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    Yes. So the density of ice at 10 degrees Celsius seems to cover an impossible situation.
     
  13. Jan 29, 2015 #12
    I'm sorry for not pointing this out earlier, but this is correct.
     
  14. Jan 30, 2015 #13

    Borek

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    Please reread my first post in the thread. Final volume of the ice is not 1.5L.
     
  15. Jan 30, 2015 #14
    Okay, 1.50 L of water (at 25 degrees Celsius) is poured into water. It has a mass of m = 1500(0.997) = 1495.5 g. This mass does not change, even when the water is frozen. However, its volume of the water does change as it turns to ice? Given that the density of ice is 0.917 g/mL, I can calculate the volume from that and the mass.

    m = 1495.5
    1495.5 = V(0.917)
    V = 1495.5/0.917
    V = 1630.862 mL
     
  16. Jan 30, 2015 #15

    Borek

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    And that would be my approach to solving the question.

    Watch your significant figures.
     
  17. Jan 30, 2015 #16
    Okay, thanks.
     
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