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The use of P*V=n*R*T

  1. Dec 3, 2013 #1
    1. The problem statement, all variables and given/known data

    In a sealed drillhole with volume 0.80 dm ³ are 100 grams of ammonium nitrate, NH ₄ NO ₃. The explosive can be made to explode and disintegrate by the formula:
    2 NH ₄ NO ₃ (s) -> 2N ₂ (g) + O ₂ (g) + 4H ₂ O (g)
    In the explosion moment - before the mountain exploded - there is a high pressure. What pressure gives the "gas law" theory, if the temperature is 1000 ° C?


    2. Relevant equations

    P*V=n*R*T

    3. The attempt at a solution

    P=?
    V= 0.8dm^3=0.0008m^3
    n= 100/80.043 = c.a 1.25mol
    T = 1273.15 K
    R= 8.314

    1.25*8.314*1273.15= c.a 13231 = P*V

    13231/0.0008 = 16539014 kPa (This is what I am very uncertain of, I assumed that because I made 0.8dm^3 to m^3 I thought that the answer became in kPa. I then divided 13231 by 0,8dm^3 and got ~16538 (This I thought would be kPa and obviously doesn't make sense then).
    Can someone explain to me what is correct and why? I am a little bit confused.
     
    Last edited: Dec 3, 2013
  2. jcsd
  3. Dec 3, 2013 #2

    Borek

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    Staff: Mentor

    That's the number of moles of ammonium nitrate, but that's not the number of moles of gases produced.

    What are units of R with this particular value?

    There is no need to guess what your pressure is in, just follow the units step by step and in the end you will see what you have.
     
  4. Dec 3, 2013 #3

    Now I think I understand why I made 0.8dm^3 to m^3. R is a constant with the value of 8.314 and for that constant to be relevant all volume need to me in m^3. Is this correct?


    As for the gases produced, I know how many moles are in 2NH₄NO₃ but that is irrelevant because I should focus on the ammount of moles in the produced gases which is 2N₂(g) + O₂(g) + 4H₂O(g)?
    This is really hard for me, I had no problem in finding the molarmass of ammonium nitrate but when I try to find the molarmass of oxygen etc I find nothing. How do I go about calculating the ammount of moles in the gases produced? Since there is 3 different gases how do I know how much of each is produced? (the 100g explosive I assume is divided somehow among the gases produced)
     
  5. Dec 3, 2013 #4

    Borek

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    Staff: Mentor

    You don't need molar masses of these gases (besides: you don't "find" them you calculate them using atomic masses taken from the periodic table). All you need is the reaction stoichiometry - you know how many moles decomposed, so you should be able to calculate number of moles of gases produced. Compare

    http://www.chembuddy.com/?left=balancing-stoichiometry&right=stoichiometric-calculations

    You have not answered my question: what are units of the R constant of the given value?
     
  6. Dec 3, 2013 #5
    Oh, it's energy (Joule). So the answer is in joules and not pa's? (My english is kind of bad so I didn't understand your question at first. Apologies)
     
  7. Dec 3, 2013 #6

    Borek

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    Staff: Mentor

  8. Dec 3, 2013 #7
    Ye ur right, I am pretty much clueless. Thank you for the link!
     
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