Results 1 to 6 of 6

Math Help - chemical solution

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    8

    chemical solution

    a tank initially contains salt in the pores of inert materials and 10 gal of fresh water. The salt dissolved at a rate per min of 2 times the difference between 3lb/gal and the concentration of the brine. The two gal of fresh water enters the tank per min. How much salt will be dissolved in the 1st 10 min?

    Can I get the initial value of salt from the equation?

    what equation should i use?
    dE/dt = 2(3-C)
    where C = E/(100+2t) or C = (X-E)/(100+2t)
    x=initial value of salt
    E=dissolve salt
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by sean123 View Post
    a tank initially contains salt in the pores of inert materials and 10 gal of fresh water. The salt dissolved at a rate per min of 2 times the difference between 3lb/gal and the concentration of the brine. The two gal of fresh water enters the tank per min. How much salt will be dissolved in the 1st 10 min?

    Can I get the initial value of salt from the equation?

    what equation should i use?
    dE/dt = 2(3-C)
    where C = E/(100+2t) or C = (X-E)/(100+2t)
    x=initial value of salt
    E=dissolve salt
    The red one. Only the dissolved salt contributes to the concentration of the brine, not the salt still inside the material.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    8
    ok. thank u! how would i know the initial value of salt?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by sean123 View Post
    ok. thank u! how would i know the initial value of salt?
    At t = 0, all the salt is inside the inert material (and you're told that initially the water is fresh) .....
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Jul 2010
    Posts
    2
    uhmm sir...
    I have the same problem as well... using the D.E. dE/dt = 2(3-C) and C = E/100+2t, i got

    dE/dt=2(3-E/100+2t)
    dE = 6dt - E/50+t dt so...
    E(e^ln(50+t) = ∫6e^ln(50+t) dt
    E(50+t) = ∫6(50+t) dt
    E(50+t) = ∫(300 + 6t)dt
    E(50+t) = 300t + 3t^2 +c
    E = (300t + 3t^2 +c)/50+t... that's how i got my equation... then from there, when t = 0, E = 0, i got C = 0.
    any mistakes on my solution??? please tell me so i can fix it.. thank you...
    Last edited by mr fantastic; July 18th 2010 at 05:21 AM. Reason: Merged posts.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Mrnerd View Post
    uhmm sir...
    I have the same problem as well... using the D.E. dE/dt = 2(3-C) and C = E/100+2t, i got

    dE/dt=2(3-E/100+2t)
    dE = 6dt - E/50+t dt so...
    E(e^ln(50+t) = ∫6e^ln(50+t) dt
    E(50+t) = ∫6(50+t) dt
    E(50+t) = ∫(300 + 6t)dt
    E(50+t) = 300t + 3t^2 +c
    E = (300t + 3t^2 +c)/50+t... that's how i got my equation... then from there, when t = 0, E = 0, i got C = 0.
    any mistakes on my solution??? please tell me so i can fix it.. thank you...
    That looks OK. Confirmed here: solve dy/dx + y/(50 + x) = 6 and y(0) = 0 - Wolfram|Alpha
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. chemical reaction....
    Posted in the Differential Equations Forum
    Replies: 4
    Last Post: April 4th 2011, 08:06 PM
  2. Chemical solution question.
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 30th 2011, 08:03 PM
  3. Finding how much chemical is left over
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: September 25th 2010, 03:16 AM
  4. balancing chemical reaction
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: January 25th 2010, 05:12 PM
  5. Chemical engineering...
    Posted in the Advanced Applied Math Forum
    Replies: 1
    Last Post: February 13th 2009, 09:13 PM

Search Tags


/mathhelpforum @mathhelpforum