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Homework Help: Change in concentration over time

  1. Jul 26, 2011 #1
    1. The problem statement, all variables and given/known data
    A tank with a capacity of 400L is full of a mixture of water and chlorine with a concentration of 0.05g of chlorine per liter. The chlorine concentration is to be reduced by pumping in fresh water at the rate of 4L/s. The mixture is kept stirred and pumped out at the rate of 10L/s. What is the concentration of chlorine in the tank 15 seconds later?

    2. Relevant equations
    Let x= g chlorine in the tank
    let t= time in seconds
    3. The attempt at a solution
    dx/dt=(rate in)-(rate out)

    dx/dt= [(4L/s)(0g/l)]-[(10L/s)(x/(400-6t))]




    integrating both sides:






    e^ln cancels


    solving for C, When t=0, x=400*.05=20



    then solving for x when t=15


    this gets a -2300ish, which im sure is not right. what did i do wrong? lol
  2. jcsd
  3. Jul 27, 2011 #2


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    Homework Helper

    "]" is at the wrong place: |x|=e^[(5/3)*ln(|200-3t|)+C]

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