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Material Balance Problem

  1. Mar 5, 2015 #1
    Two liquids, A and B, are mixed together. A is 5.00% solids, the rest water. B is 11.0% solids, the rest water. To the mixture is added 18.5 kg of bone-dry solids resulting in a mixture of 2 150 kg containing 8.25% solids. What were the original amounts of the liquids A and B?
     
  2. jcsd
  3. Mar 5, 2015 #2

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    How many equations in how many unknowns?
     
  4. Mar 5, 2015 #3
    2 unknown. A and B.
     
  5. Mar 5, 2015 #4
    one example related to
    Q.Anna's Purification Co. produces drinking water from saltwater by partially freezing the saltwater to create salt-free ice and a brine solution. Tf saltwater is 3.50% salt by mass and the brine solution is fow1d to be an 8.00% concentrate by mass, determine how many kilograms of saltwater must be processed to form 2.00 kg of ice.
    Ans: Eqauation: input= output
    Overall balance : S = B + 2.00
    salt balance : 0.035S = 0.08B
    water balance : 0.965S = 0.920B + 2.00
    then solve for S and B.
     
  6. Mar 5, 2015 #5
    one example related to
    Q.Anna's Purification Co. produces drinking water from saltwater by partially freezing the saltwater to create salt-free ice and a brine solution. Tf saltwater is 3.50% salt by mass and the brine solution is fow1d to be an 8.00% concentrate by mass, determine how many kilograms of saltwater must be processed to form 2.00 kg of ice.
    Ans: Eqauation: input= output
    Overall balance : S = B + 2.00
    salt balance : 0.035S = 0.08B
    water balance : 0.965S = 0.920B + 2.00
    then solve for S and B.
     
  7. Mar 5, 2015 #6
    In terms of A and B, what is the total mass of the final mixture?

    In terms of A and B, what is the mass of solids in the final mixture?

    Chet
     
  8. Mar 5, 2015 #7
    initial amount of A n B in the total mixture. How much kg of A and B was added in the mixture
     
  9. Mar 5, 2015 #8
    Answers for this question is, A = 1260 kg, B = 872 kg
     
  10. Mar 5, 2015 #9
    I have no idea what you are saying here. Can you please answer the questions I asked (in the form of equations).

    Chet
     
  11. Mar 5, 2015 #10
    No equations are given. From this, We have to make our own equation to get the solution.
    I have tried with this equation:
    For solid : 0.05A+ 0.11B = 18.5+ 2150(0.08125)
    For Water: 0.95A+ 0.89B = 2150(0.9175)
    solve the equations.
    but i wrong answer,which means something is wrong in my equation
     
  12. Mar 5, 2015 #11
    how many equations it can be here, thats the confusion because i dont know wether its a batch process or rate process.
     
  13. Mar 5, 2015 #12
    Batch process : total input = total output.
    Rate process: rate of input- rate of output= rate of accumulation.
    if the rate process is uniform then ,
    rate of input= rate of output.
     
  14. Mar 5, 2015 #13
    This is what I was looking for. Your formulation is very close to being correct. There are just a couple of minor errors.

    1. In the solid equation, are you sure that 18.5 belongs on the right hand side of the equation?
    2. In the water equation, recheck that 0.9175. There's an arithmetic error.

    Chet
     
  15. Mar 5, 2015 #14
    if 8.25% is solid then (100-8.25)% is water which is 91.75%
    and i tried by giving 18.5 on the left hand side, but answer didnt came. It was more far than the actual answer.
     
  16. Mar 5, 2015 #15
    in the first equation i made a mistake it is 2150(0.0825) not 0.08125
     
  17. Mar 5, 2015 #16
    I know. I just noticed that. Do you get the right answer now with the 18.5 on the left?

    Chet
     
  18. Mar 5, 2015 #17
    No, i didnt. I am now trying with by corrcting that value in the equation
     
  19. Mar 5, 2015 #18
    Didnt came again :( with this value .
    somewhere is wrong, i dont know where!!
     
  20. Mar 5, 2015 #19
    Here are the equations I solved, and I got the correct answer:

    For solid : 0.05A+ 0.11B + 18.5 = 2150(0.0825)
    For Water: 0.95A+ 0.89B = 2150(0.9175)

    If you didn't get the correct answer using these equations, then you need to check your algebra.

    Chet
     
  21. Mar 5, 2015 #20
    i was checking by putting the actual value in the equation then i get for the 1st equation , 18.5 would on left side .
    and my second equation is wrong.
    Ohk, thank you :)
     
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