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Catseyeglint911

  • 4 months ago

Who wants a medal? How much of a 60% acid solution must be mixed with 50 gallons of a 24% acid solution to obtain a solution that is 50% acid? a. 130 gal c. 13 gal b. 125 gal d. None of these

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  1. JoannaBlackwelder
    • 4 months ago
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    I would use the idea of a mass balance of the acid.

  2. JoannaBlackwelder
    • 4 months ago
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    For example, the amount of acid in the 50 gallons of a 24% acid solution would be 50*.24=12 gallons of acid.

  3. JoannaBlackwelder
    • 4 months ago
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    Make sense so far?

  4. Catseyeglint911
    • 4 months ago
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    yes

  5. JoannaBlackwelder
    • 4 months ago
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    Sweet. Since we don't have the volume of the 60% acid solution, I will call that x.

  6. JoannaBlackwelder
    • 4 months ago
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    Can you write an expression that shows the volume of acid of the 60% acid solution?

  7. Catseyeglint911
    • 4 months ago
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    0.5 = 0.6x + (50*0.24) I have a feeling that this isn't right.

  8. JoannaBlackwelder
    • 4 months ago
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    That is close. The addition side looks good, but what about the volume of the combined solution?

  9. JoannaBlackwelder
    • 4 months ago
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    @Catseyeglint911?

  10. Catseyeglint911
    • 4 months ago
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    sorry I had to step a way for a bit

  11. JoannaBlackwelder
    • 4 months ago
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    No worries :)

  12. Catseyeglint911
    • 4 months ago
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    (0.5*50) = 0.6x + (50*0.24) Is this what you meant?

  13. JoannaBlackwelder
    • 4 months ago
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    Closer. :) The volume of the 24% solution is 50 gals and the 60% acid solution has volume x gals, so wouldn't the combined 50% acid solution have more volume that 50 gals?

  14. Catseyeglint911
    • 4 months ago
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    So we would have to use two variables since we don't know the number of gallons need of the 60% solution nor do we know the number of gallons of the final solution?

  15. JoannaBlackwelder
    • 4 months ago
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    We could, but we don't have to. Since we know we are adding two volumes together and one volume is 50 gallons and we defined the second volume to be x gallons. So the combined volume is 50+x gallons.

  16. Catseyeglint911
    • 4 months ago
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    (x+50) = 0.6 + (50*0.24) It's still wrong isn't it?

  17. JoannaBlackwelder
    • 4 months ago
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    Last time you put (0.5*50) = 0.6x + (50*0.24) which was closer. The only thing you needed to change was (0.5*[50+x]) = 0.6x + (50*0.24)

  18. JoannaBlackwelder
    • 4 months ago
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    The 50 to a 50+x

  19. JoannaBlackwelder
    • 4 months ago
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    Do you follow me?

  20. Catseyeglint911
    • 4 months ago
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    Ooohhh! I see now. :D

  21. JoannaBlackwelder
    • 4 months ago
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    :D

  22. JoannaBlackwelder
    • 4 months ago
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    Can you solve for x?

  23. Catseyeglint911
    • 4 months ago
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    (0.5*[50+x]) = 0.6x + (50*0.24) 25 + 0.5x = 0.6x + 12 13 + 0.5x = 0.6x 13 = 0.1x 130 = x right?

  24. JoannaBlackwelder
    • 4 months ago
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    Awesome! :)

  25. Catseyeglint911
    • 4 months ago
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    Thank you so much. :)

  26. JoannaBlackwelder
    • 4 months ago
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    No worries

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