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Find ph based on given volume and molarity of HCl and NaOH

  1. Jun 19, 2016 #1
    Hello!
    I am trying to crack the following problem:

    What is the pH of a solution formed by mixing

    125.0 mL of 0.0250 M HCl with 75.0 mL of 0.0500 M

    NaOH?

    Here is how I am approaching the issue:
    both HCl and NaOH are strong acid and base respectively. Hence the concentration of [H3O+] = 0.003125M (this is the amount of moles of HCl in 0.125 L) and [OH-] = 0.00375M
    Kw = [H30] x [OH] = 10^(-14)

    the difference between [H30] and [OH] = 0.00375 - 0.003125 = 0.000625, which tells me that there are more [OH] in solution; hence it is a basic solution. -log(0.000625) = 3.204
    But if I subtract 3.204 from 14 I will get 11.8, but the answer is 11.495

    I can get 11.495 if 10(-14) / 0.003125 and take a log. But it can't be right because that would give me pOh not Ph.

    I will be grateful for your help!
     
  2. jcsd
  3. Jun 19, 2016 #2

    SteamKing

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    Have you considered what happens when some of the HCl is neutralized by the NaOH?
     
  4. Jun 19, 2016 #3
    I am not sure I understand your question correctly. You say "some" of HCl. HCl is a strong acid and NaOH is a strong base, for 1 mole of HCl we need 1 mole of NaOH.
     
  5. Jun 19, 2016 #4

    Borek

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    Please explain where this number comes from.
     
  6. Jun 19, 2016 #5

    SteamKing

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    Yes, but chemicals are stupid. They will react even if precisely correct stoichiometric ratios are not present. The reaction stops when one of the reagents has completely reacted with the other, leaving an excess amount of the second reagent left over.
     
  7. Jun 19, 2016 #6
    We have 0.0250 moles of HCl in 1 liter and there are 0.125 liters; hence we have 0.003125 moles of HCl. HCl is a strong acid, hence the concentration of [H3O] is also 0.003125[/QUOTE]
     
    Last edited: Jun 19, 2016
  8. Jun 19, 2016 #7
    Ah! Indeed, HCl is a limiting reagent here. I have to think further. Thank you! I will be back if I can't solve it.
     
  9. Jun 19, 2016 #8

    Borek

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    No. While your calculation of number of moles is correct, number of moles doesn't equal concentration (unless the volume is exactly 1 L).
     
  10. Jun 20, 2016 #9
    maybe the word concentration is wrong, but I mean that there are 0.003125 moles of [H3O]
     
  11. Jun 20, 2016 #10

    Borek

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    pH is a function of concentration, not number of moles.
     
  12. Jun 20, 2016 #11
    I am at my wit's end: if I have 0.003125 moles of [h3o], and based on the fact that HCl is the limiting reagent, I should have used, as I would usually do, -log function to find Ph. But here that would generate incorrect answer. Please, help to understand
     
  13. Jun 20, 2016 #12
    Indeed. My bad )))
    If HCl is a limiting reagent (because according to stoichiometry there are 1 mole of HCl per 1 mole of NaOH), then the reaction requires 0.003125 moles of HCl and takes only 0.003125 moles of NaOH. Is this correct?
     
  14. Jun 20, 2016 #13

    Borek

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    Correct so far.
     
  15. Jun 20, 2016 #14
    Thank you.
    HCl is a strong acid, and hence will dissociate completely producing 0.003125 moles of [H3O+]. To compute pH I need to find the molarity of H3O. But it's molarity will be the same as HCl? I am truly stuck with this task.
     
  16. Jun 20, 2016 #15

    Borek

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    What is the definition of the concentration?
     
  17. Jun 20, 2016 #16
    Concentration (like density) = the amount of any given substance in a given volume.
     
  18. Jun 20, 2016 #17

    Borek

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    And how do you calculate the concentration? Say, you have 1 mole of substance in 5 liters of the solution, what is the concentration?
     
  19. Jun 20, 2016 #18
    It will be 1/5. To find the concentration I divide moles by volume.
     
  20. Jun 20, 2016 #19

    Borek

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    So why don't you do the same to solve the initial problem?
     
  21. Jun 26, 2016 #20
    Sorry, but I don't see it.
    If I have 0.003125 moles of HCL, then I need also 0.003125 moles of NaOH. The molarity of NaOH is 0.0500, so I need 0.0625 liters of NaOH for this reaction.
    0.125 l of HCl + 0.0625 L of NaOH gives total 0.1875 liters of solution, in which there are 0.003125 moles of HCl. Therefore, in 1 liter of such solution I should have
    0.017 moles of HCl. Is it correct?
    If yes, it will be the concentration of [H3O+] in the solution.
    Taking -log of this gives me an incorrect answer.
     
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