Hydronium Concentration Calculation

HopefulOncoDoc

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    What is the hydronium concentration in a gastric solution where the pH is 2.3?

    A. 5x10^-2 M
    B. 2x10^-2 M
    C. 5x10^-3 M
    D. 2x10^-3 M

    Alright so I got it all the way down to [H3O+] = 10^-2.3 but my math is pretty bad from there. Could someone please explain the mathematics involved after this? Thanks a lot! The answer is C by the way.
     
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    G1SG2

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    1. Pre-Medical
      What is the hydronium concentration in a gastric solution where the pH is 2.3?

      A. 5x10^-3 M
      B. 2x10^-3 M
      C. 5x10^-3 M
      D. 2x10^-3 M

      Alright so I got it all the way down to [H3O+] = 10^-2.3 but my math is pretty bad from there. Could someone please explain the mathematics involved after this? Thanks a lot! The answer is C by the way.

      [H3O+] = 10^-2.3==> 10^1/2 x 10^-2.8 ==> sqrt10 x 10^-2.8 ==> 3.2 x 10^-2.8, which is equal to 5 x 10^-3.
       
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      amine2086

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        Would you mind explaining how to do that math in your head? I had some trouble following your explanation. Thanks!

        Laura S.

        You know the equation, pH = -log[H+]. We are given pH of 2.3

        2.3 = -log[H+]
        -2.3 = log [H+]
        [H+] = 10^-2.3

        From this we know that the hydronium ion concentration must be smaller than 10^-2 and greater than 10^-3. Only answer that fits that criteria is C.
         

        fbradley99

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          I solved it in my head without using any math. I used the ph/Ka trick. You know the one with if the number is greater than 3. Use the search tool to find out how to solve this with the trick. I can't remember exactly what thread its in. :)

          Thank you for whoever posted that because it has totally helped me out so much!!!!!!!!!!!!!!
           
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