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Decimal points...

Discussion in 'MCAT Study Question Q&A' started by TheJourney, May 12, 2014.

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  1. TheJourney

    TheJourney

    74
    7
    May 9, 2013
    If the Ka of the HClO is 33 x 10^-8, the Kb value of ClO- is:

    A. 3 x 10^-7
    B. 3.3 x 10^8
    C. 3.3 x 10^6
    D. 14

    Very simple question, but the decimals have me all worked up. I was able to figure this one out knowing that 1x10^-14 = Ka x Kb. All decimal places aside, knowing it must be equivalent to an integer of 1, I was able to reason that 33x3 = 99 which is approx 100 (a factor of 1) and 33x3.3 would be greater than 1. However when I try to solve it, I can't seem to get the right exponent doing it in my head. Kb = (1x10^-14)/(33x10^-8), I re-wrote as (100x10^-12)/(33x10^-8) then dividing I get 3^(-12- -8) = 3^-4, the correct answer choice A which has it to the ^-7. I thought maybe I should have written it as 100x10^-16 and not 100x10^-12, but that would be 3x10^-8, still not 10^-7.
     
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  3. DrknoSDN

    DrknoSDN

    450
    104
    Feb 21, 2014
    The answer is wrong I believe it should be 3 x 10^-8. I Think i remember doing that problem and finding error posted on EK web forums.

    Taking the product of the Kb and Ka you would expect to get: 1*10^-14 and not 9.9*10^-14
     
    Czarcasm likes this.
  4. TheJourney

    TheJourney

    74
    7
    May 9, 2013
    How is it wrong? Wouldn't the error have to be in the exponents.

    .33x3 = .99, .99 is close enough to 1, or no?
    If I'm mistaken, could you please elaborate.
     
  5. DrknoSDN

    DrknoSDN

    450
    104
    Feb 21, 2014
    So 9.9 * 10^-14 is almost 1.0 * 10^-13
    So it's off by an order of magnitude.

    Alternatively use 34 instead of 33.. you would expect to get slightly more than 1x10^-14.
    But you don't. You get: 1.02 * 10^-13
     

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