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show why ka(kb)=kw for this pair of conjugate acid-base: H2C6H6O6 and HC6H66 ^-1

  • chem -

    It's too long and too confusing using long formulas. Let's cut that to ANY acid and its conjugate base, HA.
    The conjugate base is A^- so if we add that to water we have
    ..........A^- + HOH ==> HA^- + OH^-

    ----------- = Kb for the conjugate base.

    Now let's multiply that by (H^+)/(H^+)
    I must use ..... for spacing and it still may not look very good.
    ----------- x ------ = Kb
    Now look at the equation.
    In the numerator, (H^+)(OH^-) = Kw.
    In the denominator, we have the reciprocal of Ka. Note that is (A^-)/(H^+)(A^-) which is just 1/Ka. Therefore, Kb = Kw*1/Kb or just Kw/Kb.

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