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Can equilibrium rate constant has unit of [time^-1]?

  1. May 7, 2014 #1
    Hi all,
    I am having a homework problem that is statement really bothers me and I think it might be a typo.
    It goes in the following:

    1. The problem statement, all variables and given/known data
    A is a short life unstable state and it is in equilibrium with B and C.
    A[itex]\Leftrightarrow[/itex]B
    A[itex]\Leftrightarrow[/itex]C

    The equilibrium rate constants are K[itex]_{AB}[/itex]and K[itex]_{AC}[/itex] with units [time]^-1.

    Question: what is the mean lifetime of the state A?


    Is this making sense?? Even for non-elementary reactions the equilibrium rate constants can only have the dimension of concentration. So I really don't know how the [time]^-1 came from.
     
  2. jcsd
  3. May 7, 2014 #2
    Your statement:"Even for non-elementary reactions the equilibrium rate constants can only have the dimension of concentration." is wrong. see here: http://en.wikipedia.org/wiki/Rate_constant#Units
    R ⇌ P ⟺ Keq = [P] ÷ [R] (at equilibrium) ⟺ Moles/L ÷ Moles/L ( or P/V ÷ P/V for gas phase...)
    as long as there are as many product molecules (product species) as reactants, you will have [P]ⁿ/[R]ⁿ which will result in (Moles/L ÷ Moles/L)ⁿ which is unitless.
    The rate of reaction of species X is, of course, d[X]/dt.
     
  4. May 7, 2014 #3
    If the kinetics of the reaction from A to B are described by

    [tex]\frac{dB}{dt}=-\frac{dA}{dt}=k_{AB}A[/tex]

    what you assess the units of the rate constant kAB to be?

    Chet
     
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