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

[ggyyzdq]

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:

Homework Statement

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.

 

[abitslow]

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.

 

[Chestermiller]

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:

Homework Statement

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.

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 k_AB to be?

Chet