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

1. May 7, 2014

### 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:

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$\Leftrightarrow$B
A$\Leftrightarrow$C

The equilibrium rate constants are K$_{AB}$and K$_{AC}$ 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. May 7, 2014

### 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.

3. May 7, 2014

### Staff: Mentor

If the kinetics of the reaction from A to B are described by

$$\frac{dB}{dt}=-\frac{dA}{dt}=k_{AB}A$$

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

Chet