## Relationship between K and k

$K = \frac{k_{forward}}{k_{reverse}}$

nelms6678
Posts: 53
Joined: Fri Sep 29, 2017 7:07 am

### Relationship between K and k

I understand the formula, but what is a more conceptual explanation between big K and little k?

Jonathan Tangonan 1E
Posts: 50
Joined: Sat Jul 22, 2017 3:01 am

### Re: Relationship between K and k

If we were to look at a reaction that reaches equilibrium like
A+B<=>C+D
then the equilibrium constant would be the concentration of the products over the reactants where:
K= [C][D]/[A][B]
If we were to write the forward and reverse rate laws for this reaction, they would be:
A+B->C+D where the Rate= k[A][b]
C+D->A+B where the Rate=k'[C][D]

Since at equilibrium these rates are equal,

k[A][B]=k'[C][D] which can be rewritten to be [C][D]/[A][B]=k/k'

So therefore we can write K=k/k'

Sabrina Fardeheb 2B
Posts: 51
Joined: Sat Jul 22, 2017 3:00 am
Been upvoted: 1 time

### Re: Relationship between K and k

Big K represents the equilbrium constant of an equation.

Little k represents the rate constant of an equation.

When you derive the equations for each, they contain concentrations of the same elements. Therefore, with substitution, you can conclude that the ratio of the forward and reverse rate constants is equal to the equilibrium constant.