How to calculate pH-dependent proton binding curves?

[hannoit]

Hello,

I have a (simple) question concerning proton binding behaviour. Maybe someone can help me to understand the topic.

Let us regard one type of molecule in solution with only one binding site and let f(pH) describe the percentage of protonated molecules of all molecules.
Then for low pH
f=1 (1)
and for high pH
f=0. (2)

According to Onufriev et al. "A novel view of pH Titration ..." (2001) the average protonation in equilibrium is described by f(x)=a*x/(a*x+1).
At first sight this seems to fullfil (1) and (2). But actually in this paper the variable x is not the pH-Value but the proton activity.

Am I right that a ligand activity is in [0,1]?
But if so, then I don't understand how this equation gives a titration curve?

Thanks a lot and kind regards,

Hannoit

 

[BigJDubs]

.Yes, you are correct that the ligand activity is in a range of 0 to 1. The equation you mentioned is a way of modeling the titration curve. The equation takes into account the proton activity as one of the factors that determine the titration curve. The other factors include the pKa and the ionization constant of the molecule. The equation can be used to calculate the protonation state of the molecule at different values of pH. This allows for you to plot the titration curve which shows the relationship between the protonation state of the molecule and the pH.