# Acids and Bases – pKa, Equilibrium Constant and logs

The best place to start is at acids – and as we know acids can give up a proton to become deprotonated.

The acid will dissociate into a proton (H+) and cunjugate base (A-). Note that this is in equilibrium – there is a mixture of both sides of the equation present. The constant for this equilibium (the acid dissociation constant, Ka) tells us the position of the equilibrium. Ka is the concentration of the products over the concentration of the reagents:

therefore, for Hydrochloric Acid (HCl):

Simple, huh? What Ka tells us is a numeric value for the strength of an acid in solution. The larger the value, the smaller the extent of dissociation.

To illustrate, a strong acid like HCl has a Ka value of 1×10^7, which clearly shows a large bias towards products. Acetic acid on the other hand has a Ka value of 1.7×10^-5 – which strongly favours reagents.

### So, what’s all this ‘log’ stuff?

We use logs to convert long numbers into a user friendly scale – as the numbers we often get are on a huge scale (see HCl and Acetic Acid above). To do this we put p into our acid dissociation constant Ka.

Simply, p = – log, so the result is the logarithm of negative Ka.

Going back to HCl & Acetic Acid:

HCl Ka = 1×10^7; – log Ka = -7, therefore pKa = -7.

Acetic Acid Ka = 1.7×10^-5; – log Ka = -4.76, therefore pKa = 4.76.

So stronger acids have lower pKa‘s (or have higher Ka‘s).

We can easily convert back into Ka:

### pH and pKa

If the pH of a solution = the pKa, then the acid is in equilibrium – it is half dissociated. This scale goes either way – if pH is less than pKa then it’s mainly protonated acid; if pH is more than pKa it’s mainly deprotonated.

In the next post I’ll look at the equilibrium constant for bases & for acid base reactions.

## 2 thoughts on “Acids and Bases – pKa, Equilibrium Constant and logs”

1. Matt

Hey,
Just wanted to say thanks. I’m in my first semester of biochemistry, and it seems like I’ve forgotten everything from first year chemistry.
Very nice layout, you’re speaking my language.

Take care,
Matt

2. Wai Shun Mak

Just want to make a reminder that when pH = pKa, the acid is NOT at equilibrium. It simples denotes the fact of half dissociation.