So fractional compositions are just a way of determining the amount of acid to base at a given or specific pH. As our pH decreases, our solution becomes more acidic because the amount of acid present is increasing. As we increase pH, it becomes more basic because we're increasing the amount of conjugate base. Now remember, with weak acids, we have the formation of an equilibrium because weak acids are weak electrolytes. So they don't completely ionize into their products. Here, our weak acid, which is just a simple generic formula, partially ionizes to form H^{+}ion and A^{-} as our conjugate base.

Setting up the equilibrium expression gives us the acid dissociation constant Ka equals the ions as products on top divided by the initial concentration of my weak acid. Now the formal concentration of my solution equals the concentration of my weak acid plus the concentration of my conjugate base. Now when we talk about the fraction of acid molecules present, we use the variable α to represent HA here. If we take a look here, what this chart is showing me is at a pH, the lowest possible pH, the composition of my solution will be 100% in the acid form, and 0% of the basic form.

As the pH begins to increase as we move from left to right, we're going to have an increase in the amount of conjugate base and a decrease in the amount of weak acid. Here, they intersect at this point here. At that pH, we have 50% of the weak acid form and 50% of the conjugate base form. This is true when the pH is equal to my pKa. So when those two equal each other, it's because the amount of conjugate base and weak acid are equal in amount.

Remember this coincides with the whole Henderson-Hasselbalch equation, which is pH = pKa + log(conjugate baseweak acid). When they're both equal to each other, this all becomes equal to 1. The log of 1 is simply equal to 0, and that's why pH = pKa.

So when pH equals pKa, the amount of weak acid is equal to the amount of its conjugate base, and if we continue past this pH point, we're going to continually have a drop in my weak acid form and a steady rise in the amount of my conjugate base form, until we get to a pH where the weak acid form is basically near 0 and the conjugate base is near 100%.

Now here we'd say that the concentration of my weak acid is equal to the concentration of H^{+} times the formal concentration of my solution divided by H^{+}+Ka. Here, if we want to find out the fraction that exists in the acid form, that just simply gets broken down into the concentration of H^{+} divided by the concentration of H^{+}+Ka, so that there represents the fraction in the acid form and here the fraction in the conjugate base form or A^{-} is represented by α_{a-}. Here, that would just be equal to Ka / (H^{+}+Ka).

So these are the two equations we can utilize in order to figure out the fraction of either my conjugate acid or my weak acid form, and remember together both of them would equal 1, and if you multiply that by 100, it would be 100%. Okay? So if you know one, you know what the other one is because together they represent 100% of all possible molecules and ions present within my solution at any given pH. Now that you see it in terms of a weak monoprotic acid, click on the next video to look at it in terms of a diprotic acid.