Strong/Weak Titration Graph

 

Let's look at how the pH changes during a weak/strong titration from a graphical perspective. (A strong titration graph is found here) 

We will be looking at this for the problem here: 

50.00 mL of 2.00 M HA (an imaginary acid with \(K_a = 2.56x10^{-5}\) ) are titrated with 1.00M XOH (an imaginary base). What will the pH be before any base is added and after additions of 1.00 mL, 10.00 mL, 50.00 mL, 98.00 mL, 100.00 mL, and 120.00 mL of the base?

We did all of the calculations here, so if you haven't looked through those yet, it would be worth checking out.

If we graph the points from that problem, we get this:

Adding in a few more points to "smooth" things out a bit, we get this:

In simplest terms, at the beginning, when we have excess acid, the solution is acidic (with a low pH). When we to equivalence, the pH becomes 7. Once we pass the equivalence point, the solution contains excess base and the pH is high. The equivalence point is the middle of the steep vertical part of the graph. Stated differently, the equivalence point is the point in the graph where the slope is the most vertical.

We can find that point graphically, by making a graph of the slope vs. volume of base added. For those of you with some level of higher math, this is simply the derivative of the previous graph.

If it helps to visualize what this graph is showing, here are the two graphs on the same axes:

Strong graphs vs. weak graphs

It's worth pointing out the differences between this graph (for a weak titration) and the graph of a strong titration. Here they are side by side:

The first difference to note is that in the strong titration, the pH at the equivalence point is 7, while in the weak titration it is above 7. (For the record, if we had used a weak base with a strong acid, the pH at equivalence would have been below 7, so the key issue here is that it is NOT 7.)

Secondly, the pH starts much lower in the strong titration than it does in the weak titration. This, of course, depends to some extent on the concentration of the acids, but in this comparison, both acids were of equal concentration.

It's also important to note that in the strong titration graph, both the beginning and end of the titration graph are nearly flat, while in the weak titration graph, the beginning of the graph is a more gradual slope. This gently sloped area is the buffer region.