So we've talked about the endpoint in previous chapters when we discussed acid and base titrations. Remember, within acid-based titrations, the endpoint represented the range in which our indicator would change colors. This was used as an estimate to help us determine what the equivalence point would be for titration. Remember, at the equivalence point, we'd have equal moles of our acid and base at that point. Now, with endpoints dealing with redox titrations, we're going to say within a redox titration, we can utilize indicators and electrodes to determine the endpoint.
In this case, the endpoint, we're not really using it as an indicator to determine what the equivalence point is, rather we're using it to help us determine what our potential would be, our greatest jump in potential in terms of a redox titration. Now when it comes to redox indicators, we're going to say when we add a redox indicator to the analyte or what's called the titrant, the indicator will change colors based on the solution's potential. Now the way it works is we're going to have our titrant that we're adding. This titrant here will basically affect my solution's potential, oftentimes causing an increase in the potential of the solution. What this is going to do is the titrant will be interacting with the indicator.
In this case, the indicator can either be reduced or oxidized by the titrant that we're using. If we're using an oxidizing reagent, then that oxidizing reagent would oxidize my indicator, removing an electron from it. If we're dealing with a reducing agent, then that reducing agent would add an electron and therefore reduce my indicator. So we're going to say here the indicator will have a change in the oxidation state. Okay.
So let me just write out the word change in oxidation state. By having a change in its oxidation state, this will cause a color change within the indicator. And that color change signifies that we are at the endpoint in terms of my redox titration. Now, here we're going to see the reduction half-reaction for a redox indicator can be seen as we have the oxidized form of the indicator. Here we can add some number of electrons and could represent one to any other larger whole number which are added to my oxidized form of my indicator.
As a result of this, my indicator is now in its reduced form. Here, we can use this half-cell reduction reaction to create our Nernst equation. In this form, we'd say that the Nernst equation is the cell potential under non-standard conditions equals the cell potential under standard conditions minus 0.05916n volts divided by the number of electrons transferred. Here we're going to have times log of the indicator in its reduced form divided by the indicator in its oxidized form. Here, we've seen this type of ratios before when we dealt with the Henderson Hasselback equation.
Like the Henderson Hasselback equation, this ratio also has a range. It's best if they don't differ from one another by a magnitude of 10. So if we had the indicator itself, that's in its reduced form was 1, and let's say our oxidized format most can be 10. When we do the log of that, that give me negative one, or we could have log of 10 over 1, and that would give me 1. This range of negative one to positive one is what we deal with when we're discussing our indicator and how it's being affected by the titrant added.
Because of this minus one plus one range, we can recreate our Nernst equation in this form in which we have plus or minus 0.05916n volts. And again, it says by assuming that the indicator's color change from the oxidized state to the reduced state when the ratio changes from 0.1, 0.1 meaning when it's 1 over 10, to 10 where it's 10 over 1. That's how we're able to come up with this new range in which our indicator can operate. Now, we're going to say the indicator transition range should overlap the portion of the curve that has the sharpest increase in potential. Just like in acid-base titration, we were able to determine what the pH was at the equivalence point by looking at the highest increase in my pH.
Now we're looking at the highest increase in my potential. Here we can also use a grand plot to help us identify the endpoint in which we use the maximum value of the first derivative, which is a change in your charge, your potential divided by your change in volume. Here we can take a look at a basic titration curve in which we're dealing with 50 ml of 0.100 molar Fe2+. So this would be my analyte or titrant. And here we're adding to it cerium 4+.
Cerium 4+ is an example of an oxidizing agent. It represents my titrant. Here we're using 2 different indicators. One indicator that we're using is Diphenylaminesulfonic acid. Here in this colored region, we see that this is where the color change of my indicator takes place.
We also have here our second indicator. Here, its color change happens within this range here, and it coincides with a large increase in my potential. That's when we've reached basically, our equivalent volume, which causes a sharp increase in the potential for my reaction. Here, out of the 2 indicators, we'd say that the second one would be better in terms of determining the correct endpoint because it lies within the region where we have the greatest increase in our potential. Realize here that endpoints, whether they're dealing with acid-base indicators or dealing with redox titrations, they help us to determine what the endpoint of my titration reaction will be.
For acid-base indicators, we can correlate this with our equivalence point where the moles of acid equal moles of base. And for redox reactions, we can correlate this with the endpoint, which represents the state in which my indicator goes from its oxidized form to its reduced form in this case. So keep that in mind when we're looking at any type of titration curve in which we have to spot the endpoint. Look for the sharp increase in pH or potential, and then look to see where the color change happens for the indicator as an estimate of your endpoint.
