Instead of the titration of 55 mills of 0.120 molar hydrocyanic acid with 0.160 molar lithium hydroxide, I'll give you the volume needed to reach the half equivalence point. All right, so let's look at the following steps that we can utilize to help us find this answer.
So step one, we determine the volume of the titrant to reach the equivalence point. All right, so who's our titrate? We're not given the volume of looking hydroxide. That's because it's behaving as a titrant here. We'd say that M acid times V acid equals M base times V base. When it comes to asset based hydration, there are formulas that you can keep in mind. So our equivalent volume can be calculated using this equation. Acid times V acid equals M base times V base.
Now before the equivalence point, we have a buffer region that can exist and because of that we utilize the Henderson Hasselbeck equation. Here I'm just showing the variant where we have PKA involved. pH=pKa+log(conjugate baseweak acid) and then our half equivalence point is where the amount of weak acid and conjugate base are equal to one another, meaning that this would be equal to 1 and so we drop out because log(1)=0. The Henderson Hasselbeck equation would simplify to just pH=pKa, and if we were to isolate Ka, it would be restructured as Ka=10-pH.
Now let's go back. We're using the equivalence volume formula so that we can figure out the volume of the titrin to reach the equivalence point. So here we're going to say we have 0.120 molar of our acid, 55 MLS of our acid. Our base is 0.160 molar and we don't know the volume of our base. Divide both sides by 0.160 molar so cancels cancels volume of our base. To get to the equivalence point would be 41.25 milliliters.
Step 2 Utilize the correct formula based on the region of the titration curve. Utilize this step only if necessary. All right, so we just determined the volume to get to the equivalence point. Well, the half equivalence point would just mean we need half of that volume. So all we do here is we divide this by two and that will give you my half equivalence volume. What y'all just put as B sub half. So dividing 41.25 MLS by two gives me 20.625 milliliters. So this would represent the volume to get to the half equivalence point for this particular example question.