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Problem 63 Medium Difficulty

The first and second ionization constants of a diprotic acid $\mathrm{H}_{2} \mathrm{A}$ are $K_{\mathrm{a}_{1}}$ and $K_{\mathrm{a}_{2}}$ at a certain temperature. Under what conditions will $\left[\mathrm{A}^{2-}\right]=K_{\mathrm{a}_{2}} ?$

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Video Transcript

okay for this problem. We're going to talk about dissociation constants for die Protic assets and were given in the following information. We have a die product acid H two A and we're going to call its dissociation Constant. Gonna write it over here, Actually read it down here as a dissociation. Constant one. Um and this is going to so to dissociate into a hydrogen ion and h a minus all of these air Equus and then this substance to a J minus will become for step two. I worked acid, and that will further disassociate into this again. These are all a quiz we have Step one and step two for the dissociation of a die product. Gas it and we'll call the dissociation constant for this one k A. To our question is the question that we're trying to answer is when, Under what conditions? When will the concentration of the eight to minus ion be equal to K A. To that's our question. Let's go ahead And writer dissociation constant expressions for each of these K one is going to be equal to We'll have our hydrogen ion on the top for the numerator and our H A minus in the numerator and our age to a concentration in the denominator for a second reaction will have its K two again H plus on the top, and this time we'll have a to minus in the numerator, and the denominator will have a J minus. So when will this quantity be approximately equal to that quantity? Let's look, we want to know when this quantity will be equal to this quantity. So that will be true when my age plus and my age A's when this quantity is equal to one, or when these are both approximately equal to one. More importantly, when this quantity is one. So let's look up here for our first step. We know that these two values are equal to one another. So if k a one, if K a one is substantially larger, then k a. To what will happen. That means that there's going to be very little these air going to be next to nothing. They're going to become insignificant because if K 81 is very much larger than K A. To this is the reaction that's most of your I'm hydrogen is and you're A J. plus will be present up here. The A J minus isn't going to furthered associate. So when K A one is quite a bit greater much greater than K A to then que a two will be equal to a two minus. Thanks for listening.

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