What is the ratio of [conjugate base] to [conjugate acid] for ...

Question

What is the ratio of [conjugate base] to [conjugate acid] for each of Histidine's three ionizable groups at pH 7?

A) Amino group ratio: ________________

B) Carboxyl group ratio: ________________

C) R-group ratio: ________________

D) Use the ratios above to determine the average net charge of the ionizable groups & the entire His molecule.

1. Net charge of Amino groups: ____________

2. Net charge of Carboxyl groups: ____________

3. Net charge of R-groups: ____________

4. Net charge of His: ____________ (Hint: sum previous 3 charges).

Accepted Answer

Alright, So here's a four part practice problem broken up into parts A, B, C and part D down below. And so what you'll notice is the first three parts to our problem. Parts A, B and C are just asking us to perform pretty straightforward calculations using the Henderson Hustle back equation. And so I provided the Henderson Hasselbach equation up above in this box, And that's because it's asking us what is the ratio of the concentration of conjugate base to the concentration of conjugate acid for each of histamines. Three i invisible groups, specifically at a Ph of seven and so noticed that were given the structure of his sitting and were also given The P K is for each of his sittings. Three i invisible groups. And so what you'll notice is Part is asking us for the ratio of the amino. Group B is asking us for the car boxing group ratio and sees asking us for the our group ratio and for all three of these calculations, notice that the pH of the solution is the same. It's a ph of seven, and so notice that the Ph is going to be the same for all of the calculations. And really the only thing that's gonna change is the P K. A value for the calculations on That's because each group has its own PK and so we can perform the calculation for the first group here. The Amino Group and the Amino Group has shown to have a PKF nine so we could go ahead and plug that PK a values n So p k A value is nine for the amino group. And so we're gonna be solving for this ratio of the concentration of kinda get based to the concentration to kind of get asked. And so we can subtract nine from both sides of the equation. And what we end up getting is negative. Two on the left side of the equation is equal to the log of the concentration of conjugate base over the concentration of conjugate acid. And so again, we're trying to isolate for this ratio. So we need to get rid of this log, and the way that we get rid of the log is to take the anti log, and if we take the anti log of the left right side of the equation, we have to take the analog of the left side of the equation. And the analog of a number is literally just 10 raised to the power of the same exact number. So 10 raised to the negative, too. And that is going to be equal to the concentration of conjugate base over the concentration of conjugate acid. And so 10 rates of the negative two is the same. Thing is saying 1/10 squared, which is the same thing as saying one over 100. And so this is essentially the ratio here that we were looking for and so we could go ahead and put up above that. The amino group ratio is going to be one over 100. And so we know that the amino group eyes gonna have a conjugate base, which is the top number of an N H two. That's the conjugate base of the amino group. It's deep protein aided, and the conjugate acid form of the amino group is gonna be an NH three plus that is protein ated. And so really, what this 1 to 100 ratio really means is that for every one molecule of NH two there are 100 molecules of NH three plus. And so now that we're finished with this ratio here for the immuno group, we can move on to part B and do the same for the car boxing group. And so, for the car boxes were given a PK of two so we could go ahead and plug that into our equation here, so literally just swapping out the PK. So PKF too. And so we're just gonna perform the same calculation. So we're going to subtract two from both sides of the equation. So what, we end up getting us five on the left is equal to the log of the concentration of conjugate base over the concentration of conjugate acid. And of course, we're going to be isolating for this ratio here. So we need to take, uh, the anti log to get rid of this log here. And the anti log of both sides of the equation is what we need to do. So the anti log of five is just gonna be 10 raised to the fifth raised to the same power here, and that's gonna be equal to the law. Uh, the concentration of congregate based over the concentration of conjugal acid. All right, so 10 to the 5th 5th is the same thing as just 1000. And this is a ratio of 100,000 over one. So that is the ratio of concentration of content based over the concentration of conduct acid that we're looking for. So we could go ahead and plug that end up above. Over here, 100,000. It's a one. And so really, what this ratio means is we know that the car boxer group has a conjugate base form that is going to be the car Boxley. An eye on it is deep ruminated. So it's gonna be C O minus. And the conjugate acid form of the car Boxer group is gonna be pro donated. It's gonna be C 00 H with a neutral charge. And so this ratio of 100,001 just means that for every 100,000 molecules of conjugate base form of the car boxer group, there's gonna be one molecule of conjugate acid form of the car Boxer group. And so now that we've calculated the ratio for the car boxer group, we could do the same for the our group ratio down below and again, all we're gonna be doing is swapping out the P K. And so the PK or the PKR for the our group is six. So we could go and plug that in here. And so we're gonna do the same calculation. Subtract six from both sides of the equation. So what we end up getting is one is equal to the log of the concentration of conjugate base over the concentration of conjugate acid. And again, we're gonna take the anti log of both sides of the equation. So what we end up getting is 10 raised. The one is equal to the concentration of conjugate base over the concentration of conjugate acid. And so 10 races. One is the same thing as just 10 and this is a ratio of just 10 toe one. And so this is the our group ratio that we're looking for. It's literally just 10 toe one. And so if we take a look at the our group of history and over here, notice that the group that's ionized is really this nitrogen atom that's here, and so the protein ated the conjugate acid form which is on the bottom here, eyes really just going to be an N h with a positive charge on it. And then the deep protein ated form of this nitrogen atom is going to just be a nitrogen, and it's going to be neutral. And so this ratio here means for every nitrogen atoms in the our group of history, there's going to be one positively charged conjugate acid form of thea, our group. And so, essentially, we have finished with Parts A, B and C. So now we can finally move on to Part D and Part D Down below wants us to use the same exact ratios. So it wants us to use the ratios that we just calculated above to determine the average net charges of the ionized herbal groups and the entire history molecule at Ph. Seven. And so notice that the first one that we're gonna calculate here is the net charge of the amino group. And so if we go back up to our ratio up above for the amino group, notice that it was one toe 100 ratio and so because we're looking to calculate the net charges here. We're looking to calculate the average net charges. Uh, we're on Lee interested in the groups that are gonna have a charge in them. And so notice for the amino group. It's the conjugate acid that has a charge on it. And so what that means is we have 100 charges. This ratio means that we have 100. Uh, can you get acid forms of the amino group for every one of the, uh um, can you get base form? And so there is a total of 101 molecules. We have 100 of this and one of this, and so we have a total of 101 so down below. Here we can say we have 101 total molecules, and of those total 100 of them. So 100 positive charges. And so this is really the ratio that we're looking for here. And so if you take your calculator and do 100 divided by you'll get a ratio of about 0.9901 And so this rounds off to about 0.99 And this is a positive number, which means that the net charge of our amino group is gonna be a positive 0.99 And so that is the answer for this first part over here. So now we could do the same thing for the net charge of the car boxer groups. So going up to the ratio for the car Boxer group noticed that it was 100,000 to 1. But this time it's actually the conjugate base, which is the top number here. It's the conjugate base that has a charge on it. And remember, because we're determining the average that charge were only interested in the ones that have a charge in it. So out of the total amount of molecules so 100,000 here and one down below, that's 100,000 and one. There are 100,000 charges so we could go ahead and indicate that down below. So we can say out of 1001 total molecules, we have 100,000 of them that are going to have a negative charge. And so essentially what we need to do is take our calculators and do negative 100,000 divided by 100,000 and one, and that comes out to an answer of about negative 0.9999 which, of course, rounds off to about negative one. And so what this means is that our net charge on our car boxing groups is gonna be negative one. All right, so now we need to do it for the our groups over here and essentially our our group ratio is 10 toe one. And this time it's the conjugate acid on the bottom that has a charge on it. And so, essentially out of 11 total molecules, so 10 on of the conjugate acid. I'm sorry, 10 of the conjugate base and one of the country acid 11 total. So out of 11 total, we can write that down here. So, out of 11 total we have on Lee, one that's going to have a charge on it, So we're gonna have one positive charge. And so if you take your calculators and you do one divided by 11 you'll get an answer of 0.909 which rounds off to about 0. And so this is a positive number here. So, uh, this is gonna be a positive 0.9 charge on the our group. And so now that we've finished with the first three parts, we could move on to the net charge of the entire history in molecule here, and it gives us this hint to just some the previous three charges. And so, essentially, all we need to do is take the, uh, charge here, the average net charge on the amino group. So 0.99 and essentially, we can subtract one here for the net charge of the car boxing group, so minus 1.0 and then we can add on the charge for the our group here, which is plus 0. 0.9 And so we could go ahead and add all of these numbers up together, type it in your calculator and you'll get an answer of 0.8 And this is a positive number. So that means that we have a positive 0.8 charge on the histamine molecule. And so, essentially, what this means is that at a ph of seven, notice that our history in molecule does have a positive charge on it, but it's a really small, positive charge. It's on Lee, a positive 0.8 charge. And really, the reason for this is you'll notice that the, uh, Amino the Amino group has a 0.99 charge. So that's about ah, positive one charge. And the car boxer group has a negative one charge. So that, uh, is negative one. And so these two charges here, the 0.99 and negative one, they pretty much cancel each other out. And the our group of history at a Ph of seven on Lee has a really small, positive charge. And so that's why overall history in has such a small, positive charge at neutral pH. So that's something interesting to keep in mind about his sitting at neutral pH that it has, ah, fraction of a charge. And so that concludes this long problem. And I'll see you guys in our next video

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