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What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H,A, HA - A2-) at pH 6.162 The acid dissociation constant values for piperazine ar...

Question

What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H,A, HA - A2-) at pH 6.162 The acid dissociation constant values for piperazine are Kal = 4.65 X 10 and Ka2 = 1.86 x 10-10,QHAQHA

What fraction of piperazine (perhydro-1,4-diazine) is in each of its three forms (H,A, HA - A2-) at pH 6.162 The acid dissociation constant values for piperazine are Kal = 4.65 X 10 and Ka2 = 1.86 x 10-10, QHA QHA



Answers

Calculate the percentages of dissociated and undissociated forms present in the following solutions: (a) $0.0010 \mathrm{M}$ glycolic acid $\left(\mathrm{HOCH}_{2} \mathrm{CO}_{2} \mathrm{H} ; \mathrm{p} K_{\mathrm{a}}=3.83\right)$ at $\mathrm{pH}=4.50$ (b) $0.0020 \mathrm{M}$ propanoic acid $\left(\mathrm{p} K_{\mathrm{a}}=4.87\right)$ at $\mathrm{pH}=5.30$

Goes to improve in 1 96 of Chapter 14. So Naked solution. Anything to make sure 140.5 Moeller H c o h of que es of 1.77 times 10 to make it 1/4 and and 0.150 Mueller C H three c two c o H h k of 1.34 times sending a five actually the pH of this solution. Because both has a conference strength EA H plus consecration. Both assets must be considered. It's okay, so we're gonna put everything in our ice charts. A shirt. So now let's start with the first contribution. K A. Is equal to age plus times a minus over h A. Hey, now X squared over. You're a point 05 is here. Zero. Let's assume there's no so there's less than 5% ionization, and then we're gonna equal r K A value, which is going to be on 0.77 times 10 to the negative forth. So X squared is going to be Thank you. Meet shrink this a bit 1.77 10 to the negative as they retest the wrong one. A 0.85 times 10 to the sixth, 60 X is going to be 2.97 times 10 to the negative, 1/3. And now we're going to see what a percent ionization is. 2.97 times 10 to the negative. Third over 0.5 It kinds 100 so there's gonna be 5.94% which is great than 5% organization. So we do have to take things to do. We do it. Take a association into account. That was plug everything in. So X squared is going to be equal. A cool 2.9 it 0.85 times 10 to the negative sixth, minus 1.77 times. And to the negative fourth ex squeeze me X squared plus 1.77 I was 10 to the negative. Forth X, minus eight 0.85 times 10 to the negative. Six is going to be equal zero. They're gonna plug ins or a quadratic equation. X is going to be equal to negative 1.77 times 10 to the negative. Forth lesser minus radical. One 0.77 times 10 to the negative for it fourth squared minus four times a, which is one and then minus eight 0.85 times 10 to the negative six over to a That's what I mean X is going to be honey, we're gonna take everything in. That means our X is going to be five point 0.7 eight times 10 to the negative third, which is going That means our first Proton concentration, and that's going to be that's going to be equal to this. All right, Next we're gonna look at the other one. So 1.5 zero 0.150 ex NRK is gonna be 1.34 times 10 to the negative fifth. And let's start out by assuming that there's less than 5% ionization X square and is going to equal 2.0, one times 10 to the negative six. It means X is going to be one point for two times 10 to nick 1/3 and we're gonna see if this less than 5% so one point for two times sent in negative Third over 0.150 times. 100 that's gonna equal you're a 0.95% so we can see that there's less than 5% ionization. So this could be our second and H plus. So we're gonna add these together. Just erase this during said it's gonna be seven point two times 10 to the negative third. So then we're gonna find Ph was gonna be the negative log of this concentration. There it is. That's gonna be too 0.14

So in This problem we've got going on is that we have grassed if they got the pH of two different salts with two different concentrations. And so these are two entirely separate problems, but they're done this similar way. And so let's focus in on the search one where we have C H three and H three c out. And this is assault of ch three and H three plus and seal minds. And so you should know by now that since still nice is a country base of HCL, which is one of strongest assets we have, C O minus is basically neutral I own. So this doesn't really play a role in what we're working with. Your figure out the pH. On the other hand, C h three n actually plus, is the conjugal asset of ch three and age to which is metal of me. And this is something that has a K B. That you could look up. In fact, I did look it up and we get 4.4 times 10 to the negative fourth. And so since we're asked to figure out basically what is the acidity of 0.1 Moeller ch three an instinct. Plus, we need to figure out k of this of this value, and this is really easy to do, since we have the K B of its cars, good base and so remember that que oven acid times K B of its contra bass use tense interview to 14th. We have that KB of methyl amine 4.4 times 10 to the negative fourth. And so if you plug this into a calculator, you'll find that K equals two point 272 time sense of negative 11th. And so the next step is we need to, uh, plug this into a mass action expression. So if you do a nice table, you'll and this is something that, after doing many times you'll recognize there's always gonna be the case of an acid acting water. You'll have that the ice table equals X squared over the initial concentration, which we were told was 0.1 Moeller minus X. But we'll ignore acts because it's going to be much smaller than 0.1 Now. If you don't understand where this is coming from, go ahead and do a nice table for the reaction of at N. H. of C H three, NH three plus and water becoming methyl amine And, um hi, Joanie, Um And then prove to yourself that this is the result you'll get. But either way, way can now solve for X and X is going to be, um, equal to 1.5 times 10 to the negative six. And that because this was an acid association is equal to our concentration HDL plus, and that makes this very convenient. We can just go directly from HBO plus into solving for the pH. Because the pH is by definition, the negative log of the concentration of HBO. Plus will plug that in here, and we put this in a calculator. You get the answer of five. Quite a to straight now. He approached the second problem. The second problem had, um, let's take a look. We had 0.5 Moeller sodium cyanide. And so this is assault of N A plus and C N minus and a plus is a neutral I on. So this is not really playing a role in what will look in here, but CN minus is the conjugal base of H. C N, which is a weak acid and I mean CN minus is going to be somewhat of a stronger base. They will have some non negligible basis t to it. And so we can look up the k of h c n. And that will be equal to 6.2 time sensitive tough partly. And since we have k A of h c n, we can figure out the baby of its country based the same way we did before that, que times k b he goes tense, the negative 14th and so plugging this in I'll do, uh, do the calculator work for you. K B is equal to 1.61 time stance and get it fit. Great. So now this is the equilibrium constant that is going to govern this reaction CN minus and water being an equilibrium with O h minus and H c n. And so, if you didn't I stable for this, you would fine. That baby is equal to x square over the initial concentration with this 0.5 minus X. Um, And like I said earlier, if you're not convinced about this, you go ahead, do a nice table and convince yourself that this is what it's always going to end up. But either way, this X value here is gonna be much smaller than 0.5 So we ignore it. We have K B from the other side over the right. That's a 1.61 time sensitive your fifth. Now we can solve for X in X is going to be 8.98 times 10 to the negative. Fourth more. And since O. H minus is our product not Hi, Joanie Mound. This ax is equal to the concentration of O. H minus. And unlike before, we can't go directly to finding the pH. We first need to find the concentration of extreme Plus. The good thing is, there's a really good relationship between the concentration of O H minus and X three plus, which is that their product is equal to 10. So negative 14th. This is, uh, ah product. This is a result of the organization of water and so plugging in that value that we got 8.98 Some sense a negative Fourth we can find the concentration of HBO plus is equal to 1.1 ones have sense a negative 11th and from there remember the by definition, as he did earlier. Ph is negative. Log the concentration of hi, Joanie. Um, and that gives us 10.95

Let me write the reaction. It's too S. 03. I was walking. Yeah Product will be h. s. 0. 3 negative Plus H. 30. Positive equilibrium constant will be H. s. 0. 3 concentration. H. 30. Positive concentration Reacted concentration H. two so three. No we are provided with the value of K. A. Already. So To be 1.7 10 days super -2 equals concentration of product is unknown. So X. Multiplied with eggs and For reacting 0.45 -X. So overall it can be written else. X Square plus 1.7 10 days to part -2 x -7.65 10 raised to 4 -3 is equal to zero solving this. The value of X turns out to be 7.9. 10 days to power negative too. This is the concentration of H. This is the concentration of H. 30. Positive. Mhm. No we need to calculate the P. H. Is equal to negative log of H. 30. Positive concentration equals negative log of 7.9. 10 days. Super negative too. Which is equal to 1.10

Here we have to calculate percent organization in a 0.4 to five Mueller solution of. For me, cassie. Now let's write the organization equation eight c. W. eight. Yeah. Sweet water. What do you says A C. W minor sound and high dona higher. Now let's make the ice double Initial concentration. 0.04-5 mortar, gino, gino change concentration minus eggs plus X plus eggs, equilibrium concentration of the acid 0.4 to five minus eggs, hair, eggs and eggs. Now we'll write the expression for and see dissociation constant K. It is concentration of for me down times confrontational hydro nia martin at equilibrium and concentration equilibrium concentration of the acid. Yeah. Now the K. A. For farming as it is 1.8 times 10 to the power negative four. Here is C. W minus is eggs concentration of Padania man. Also X. O. X square Divided by 0.04: 5 -1. There are four X square Is equal to 1.8 times 10 to the 4 -4 times 0.04-5 -8 times 1.8 times 10 to the 4 -4. Therefore X square plus 0.18 X minus 7.65 times 10 to the poor negative six is equal to zero. So this quality key question if I compare with X square plus B. X Plus C. is equal to zero. Here, a. is one B E. S 0.18 and C. Is negative 7.65 times 10 to the power negative six. And they go a route X is minus B plus minus route over be square minus four A. C by two. If you place the value for E b n C, we get the value for X is 0.267733 or -0.00285733. And It means concentration of Macedonia Mayan, which will be 0.0027 moller. And we are ignoring the negative value. So percent organization 1%. Ionization will be 0.27 divided by original condition zero concentration 04 to five times 100 the hello 4% organization. He's 6.4%.


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