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One of the most common antibiotics is penicillin G (benzylpenicillinic acid), which has the structure shown next:where HP denotes the parent acid and $P$ - the conjugate base. Penicillin G is produced by growing molds in fermentation tanks at $25^{\circ} \mathrm{C}$ and a pH range of 4.5 to $5.0 .$ The crude form of this antibiotic is obtained by extracting the fermentation broth with an organic solvent in which the acid is soluble.(a) Identify the acidic hydrogen atom. (b) In one stage of purification, the organic extract of the crude penicillin G is treated with a buffer solution at $\mathrm{pH}=6.50 .$ What is the ratio of the conjugate base of penicillin G to the acid at this pH? Would you expect the conjugate base to be more soluble in water than the acid? (c) Penicillin G is not suitable for oral administration, but the sodium salt (NaP) is because it is soluble. Calculate the $\mathrm{pH}$ of a $0.12 \mathrm{M}$ NaP solution formed when a tablet containing the salt is dissolved in a glass of water.

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Chemistry 102

Chapter 16

Acid-Base Equilibria and Solubility Equilibria

Acid-Base Equilibria

Aqueous Equilibria

Rice University

University of Maryland - University College

Brown University

University of Toronto

Lectures

00:41

In chemistry, an ion is an atom or molecule that has a non-zero net electric charge. The name was coined by John Dalton for ions in 1808, and later expanded to include molecules in 1834.

24:14

In chemistry, a buffer is a solution that resists changes in pH. Buffers are used to maintain a stable pH in a solution. Buffers are solutions of a weak acid and its conjugate base or a weak base and its conjugate acid, usually in the form of a salt of the conjugate base or acid. Buffers have the property that a small change in the amount of strong acid or strong base added to them results in a much larger change in pH. The resistance of a buffer solution to pH change is due to the fact that the process of adding acid or base to the solution is slow compared to the rate at which the pH changes. In addition to this buffering action, the inclusion of the conjugate base or acid also slows the process of pH change by the mechanism of the Henderson–Hasselbalch equation. Buffers are most commonly found in aqueous solutions.

01:37

One of the most common a…

01:13

1. Penicillin-Streptomyci…

02:21

Penicillin is hydrolyzed a…

Hello. So today we're going to be looking at this molecule right here, which is penicillin G. So let's start off first by identifying which of these protons is acidic because penicillin G is an acid. So which one of these protons would be acidic while hopefully you'll notice that this section right here is a car broke Cilic acid. So essentially, what happens in here is there to lone pairs on this oxygen, and it can resonate, which causes there to be a she sort of ah less electron density on this oxygen. So pull the electrons from hydrogen and that that makes this hydrogen very easy to take off because it's Kontic, it base will be residents stabilized. So this proton right here will be acidic. Now let's take a look at say we have we've put it in a buffer solution. So the pH is 6.5. Well, what will the ratio of the country get based to the acid B? Well, we know that the K A is 1.64 times 10 to the negative three, so that makes so let's find its peak A and the P. K K is the negative log of the K A. So let's take the negative log and we will see that the peak PK is 2.7 eight five. So now to find the ratio, let's just use the Henderson Hustle Buck equation. Because we have the pH we have pick A and at the Henderson Hasselbach equation gives the ratio of the con trick it base to, uh, acid. So let's plug in and see what it should be. So we've got some 0.5 here and 2.785 here. So now to find the ratio, we just take 10 to the 3.715 power, and we will see that is 5000 190. So there is a lot more conjugated base than acid. And does that make sense? What it this Be more soluble with the country? Get based, be more soluble in water, and the answer is yes. But con trick it base is residents stabilized. If you'll notice we would have, and one lone pair could just go there, and we could have residents between these two and remember that water really likes water. Really likes thing charged things it likes I owns likes polar things, and so if there's a negative charge on this compound, would make probably making more soluble. So now let's take a look at assault that contains the conjure. Get base. We're going to have 0.12 polarity of sodium with this penicillin conjugated base. So now we'll with the Ph. B. So let's draw. Let's write really quickly the re equal a broom. Here it would reform it's consequent acid and hydroxide. So how do we find the PK? The K B? Well, it's K W, divided by the K A. So it's 10 to the negative 14 divided by 1.64 times tone to the negative three solely. See, that would be six point 10 times 10 to the negative 12. So we start off. Let's write a nice table with 0.1 to malaria t off this country of the conjugated base. Then we're going to be reforming the acid. But right now there's zero and at the hydroxide in water, while the Constitution of my dark side is tend to the negative seven. So some ex moles of this, um, con jacket base or going to react to reform the acid and next Mel's and X moles of hydroxide. Now I've noticed that this number is very small, so we can just approximate the Taliban concentration is 0.12 and then we will have X in 10 to the negative seven plus ax So six point 10 times 10 to the negative 12 sequel to X times 10 to the negative seven plus X divided by 0.12 So let's see. So we're going to have to use the quadratic formula to figure out what exactly would go here, what X would be so This is S O A is one b is 10 to the negative seven and C is equal to 7.32 times 10 to the negative 13. So let's take a look. So we're going tohave negative b And since this negative and we want X to be positive, we need toe ad. We're gonna check the square root of B squared minus four times a him see divided by two a. So let's take a look at this. We've got negative 10 to the negative seven plus got 10 to the negative 14 and we're going to add 2.9 three times, 10 to the negative 12 divided by two. So let's add 2.93 temps into the negative 12 with tend to the negative 14. We will see that is 2.94 times 10 to the negative 12. Let's take the square root of that and we will get negative 10 in it. Negative seven plus 1.7 one times 10 to the negative six divided by two. So now we just add these together Well, we take 1.71 time stunted in a good six. Subtract 10 to the negative seven and then divide that by two and we will see that we will get My ex is equal to eight point 07 times 10 to the negative seven. That's a concentration of hydroxide. Well, the concentration of hydroxide would be this plus 10 to the negative seven. So the concentration of hydroxide would be nine 0.7 times 10 to the negative seven. So let's take the negative log of that which will give us the p. O. H. So the peel h take the negative log P, which would be 6.4 The pH is 14 minus the pillage, so the Ph would be 7.9 six.

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