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(a) Calculate the percent ionization of a $0.20 M$ solution of the monoprotic acetylsalicylic acid (aspirin) for which $K_{\mathrm{a}}=3.0 \times 10^{-4} .$ (b) The pH of gastric juice in the stomach of a certain individual is 1.00. After a few aspirin tablets have been swallowed, the concentration of acetylsalicylic acid in the stomach is $0.20 M .$ Calculate the percent ionization of the acid under these conditions. What effect does the nonionized acid have on the membranes lining the stomach? (Hint: See the Chemistry in Action essay on p. 706.)

a. $3.9 \%$b. $0.3 \%$

Chemistry 102

Chapter 15

Acids and Bases

Liquids

Carleton College

University of Central Florida

Rice University

University of Kentucky

Lectures

03:07

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, a liquid is one of the four fundamental states of matter (the others being solid, gas and plasma). A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Water is, by far, the most common liquid on Earth. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena.

04:38

A liquid is a state of matter in which a substance changes its shape easily and takes the form of its container, and in which the substance retains a constant volume independent of pressure. As a result of this, a liquid does not maintain a definite shape, and its volume is variable. The characteristic properties of a liquid are surface tension, viscosity, and capillarity. The liquid state has a definite volume, but it also has a definite surface. The volume is uniform throughout the whole of the liquid. Solids have a fixed shape and a definite volume, but they do not have a definite surface. The volume of a solid does not vary, but the volume of a liquid may vary.

05:47

(a) Calculate the percent …

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Calculate the percent ioni…

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A typical aspirin tablet c…

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A handbook lists the follo…

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Find the $\mathrm{pH}$ and…

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Find the pH and percent io…

02:25

06:37

okay for this problem. We start off with 0.2 moles per liter off acetyl salicylic acid, commonly known as aspirin. Um, we need to find the percent ionization. And let's just make sure remember percent ionization. You need the proton concentration after equilibrium, his reach. And then you divide that by the aspirin concentration, the initial aspirin concentration, which is what we have 0.2 molars, times 100. So that is what we have to find the proton concentration at equilibrium. So that's what's gonna take a little time to again. And to find out we used the acid ionization constant, which was given to us in the question. And it's equal to the proton concentration at equilibrium and ion concentration divided by the acid. In this case, the aspirin concentration. Um, so three point all times 10 to the negative for is what we know is the aspirin ionization constant. We can represent the proton concentration as well as the Anna and concentration as X, because they're both the same. So x times X can be written is X squared. Um, the aspirin concentration equilibrium will be the point to minus e X, but it's not. The X isn't gonna be a very big numbers. We can just approximate that it it should be closed 0.2, which will make the problem easier. So rewrite it as X squared equal to six point all times 10 to the negative five. And we got that from multiplying 0.2 times the three times 10 to the negative for So continue on by taking the square root both sides so that you get a value for X, which is 7.7 times 10 to the negative three. And that that equals acts. Which means that also equals the proton concentration at equilibrium, which is what we wanted to get. The percent ionization Z and I were ready to solve letter a so percent ionization we complied that number in now some 0.7 times in the negative three divided by the original aspirin concentration times 100 and you should end up with is sorry, 3.9 percent. That's rounded to two significant figures. Okay, so that's the how much it lionizes the percent. So three, about four out of every 100 we lionize Tom, so let her be. Gives us a slightly different scenario. We still have the 0.2 Mueller aspirin to begin with, but we're in this stomach where there's already a pH of one. So what we're gonna have to do is we're gonna have ah, different initial, um, Proton concentration. Where in letter A. The initial was just zero, but so we'll have to come for our pH into proton concentration. So you just go 10 to the negative pH, which is one which would give you 0.1. So that's our initial proton concentration in this stomach invite environment. So now it is probably going to help before we find this. Before we used the acid ionization constant. Let's just make sure we understand it's going on here of the initial concentrations for the aspirin. That's what they gave us. 0.2. Um, we just found that the proton concentrations 0.1, and since the aspirin has not I nice yet we will have a zero for the and I. So the change it's gonna happen is aspirins gonna lionize somewhat so it'll lose so much. Um, the proton will gain so much. In the end, I ends will gain that same amount, making our equilibrium values 0.2 minus acts for the aspirin. So this is what's going to be different than letter A is our proton concentration will be 0.1 plus x and the and I will be X still. Keep in mind, we just need the X value for our final proton concentration. We're just gonna need this x the proton concentration that the aspirin contributed. Um, but we just it's just gonna be a little hard to find. All right, So three times, 10 to the negative for then that's our ionization constant. And now we're going to plug in this for our proton concentration at equilibrium, plugging the X for the anti in concentration on. And then we're gonna have to go 0.2 minus X instead of just condoms Europe to this time. So rearrange it. Multiply the three times the 30.26 times seven, the negative five. You're also gonna do three point all times and lingered four times x. So we're gonna put X there. Um, we're going at this point, it will be equal to if we use the distributive property to multiply up up there were appointed or in pointing we get 0.1 x plus X squared. So now let's rearrange us so that the X squared stays positive. We add the 0.1 packs like we had it already. Now subtract the well, Don't subtract. I mean, ad the three point all times in that four x to that side. Subtract six times seven the negative five and said it all equal to zero. So then all we have left to do is add those two X values together, and then I should look like this and you're ready to, um, plug this in to treat this as a quadratic equation. So remember, when you have a quadratic equations this formula negative B plus minus B squared, minus four a c over to a um so you just got to know you're a is one here. B is 0.1003 and your CIA's negative six times the negative five. So it looks hard, but it's just plugging in those numbers, so you start plugging them in squaring the 0.0 point one years or three minus four times one times negative six. So I'm singling five on divided by two times one much of this too. So do some of the math here squared that value, um, multiplied those numbers to get 2.4 times 10 negative. Four. And it's all over too. So now take care of all of your square root, um, numbers. And you should end up with 0.1015 which I rounded. There was a few more digits there. Um, so now you're gonna end up with two values, the value where ad at the top or if you mind, is a top, Obviously, you have to take the positive value as a negative value doesn't make sense. Cross that out. And now we can use this. This is this is not the H plus total of equilibrium. You'd have to add the your apartment, but is the amount that came off the A C a salicylic acid, the aspirin. And that's all we need for this ionization, um, value percent ionization. Um, so now we can finally close that it We work hard to find it six times seven the negative four and weaken. Divide that by the original value given times 100 and you should get exactly 0.3 percent. So, you see, the in this acidic environment in stomach, you're not gonna get nearly as much, um, nearly as much ionization where you got almost 4%. Now you only got 40.3% like 10 times less. So, um, you can read page tool six to us it page seven or six in the textbook talks about it towards E. M. So what happens with because his aspirin doesn't I, and I so completely and so there's a lot of, um, a lot of the aspirin molecule left. It can easily penetrate this stomach meme bring because of its non polarity. But the stomach meme bring barriers and, um, it becomes trapped in there, and then it will lionize in there, and it continues to build up. And that causes bleeding in the lining of your stomach. So that's the question. Wants you to think about that. And, you know, please read. Read up on that page seven or six. It's good stuff to know why you probably shouldn't take aspirin too often. All right, Well, thanks for watching and good luck

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