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General Chemistry

Learn the toughest concepts covered in Chemistry with step-by-step video tutorials and practice problems by world-class tutors

17. Acid and Base Equilibrium

Polyprotic Acid

polyprotic acid possesses more than 2 hydronium ions (H+). 

Polyprotic Acids

Our understanding of diprotic acids and bases can be used to understand polyprotic acids and bases. 

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Polyprotic Acids

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our understanding of die product acids and bases can be used to understand, um, Polly product acids and bases. Now we're gonna say for a poly protic acid were really referring to try product acids. So they have three acidic hydrogen. The go to form. If you don't know what it looks like, is H three a. Okay, so that's our try. Product acid three. A city hydrogen Here it's in its acid form, and if it's the acid, that means water is gonna behave as the base. So it donates an H plus to the water. That's how it becomes H two a minus and water becomes H 30 plus. Because we're talking about donating the first acidic hydrogen, we're dealing with K a k one. Now remember K one is your acid association constant? All equilibrium constants are products overreacting. It's, and with them we ignore solids and liquids so the water, which is a liquid, would be ignored. This would give us at the end H two a minus times H 30 plus divided by h three a. After we've given away that first acidic hydrogen, we still have two more left to go so Now it's here again. It can still act as an acid and donate another H plus to a water, thereby becoming H A to minus. And water again becomes H 30 plus. So now the equilibrium expression is H A to minus times H 30 plus, divided by H two a minus. Then, finally, it has its last acidic hydrogen, which you can donate to another water molecule, giving us a three minus at the end and h 30 plus. Just remember that if you have a charged ion, it exists as an acquis in solution. So that's why all the charged forms are acquis. Water is the only one that's a liquid, so here this represents the three equilibrium expressions for try protic acid. K one deals with giving up the first acidic hydrogen K two represents. Dealing with the second hydrogen and K three remains means removing the last and final hydrogen off of the tri protic acid. Now, in terms of these K values, always remember that your K one is always going to be the largest. It's always easiest to remove that first acidic hydrogen, but with each one afterwards, it becomes harder and harder to remove the rest. So okay, too, would be less. But it would still be greater than K three, and K three will be the smallest, So those would be the three equilibrium expressions connected to all of them. Now that we've seen the poly product acid or try product acid forms, let's think of it in the reverse way. What if we're looking at the three basic forms for a poly product acid slash base? What would we do? We do the
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Polyprotic Acids

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So now let's take a look at the polic product base forms. So for the polic product based form is basically going the opposite direction. So the fully basic form when it has none of it's acidic hydrogen XYZ default a three minus. So here we're talking about accepting our first acidic hydrogen from water. Since we're talking about accepting that first H plus, we're dealing with a B one, so the equilibrium expression would be H A to minus times O H minus, divided by a three minus. Then that form could continue to accept H plus from another water molecule. So this would be dealing with accepting the second Age plus, so that bkb too. So we're gonna say here, that is H two A minus Oh h minus over h A to minus. And then finally, we accept the final H plus possible to turn into our fully acidic form at the end. So that be H three a times O. H minus, divided by H two a minus. So those would be the equilibrium. Expressions now realize here that when it comes to a try, product acid has basically four different versions of itself. So we have the acidic form or it has all three of its acidic hydrogen. Then we removed the first H plus from it. So we're gonna call this intermediate one. Then we could remove another H plus from it. We're gonna call this intermediate too, and then finally removed the last acidic hydrogen. And we're gonna say that this is the basic version or basic form, because it has none of it's acidic hydrogen. We're gonna say here removing the first acidic hydrogen means that we're dealing with K a one we're moving the second acidic hydrogen means we're dealing with a two. And then this would be K three in the opposite way. This basic form could start accepting H plus ions. So accepting that first a city hydrogen gives us K B one this accepting the second one means we're dealing with K B two. And finally this one here accepting the last acidic hydrogen possible gives us a K B three to give us this form. Okay, so you could either be looking at it going this way or going this way. And what you need to realize here is that K B one in K three are both connected together because they represent a connection between these two forms. Then you're gonna say here that K two and K B two are connected together because they connect these two forms. Then finally, K B three and K one are connected together because they give us these two forms here knowing that is important because that helps us go from one form to the other. So here, like I said, K one and K B three, or connect together and multiplying That gives us kw que two times K B two gives us kw and then K three and K B one gives us kw. Remember here that K W equals 1.0 times 10 to the negative 14 at 25 degrees Celsius. Even if they don't give you the temperature, you assume 25 degrees Celsius. Okay, w will be that number. If we change the temperature that changes are K w. Then they would have to tell you what the new K W value would be. But remember the connections between the different K A values and KB values when it comes to try product acids. Now that we've looked at the poly product acid forms and the poly protein basic forms. We can now look at how we approach calculating pH for these different versions of these compounds.
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Polyprotic Acids

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So like we said, when it comes to polic product acids and bases, there's four different forms. There is the acidic form, the to intermediate forms and in the basic form. Now, when dealing with Polly product acids, we're gonna say here that the acidic form, which is H three a by default on, can be treated as a mantra. Protic acid and will use K A one than a three minus, which is the basic form can be treated as the model product base. So use K B one now based on issues with, um logs as well as concentrations. When it comes to calculating the pH off the to intermediate forms. Just keep in mind these two different types of equations that help us calculate H plus very quickly. And from there we can calculate pH. So let's take a look. So here this is the first intermediate form. So intermediate one, after it's lost its first acidic hydrogen, we're gonna say H plus is approximately equal to, so that's what that wavy line means you do. What you do here is you take the K one, you multiply it by K two times the initial concentration off your intermediate one form. So, for example, phosphoric acid represents a common try protic acid. So it takes away its first acidic hydrogen to give us the first intermediate. We lose another acidic hydrogen to give us our second intermediate, and then phosphate represents the basic form. So here, if they told us we had 10 Moeller n a h two p 04 this would be the first intermediate form again. Remember, you usually won't find it this way. B h that we lose gets replaced by a metal. Okay, so this is the common way of depicting it. The initial concentration would be this number here, the 0.10 Moeller, which would plug in plus K one times You're K W, which is still 1.0 times 10 to the negative 14 divided by K one plus again, the initial concentration. When you take the square root of all of that, that's gonna give you the concentration of H plus. And if you know the concentration of H plus, just remember, Ph equals negative log of H plus. Then, if you're dealing with a second intermediate intermediate, too, this is after it's lost two of its acidic hydrogen, so it shifts a little bit. So now we're dealing with K two and K three. If we go back up to this, why is this? We'll realize that when we're dealing with the first intermediate in the formula, it's in between K one and K two. So that's why they were part of the formula. Now we're dealing with the second intermediate form and its in between two and K three. That's why, in its formula to figure out a plus concentration, we're using K two and K three. So, for example, I gave you 15 Mueller and then in a to h P 04 Okay, so that's the second intermediate form plug in the initial concentration, which is this number. Then it's K two times k w, divided by K two plus initial concentration, which gives us pH on, which gives us hpe plus take the negative log of it to find pH. So again, when you're dealing with the acidic form before it's lost, any hydrogen is use K a one to solve for H plus, which then helps us figure out pH. If you're dealing with the form that has no acidic hydrogen, that's the basic form. So we deal with K B one for the intermediate forms. It's important to remember these two equations. If you're faced with questions like this MAWR, commonly, you're going to see the acidic form of the basic form these equations air good if you're approaching any types of homework, questions that ask you to figure out the pH of any one of the intermediate forms. So keep in mind the different approaches that come with calculating pH for the different types of Polly Protic acid forms.
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Polyprotic Acids

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determine the pH of 300 Mueller sodium hydrogen phosphate, which is N A to H P 04 Here, it says phosphoric acid, which is H three people, four, contains three K values given. All right, so we have to figure out the pH of this particular form. And to be able to solve this question, we have to look and see which one of the different forms could this possibly represent? So phosphoric acid represents the acidic form of our compound. Once it's given away its first H plus, it becomes H to peel four minus. So this is intermediate one. Once it's given away its second H plus, it becomes HP all four to minus. So this would be intermediate, too. And then, when it's given away its final H plus, it becomes peel for three minus, which is the basic form we have to look and see. Sodium Hydrogen phosphate represents which one of these four forms. So if we look, it's made up of what two and a plus, which is just spectator ions, which really don't matter, plus H p +04 to minus. So we can clearly see that this ion here represents this ion here, which means we're dealing with the second intermediate form. And remember, when it comes to calculating the pH of any one of the intermediate forms, we have to remember the equations associated with them. So for the second, intermediate H plus equals square, root off K two times K three times the initial concentration of the compound, plus que two times K W divided by K two plus the initial concentration of the compound. All right, so okay, a two is this number here, So plug it in que three. Is this value here? So plug it in. The initial concentration of the compound is 0. plus que two, which is still that number 6.2 times 10 to the negative, eight times K W, which is 1.0 times 10 to the negative divided by que two, which is 6.2 times 10 to the negative eight, plus the initial concentration again. All right, so multiply these three together, make sure you put them in parentheses. Multiply these two together, make sure you put them in parentheses, and then we're gonna add these together. So when we do piece by piece we're gonna get 7812 times 10 to the negative. 21 plus 6.2 times to the negative. 22 divided by when I add those two numbers together on the bottom, it gives me point 62 makes you put them in parentheses. When you add the two numbers on top, then divide by the number on the bottom. So if you do that correctly, you'll get 2. times 10 to the negative 20 and the square root of that, which will give us our H plus equals 1.6765 times 10 to the negative 10. So pH equals negative log of H plus, which we just found. So plug that in. So that's gonna give me 9.78 as the pH of my solution. So remember, it's tricky when it comes to Polly Protic. Acid or base is so you have to look and see which one of the four forms are we dealing with. If you're dealing with the acidic form, that means you're gonna do K one and do a nice chart to find H 30 plus concentration and from there, uh, ph If you're dealing with the intermediate one or two, they each have their own separate equation, which we talked about previously. And then if you're dealing with the basic form, that means we're dealing with cabe one. So we do a nice chart again. It would react with water. Water would donate an H plus to create O. H minus as a product. When we saw for X, we'd find the concentration of H minus. Taking the negative log of that would give us P O. H, which we then subtract from Ph to get our final answer. Most attract from 14 to find pH as our final answer. So, guys, these other approaches we need to take when it comes to these types of compounds. Not that we've seen this version. Take a look at the second one and see if maybe you can figure it out before we handle it together. And if you're stuck, don't worry. Just click over to the next video and see how I approach the next example
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Polyprotic Acids

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determine the pH of 0.300 Mueller citric acid. It possesses three K values. So here we're dealing with the acidic form of our try protic acid. And remember, if you're dealing with the acidic form, that means we haven't lost our first H plus yet. We're about to donate it over toe water, so that means we're dealing with K one. We know it's a weak acid because citric acids values are less than one. Weak acids and weak bases react in ice charts, and they react with water. If it's going to be the acid, that means water has to act as the base. Remember, acids donate H plus to the base, so we'll have now is H two c six h 507 minus plus H +30 plus. We have initial change equilibrium. Remember, in a nice chart, we ignore solids and liquids, so this will be ignored. Initially, we have 300 more of this zero and zero of our products. We lose reactant, since to make products bring down everything. So 0.300 minus x plus X plus x k a one is equal to products. Overreact INTs. So are two products are multiplying. So that's X squared, divided by 0.300 minus X. Now we have to check to see Can I ignore that minus X on the bottom? To do this, we do the 5% approximation method. We basically take the initial concentration and divided by equilibrium Constant. In this case, we're using K one, so it's gonna be divided by K one. If we get a value that is greater than 500 we could ignore the minus X on the bottom. So my initial concentration is 0.300. K one is 74 times 10 to the negative. Four. When we punch that in, that gives me 405. So it is not greater than 500. So we cannot ignore the minus X. So we're gonna keep the minus X and do the quadratic formula. All right, so okay, one is 74 times 10 to the negative. Four equals X squared over 300 minus x. Multiply both sides by 300 minus X. We're going to distribute, distribute. So when I do that here, I'm gonna get 2.22 times 10 to the negative four minus 7.4 times 10 to the negative four X equals X squared. This X has the highest power, so it's my lead term. So that means everything has to be moved over to the right side. So subtract this from both sides. Add this to both sides. When we do that, we're gonna get our equation as X squared plus seven four times 10 to the negative four X minus 2.22 times 10 to the minus four. Here's my A might be and my seat. So here the number in front of a is one. That's what it is. Um eso we're gonna say my quadratic formula is negative B plus or minus B squared, minus four a. C over two way. So we're going to say, now that is going to be negative. 7.4 times 10 to the negative four plus or minus square root off. So be a 7.4 times 10 to the negative four. It's gonna be squared minus four times one. Don't forget the negative sign of scene divided by two times one. So remember this is gonna be plus or minus. So what I'm gonna do here is I'm gonna solve for everything in here and then take the square root of that. When we do that, X equals negative 7.4 times 10 to the negative four plus or minus 0.0 to 809 divided by two. So x equals. If we're toe ad, it's gonna equal 0.14 Mueller Or, if I were to subtract the top and then divide by two, that would give me negative 0. 75 Moeller, Now remember, both cannot be. Your answer is only one of them is the correct X variable. It doesn't matter where I plug it in at equilibrium. Whether it's here, here or here, it will always give me a positive answer because negative answers that equilibrium are not possible. So that would mean that the second X variable that I found cannot be used, because if I plug them here or here, that would be a negative answer at the end. So this is my correct X variable. We just found out what X is X gives me a three plus so we just find out what h 30 plus is And remember, Ph just equals the negative log of H 30 plus. So plugged that number we just found Plug it in. When we do that, we're gonna get as our ph 1. So it's a long process. But again, everything hinges on the fact that you're able to basically figure out which one of the four basic structures for Polly product acids exist within this question here, we're dealing with the acidic form before it's giving away any H plus tau water. Therefore, gonna use K one and set up a nice chart. Follow the usual steps that we're accustomed to seeing when it comes to ice chart to find what your ex variable will be, that will usually either give you a plus on H +30 plus or O H minus. In this case, since we're dealing with the acid, former gives us a three or plus, which we can use to find Ph.
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