Polyprotic Acids

Jules Bruno
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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.