Diprotic Acids

Jules Bruno
Was this helpful?
so sulfurous. Acid, which is H two s 03 represents a die product acid with K one equal toe 1.6 times 10 to the negative two and K two equals 4.6 times 10 to the negative five. Here, it says, calculate the pH and concentrations off sulfurous acid by sel fight and sulfide ion. When given 0.250 Mueller sulfurous acid here they're giving us the concentration of the acid for so we're dealing with the acid form, which is a weak acid because it's K is less than one. We're dealing with K one because we're dealing with the fully acidic form of it. It hasn't given any H plus yet. It's gonna react with water, which is the liquid. Remember acids donate H plus two bases. So we're gonna get here is we're gonna get H S 03 minus since its eye on its acquis plus h +30 plus acquis. Since it's K one is less than one, it's a weak acids. We're gonna use an ice chart in order to determine our pH and also to help us determine the final concentrations off these ions. So we have initial change. Equilibrium. Remember, in a nice chart, we ignore solids and liquids. What will be ignored? Because it's a liquid. Our initial concentration of our weak acid is 0.250 Mueller. We're not given initial concentrations of the products, so they're both zero initially, remember for change, we lose react INTs in order to make products, bring down everything we're talking about the first acidic hydrogen coming off. So we're dealing with K one, so K one equals products. Overreact INTs. Now remember, we have to determine Can we ignore the minus X on the bottom or not? To do that, we do the 5% approximation method. So we take our initial concentration and we divided by our constant that we're using, which in this case is K one. If we get a total, that's greater than 500 will be able to ignore minus X the initial concentrations 0.250 Mueller The K one is 1.6 times 10 to the negative too. When we divide those that gives me 15.6 to 5, this number is not greater than 500. So I kidnapped cannot ignore the minus X within my equilibrium expression. So this will be 16 times 10 to the negative to for K one. Both my products air X at equilibrium. So that's X squared, divided by 0.250 minus x. Again, we cannot ignore the minus X here because the total we got was not greater than 500. So we're gonna do here is gonna keep the minus X and use the quadratic formula. These cancel out, we're going to distribute, distribute. So when I distribute, I'm gonna get here 4.0 times 10 to the negative three minus 1.6 times 10 to the negative two x equals X squared. Because this X has the highest exponents, it's our lead term. So we have to subtract everything over to its side or add everything over to its side. So we're gonna add 16 times 10 to the negative two x two Both sides here and they're going to subtract 4.0 times 10 to the negative three. So we're gonna stay here. X squared equals So X squared plus 1.6 times 10 to the negative two x minus 4.0 times 10 to the negative three. So this represents our equation. So this is a B and C. We're gonna use the quadratic formula. So negative B plus or minus B squared minus four A. C over to a. So that's negative. 1.6 times 10 to the negative, too, plus or minus 1.6 times 10 to the negative. Two squared minus four times one. Don't forget the negative sign for C times Negative 4.0 times 10 to the negative three divided by two times one. Now, remember, because this is plus or minus, that means we're gonna get two possible answers here. When I do everything inside of here and I take the square root of it, what I'm gonna get is X equals negative one six times 10 to the negative two plus or minus 20. to 7 divided by two. So you get two possible answers again because this is plus or minus. So when we add, that would give us 0.5575 Moeller. And if we kept the negative sign and give me or negative 07175 Mueller, both cannot be the answer on Lee. One of them is the true answer here. E in your ice chart stands for equilibrium at equilibrium. It is impossible to have a number that is negative. So if I took this second answer and I plugged it in here or here, then we would have a negative value at equilibrium, which is impossible. So that means we cannot use this X instead will use this X here, plug it into here into here and into here to figure out each one of those compounds concentrations at equilibrium. So at equilibrium, h two s 03 equals to 50 Mueller minus X. So plug in the X variable that we just found. So at equilibrium equals 0.194 to 5 Mueller. So we got that answer at Equilibrium HS. All three minus equals X, just like h 30 plus equals X. So they both equal the same thing at equilibrium. All right, so we figured out the concentration of this one end of this one. We still have to find the concentration of vessel three to minus. Plus, we still need to determine the pH. All right. We should know what the ph is at this point because we know what h 30 plus is. PH equals negative log of h 30 plus. So we're gonna take the negative log off 0. So that's 1.25 now to figure out the concentration of S three to minus is a little bit trickier, because at this point, we don't have s all three to minus anywhere within this equation. What we would say is, if by Sulfide ion decided to donate its second h plus, that could create this particular ion. So that's what we're gonna do. We're gonna come down with that. So H s 03 negative comes down here. It's gonna donate its second H plus toe water. So that's how we're gonna get s three to minus plus H +30 plus here. We won't need to set up a nice charter calculate. This is what we need to realize if we take a look at the K is between K one and K two. Look at K one K one is 10 to the negative, too. Whereas K two is 10 to 95. They're different by a lot. A magnitude of three fold. That's a big difference. So what that means is, the amount off product we're gonna make the second time around is gonna be very, very, very small. So small, in fact, that we don't need to do a nice chart. This is how he would solve for the basic form of this die protic acid. Since we're dealing with giving away the second acidic hydrogen, that means we're dealing with K two Que two equals products. Overreact INTs. So that's what we have initially. What we need to do here is we need to solve for eso three to minus. So you're gonna multiply both sides by HS 03 minus so hs three minus times ca two equals sl three to minus times H plus divide both sides here by H 30 plus. So we're gonna get here that are sulfide ion. Concentration equals H s minus times K two divided by H plus. Here's the thing We just found out in the first ice chart that at equilibrium H s 03 minus, which is the intermediate off the dye protic acid, it equals my hydro Nehemiah on concentration and equals H plus. So that the same exact number. Now, if they're the same exact number, what does that mean? That means that they will cancel out here since their same exact number. So we'll see that at the end. The concentration of the basic form of my die protic acid is just equal to K two. So the concentration of sulfide iron is just 4.6 times 10 to the negative five Mueller. So it's important that you remember this when we're dealing with a dye protic acid here to figure out the concentration of the acidic form before it's given away any h plus, we would set up the ice charting sulfur acts and plug it in here so that X would subtract from the initial concentration of my die protic acid to find the intermediate form of the die Protic acid again, we'd still just need to find X whatever that X is, that would be the concentration of the intermediate form. Sall. Fight here represents the basic form of my die protic acid, the basic form of my die protic acid. Its concentration at equilibrium is just equal to K two. So it's important that you guys remember this. And if you're still confused of what I mean by acid form, intermediate form and basic form makes you take a look at the videos before this one. Because remember, for a dive product acid has too acidic hydrogen. So this would be the acid form after gives away its first H plus, This would be its intermediate form. And then it's basic form. Is this so H two s 03 would be the acid form. H s 03 minus is the intermediate form, and eso three to minus is the basic form. When it comes comes to being given the concentration of the acid form of a die protic acid, we set up a nice chart to help us find the concentration of the first two and then just simply say that the concentration of the basic form is equal to the K two of the die proto gas ID. So knowing that is the best way to answer this type of question and again because you're K two is so much smaller than your K one. This number is gonna be so small, in fact, that it's not gonna really affect the overall concentration of H 30 plus. Okay, so you're Ph would still be 1.25 And in fact, at equilibrium, these two would give us the same exact number of this. And if you added this concentration to the amount of H 30 plus, you would still see that we have the same exact ph at the end.