An unknown diprotic acid has an initial concentration of 0.025 M. What is the pH of the solution if pka 1 is 3.25 and pKa 2 is 6.82?

Hopefully you were able to attempt this practice question. Let's take a look. Here it says an unknown diprotic acid has an initial concentration of 0.025 molar. What is the pH of the solution if pKa 1 is 3.25 and pKa 2 is 6.82? Realize here that they're telling us we're dealing with the unknown diprotic acid. Realize here that weak diprotic acids have pKa values that are greater than 0. If it were strong, the pKa values would be less than 0. And here, we're dealing with the acid form which means we're gonna deal with Ka 1. Realize here that we're we don't have k a one. Instead, we have p k a one. So 10 so we're gonna say here that k a equals 10 to the negative p k a. So it's 10 to the negative 3.25. So it gives me 5.62 times 10 to the negative 4 for my Ka1 value. We don't know what this unknown diprotic acid looks like so we use the generic formula for 1. So we'll just say H2a is the generic formula for my diprotic acid. It will react with water. Because it is an acid, it will donate an H plus to the water. It becomes H a minus. Water gains an H plus and becomes H3O plus. What we have here is initial change equilibrium. Remember, in an ICE Chart, we ignore solids and liquids. Here, this will be 0.025 molar. These initially are 0. We're losing reactants to build up products. We're dealing with Ka1 because we're losing the first acidic hydrogen. So Ka1 equals products over reactants. So h a minus times h three o plus divided by h two a. We plug in the values that we know. So k a one is 5.62 times 10 to the negative 4 equals x squared divided by 0.025 minus x. We do the 5% approximation method to see can I ignore that minus x or not? So we take the initial concentration divided by the k a one that we're using and see if that ratio is gonna be greater than 500. So initial concentration divided by our 5.62 times 10 to the negative 4. When you punch that into your calculator, you will see that you get a value that is not greater than 500. Therefore, we have to keep the minus x and do the quadratic formula. So multiply both sides by 0.025 minus x. We're going to distribute. Distribute. So when I distribute, I'm gonna get here initially 1.41 times 10 to the negative 5 minus 5.62 times 10 to the negative 4 x equals x squared. That x squared is the lead term, so everything has to be moved over to its side. So when we do that, we're gonna get x squared plus 5.62 times 10 to the negative 4 x minus 1.41 times 10 to the negative 5. Here's my a, my b, and my c. Setting up our quadratic formula, remember it's negative b plus or minus square root of b squared minus 4 ac over 2 a. So we have negative 5.62 times 10 to the negative 4 plus or minus 5.62 times 10 to the minus 4 squared minus 4 times 1 times negative 1.41 times 10 to the negative 5 divided by 2 times 1. Now realize here we have plus or minus. So x equals negative 5.62 times 10 to the negative 4, plus or minus. And when we figure out everything inside of here and then take the square root, that gives us 0.007531 divided by 2. So for x, we have 2 possibilities. X equals if we're to take the positive, if we're to add, we get x equals 0.003484. And if we took the minus instead, it'd be x equals negative.00404 7. Now here, remember at equilibrium, we cannot have a negative value. So this x is ignored. This is the x that we will use. That x represents this x which is connected to h three zero plus. So this equals h three zero plus. Realize now because we have the concentration of h three zero plus, we can figure out pH because pH equals negative log of h three 3o plus. So plug in the concentration that we found. And when we do that, we're gonna get our pH equals 2.46 as our final answer. Hopefully, guys were able to recall some of the techniques and steps that we did in previous questions in order to find this final answer for this question. Just remember, when it comes to diapurtic species, we're either dealing with the fully acidic form, we're dealing with the intermediate form or we're dealing with the basic form. In this case, we're dealing with just the acidic form. We deal with Ka1, set up an ice chart in order to figure out our final concentration of H3O plus and from there determine our pH.