A 40.0 mL sample of a mixture of HCl and H3PO4 was titrated with 0.100 M NaOH. The first equivalence point was reached after 88.0 mL of base, and the second equiva-lence point was reached after 126.4 mL of base. (a) What is the concentration of H3O+ at the first equiva-lence point?

Video transcript

Welcome back everyone. We're told that a solution of hydrochloric acid, which is a strong acid and citric acid, which is a tri protic acid was mixed with a total volume of 50 mL. The resulting solution was tight traded with 500.1 50 moller, sodium hydroxide. It took 83.3 mL of sodium hydroxide to reach the first equivalence point and one oh 6.6 mL to reach the second equivalence point, we need to calculate the concentration of hydro knee. Um At the first equivalence point were given the acid dissociation constant of citric acid, a 7.1 times 10 to the negative fourth power, Its second K. Of 1.7 times 10 to the negative fifth power and the third K. Of 4.1 times 10 to the negative seventh power. Let's begin by recognizing that because hydroponic asset is a strong acid, it's going to undergo full association into the following ions where we form one mole of a proton and then we form our bromide, one minus an ion. Next we have citric acid which we should recognize is not a strong asset and therefore will undergo partial dissociation, where it's in equilibrium with one mole of a proton And then its conjugate base C6 H seven oh 71 minus R. Citrate, one minus an eye on now because it's try protic. We're going to consider this as the first association, but the second association will begin with its conjugate base or citrate, one minus an eye on which also undergoes a partial dissociation to form another mole of proton and then another contract at base being C six H 607 to minus. And then lastly, we have our third dissociation beginning with that two minus an ion which undergoes a third partial dissociation, where we form another proton And C six H 5073 -. Now, these are the reactions that occur before our sodium hydroxide is added. Now, once our sodium hydroxide is added, the reactions that will occur will be at the first equivalence point, which will be when our most base are equivalent to our most of acid in solution. And recognize that our sodium hydroxide once added will react with the proton from hydroponic acid. So fully consuming RHB are and will also react with the proton generated from our citric acid. And this means that the reactions that occur once sodium hydroxide is added will be the remaining species, as our conjugate base of citric acid being our citrate one minus an ion. And so we would have our citrate one minus an eye on C six H seven 07, 1 - which is in equilibrium with the proton. And we're sorry, we have our situate one minus an ion with the proton in equilibrium with our citric acid, C six H 807. And then we should understand that because we have that proton as a reactant with our situate one minus an ion. We will undergo another dissociation, where we have our citrate and ion which associates into another mole of proton to form our or sorry to form our citrate to minus an ion. And so we want to come up with an overall equation for the first equivalence point. So recognize that because we have a proton here on the react inside and a proton here on the product side, we can cancel the protons out in each of these reactions and we're just going to carry everything else down that we're left with for an overall equation. And so what we have is two moles of our citrate, one minus an eye on in equilibrium with one mole of citrate, C6 H807 and one mole of our citrate to minus an ion, sorry, one mole of citric acid and one mole of our citrate to minus an ion. We want to recall the definition of a buffer in which our weak acid, which in this case is our citric acid is in solution with its conjugate base. And so we can resist drastic changes to the ph and therefore our ph will depend on the average of our P K. A values for the first two dissociation that citric acid undergoes. And so what we have is our ph will depend on our P K one plus R P K two divided by two. Since we want to find an average. Now note that from the prompt were given K. A values. And so recalled that we can find our P. K. A. By taking the negative log of our given K. A. Values. And so for our given or to find our PK one we would take the negative log of our given K. A. One as 7.1 times 10 to the negative fourth power. For the first association of citric acid and inter calculators. This will be a value of 3.1549. Sorry correction of 3. 487. So that is our calculation for P. K. One. And then for our P. K. Two we would take the negative log of our given K. A. Two from the prompt as 1.7 times 10 to the negative fifth power. And sorry, this is to the negative fifth power which gives us our PK two of 4.7696. And so to find our ph after the first equivalence point we have our ph equal to R P K. One which we just determined to be 3.1487 plus R. P. K two which we determined to be 4.7696 divided by two. To get our average And we would find that our ph is equal to a value of seven . divided by two. And then our our final ph is the result of this quotient as 3.95915. And so for our final answer we need to find our concentration of hydro knee. Um So recall that we can calculate our concentration of hydro knee um kati on by taking 10 to the negative ph that we calculated. And so we would have 10 to the negative 3.95915 in which our concentration of hydro ni um would be the result of this, which would be 1.1 times 10 to the negative fourth power. And this is a concentration. So our units are more clarity and so it's highlighted in yellow represents our final answer as the concentration of hydro ni um at the first equivalence point of our solution. So I hope that everything I explained was clear. But if you have any questions, just let us know and I'll see everyone in the next video.