For this problem were given a few solutions, and we want to determine D. PH and PCO each of those solutions for a we've got sodium hydroxide, the we have calcium hydroxide. See, we have a mixture of acid and base and D We have the same thing, a mixture of acid and base. So we're going to do Ph MPO age of all these solutions. So in this we need a few things that we need to remember. So we know that doing the anti dog of our O H minus concentration or are H 30 plus concentration will give us T o H or pH, respectively. So negative log of O H minus gives us village negative log of H Torrio plus gives us pH. And we also know that if we have 14 minus ph, we get the O. H. And vice versa. We do 14 minus p o h. We get he age. So these will be useful things to remember for this problem. If you want to pause this and write these down, or however you want to do, just remember these for this problem, it will go a long way in helping us figure things out. So for our first solution, we have any wage and, you know, this is a strong base. So we have 100% ionization, meaning that our concentration were given applies to borrow H minus. So, in a H associates in the O. H, we have 00.450 moles of O. H and sodium. But we're gonna focus on O h. So we will do the negative log of R O H concentration 00.0 for five zero and that will give us a p o. H. Since this was in O. H minus concentration of 1.35 This is a very basic solution, as it should be using a strong face. So this is our p O H. Now, if we use the other Formula 14 minus p o h, we end up with our ph of 12.65 So these are our answers for our first example in a 1.35 for R. P O. H. And 12.65 Ferrar pH. And these make sense P. O. H is low, meaning it's basic, and our 12.650 high pH also meets that it is basic. So these numbers make sense and they add up to be 14. So we say that these are direct. These are answers to our first example going to our second example again, we have a strong base, but the biggest distinctions and making this problem is that we have to equivalents of our base. Actually, that, too, is not supposed to be inside of the bracket that's supposed to be outside of the bracket. So again, same concept we have 20 H minus is for every mole of this that we have. So we actually have another step in this one. We have to do 10.160 and we have to multiply that by two because of that to equivalents of base. And that will give us 20.3 20 moles per leader of O H minus. So our actual concentration of O. H minus is twice as high as for our overall substance. For that to acquittal. So now that we have r o H minus concentration, weaken, do the anti log of that number, and that will give us a P O. H of 1.49 and again. This makes sense because this is a strong base. So this is our P O H. Low p o. H. Means very basic. And if we want to get our pH, we can again do the same thing 1.49 out of 14 and that will give us a 12.51 pH, which also makes sense. High pH means basic low pH would mean acidic low p o. H means basic high P o. H would mean acidic, so they're opposites said these are two answers for this 11.49 p o. H. 12.51 ph. Now for see, we have a little bit different. We have a mixture. We have a mixture of equal parts a 1 to 1 mix of hydrochloric acid and calcium hydroxide, and they have the same concentration. But as we can see for this problem, we have one equivalent of our hydrogen. And again, I wrote this wrong we have to equivalents of our hydroxide. So let me actually write that in blue toe, demonstrate that so we have one equivalent of hydrogen and two equivalents of hydroxide, meaning we have twice as much based, since their concentrations are the same. So we'll do will take 0.125 and will multiply that by two and order to give us our actual concentration. Now, that is going to be Since I don't have it written down a two point or point zero to five, I think Let me double check this room. That is correct. Don't know. That is correct. We have 0.0 to 5 most of our demise twice as much of this as we dio off our ass. It. So in order to figure out what our agent, P o. H. All we need to subtract out smaller from the larger. And that's because we're going to form water with 0.125 moles of our hydrogen and 0.125 moles of our hydroxide. So our first step in this is actually going to be like a second stuff is going to be 0.25 minus point is euro 1 to 5. And that's because this is going to be our acid So r h 30 plus and this is going to be r o H minus. And remember that is because we are using up all of this acid with the base. So we're actually still going to be left with a basic solution. And we're going to be left with a concentration of 0.0 1 to 5 for our hydroxide. So if you need to pause it and make that make sense, our base. Since we have more of it, subtract out our acid that will form water and we are left over with this much hydroxide. So now, for our guests are third step is going to be the negative log of 0.125 and the is going to give us a p o H of 1.9 sirrah. So we have our p O. H. Now 14 minus 1.90 is going to give us a pH of 12.1. And this again makes sense low. P o h means basic. Hi. PH means basic, and adding these together would give us 14. So this will be our answer for this problem. 12.1. I kind of wrote over that 12.1 and 1.9. So a little bit of extra that we had to do here, but we still end up with something that makes sense. Hi. Ph Low P O H. Mawr Based. Left over. Now for this one for D We have a different ratio, but still the same concentrations of a strong acid in a strong base. So emphasizing that again if we have a 2 to 3 mix, we have a one subscript for our H plus and we have a one subscript for O. H minus this time. So we have one of each. But this time we have two equivalents of R h N 03 So two times 20.125 gives us 0.0 to 5 of our H plus and for R K O h. We have 00.125 times three because we have a three. So we multiply our 1st 1 by two because we had to equivalents of that and r k o h. We multiply that by three because we have eighth. We have three equivalents of it. So that is going to give us 0.375 for our O. H minus concentration. So we have our concentrations. Now we need to figure out which one? We're gonna have more off. So right away we can see that again. We're gonna take our larger number and subtract or smaller number out of it. Since these were both strong. So 0.375 minus went 0 to 5 is going to leave us with 0.125 Now, remember here we're going tohave o h minus. And here we have hte 30 plus. So if we have more base, we're going to be left with this as r o h minus concentration. Not our asset, because, see, all of our acid was consumed. We have less acid than we have base. They're both strong. We're left with just base. So now we can do our formula again. The negative log of our base concentration is going to give us a p o h of 1.9. And if we subtract that out of 14 we are left with again 12.1 for our ph. And you can see that this is actually the same as our last example. We just have different amounts of different components. But in the end, we're left with the same amount of base to work with. So we have for our answers 1.9 for our p o age and 12.1 for our pH. So going back through each of these, Paul's at any point that you need to We've got this for our answer. For a for answer for B Our answer for C and our answer for D.