So here it says find the ph of a saturated solution of barium hydroxide when dissolved in 0.5 moller of lithium nitrate. So here we're dealing with moller lithium nitrate here the K. S. P. Of barium hydroxide is 5.0 times 10 to the negative three. Well we know that we're dealing with barium hydroxide. So this is my ionic solid. So we're talking about how that ionic solid breaks up into its ions. We know that we don't deal with solids here. This would be X. And hear this because there's a two here, this would be two. X. K. S. P. Equals just products because we're ignoring the solid, that's the reactant. So we have B. A. Two plus now realize here that because we're dealing with non common ions, that means ionic strength is in play and therefore the activity coefficient is in play. So it's gonna be activity coefficient of barium to ion times hydroxide ion because the two here it's squared times the activity coefficient of hydroxide also squared. Alright, so we're going to need to determine what our concentration of hydroxide ion is to figure out what our P. O. H. Is. And once we do that we can find our ph but first I need to take into account these non common ions from it, I'll be able to determine my ionic strength. So this is made up of lithium ion and nitrate ion, it's a 1-1 relationship. So the concentrations will not change. So .05 molar for the lithium ion times its charge squared plus the concentration of the nitrate ion times its charge squared. That gives me .05 for the ionic strength. And now that we know what the ionic strength is. We look up on our activity coefficients chart for the activity coefficients for barium ion and hydroxide ion. So when you look those up so we have barry mayan here which is X. When you look up at its activity, cold fishing you're gonna see that it is equal 2.465 Times Hydroxide which is two x. Don't forget that it's squared times the activity coefficient. When you look it up you get .81 squared. Alright. K. S p is 5.0 times 10 to the -3 equals. Alright so we have a lot of numbers that are multiplying with one another. So we're gonna have to take all of those into account. So we have We're gonna have .465 times .81 Squared two Squared is four. So that's when you multiply all those together. That gives me 1.22035. And don't forget we have our X variables. We have X. Here and then X. Here is getting squared. So that's X squared X. X times X squared, gives me X cubed, Divide 1.22035. So X cubed Equals .004097. Take the cube root of both sides here. So when we do that that's gonna give me x equals .160016 Molar. But remember we're looking for the concentration of hydroxide ion O H minus and O h minus does not equal X equals to X. So h minus concentration equals two X. So it's two times this number we just found. So that's .320032 molar. Next we're going to figure out what the activity of hydroxide is. So the activity here would equal the concentration of the hydroxide iron. We just found times its activity coefficient. So the concentration we just found is this And we bring back that activity coefficient we found earlier of .81. So that's gonna give me .2592-5. Now that I have the activity of hydroxide, I can take the negative log of that to find P. O. H. So that's negative log of that number. So that's gonna give me a p.. h. of .586 ph equals 14 minus P. O. H. So my ph at the end is approximately 13.41. So again remember when we're dealing with an ionic compound that's dissolving in solution and then all of a sudden they introduce non common ion effect ions. That means that those are going to help increase the ability of my on ionic compound by ionic strength since ionic strength is in play, that means activity coefficients are in play. So we're gonna have to incorporate them within our calculations to find the final concentrations of the specified ions. So keep in mind some of the techniques we've used here, which is just a continuation of concepts we've learned in terms of calculating PH.
