Ksp and pH

Jules Bruno
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Hey guys. So in this example were asked to find the pH of a saturated solution of aluminum hydroxide Here we're giving the K s P of aluminum hydroxide is being one point nine times ten to the negative nine. Now, since we're giving the k sp oven Ionic compound, we're gonna take that ionic compound, which will be a solid We'll break it up into its ions. So it breaks up into Aluminum ion, which is in Group three A. So that's why it's plus three. And then we have here three hydroxide. Now remember, with ESPN means we're looking at a nice chart. Remember, in an ice chart, we ignore solids and liquids here. I don't tell you that we're dropping this in a solution that already has any one of these ions. So that means that this is being thrown into pure water, which means there's no common I in effect, which means that initially, these both are zero. Remember their products. So we're making them. So this would be plus X here there's a three year so this would be plus three x plus X plus three X. Now we say k SP just equals products because are reacting is a solid, so ignored, so equals aluminum ion times hydroxide ion Remember, the coefficient becomes the power. So here we have one point nine times ten to the negative. Ten equals x times three x, which will be cubed. So three cubed is three times three times three, which is twenty seven and then execute will be execute. So now we have X times two x cubed. So the ex just add up. So that's twenty seven x to the fourth equals one point nine times ten to the negative ten. We're trying to isolate X here, so divide both sides by twenty seven. So we'll bring this work over here now, So X to the fourth equals seven point zero four times ten to the negative twelve. Now, we don't want X to the fourth. We just want X at this point. So some of you may see this button on your calculator. We'll see the square root sign, but then you'll see an X here. Here, we need to take the fourth route. So you hit four. Then you would hit this button here that you'd see than parentheses, plugging this number, close parentheses Some of you may not have that number. So instead, what you'll do is you'll do in parentheses seven point zero four times, ten to the negative. Twelve. You should put that in parentheses in your calculator. Then what you'll see is you'll see this button. Why did the X or you might see just this carrot, whichever one you have to get that. But next and then in parentheses, you would wanna do one to the fourth. Yeah, and if you do that correctly, you should get as your answer. Point zero zero one six three Moeller So this represents the Mueller soluble ity of our compound. But what we need to realize is we're looking for pH. But we don't have pH in our formula. What we have instead is LH minus, which means that if I could figure out the concentration of hydroxide ions, I could find P o h. If I know p o. H. I can then find pH. So we don't want the concentration of the whole compound. We just want the concentration of hydroxide ion. So you take this X and you plug it in here for hydroxide ion. So you'd say, Oh, h minus equals three x and again acts equals point zero zero one six three Mueller. So multiply that by three gives me point zero zero four eight nine Mueller So there goes the concentration of hydroxide ions. So if I take the p o h of that, that means I'm gonna take the negative log of O H minus. So just plug this number in, take the negative log of it that gives you as your p O H two point three one, But again, we want Ph instead. So it's pH equals fourteen minus P o h. Okay, so that's gonna give you eleven point six nine as the pH of your solution. So this is the approach you have to take. Since they're talking about GSP, we do a nice chart to find X, which is the Moller saw the ability of the entire Ionic compound. But we're looking specifically for the ion. Any time you find the concentration of an ion, look on the equilibrium line. Take that X answer that you found and plug it in for the particular ion you're looking for. That will give us the concentration of hydroxide ion. In this case, which gives us P O h. Which then we can change later. PH So remember the steps involved in this particular type of question?