An unknown salt is either NaF, NaCl, or NaOCl. When 0.050 mol of the salt is dissolved in water to form 0.500 L of solution, the pH of the solution is 8.08. What is the identity of the salt?

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Hi everyone for this problem, it reads a solution was prepared by dissolving . moles of unknown salt and water to a total volume of .750 L, if the ph of the solution is 8.12, which of the following salts can it be? And we have potassium bromide, potassium fluoride and potassium bromate. So we want to know which of these following salts can it be? So let's start off by looking at the ph given. So we see we have a ph of 8.12. And based off of that ph we can see that this is a basic ph Okay, and so we want to look for which of the following salts is going to have a solution that is basic. Okay, so the thing we're going to want to do to solve this problem is to determine the type of solution. Each of these salts come from. Okay, so let's start off by dissociating each and to its ion. So we can start off with a and we have potassium bromide. When we dissociate, potassium bromide into its ions, we get a potassium cat ion and a bromide and ion. Okay, so we want to determine the acid and base from which the cat ion and an ion derived from and we can do that first for the cat ion by adding a hydroxide to it. Okay, and for the an ion we can add a proton to it. Okay, so for the cat eye on when we add that hydroxide, we see we get potassium hydroxide. Now, if we recall our list of bases, we know that potassium hydroxide is a strong base. Okay? So whenever we have a strong acid or a strong base, that means its conjugate is going to be weak because they have an inverse relationship. So because we have a strong base, that means its conjugate is going to be weak. So we have a weak conjugate. Whenever we have a weak conjugate, that means the solution is going to be neutral. So we know that the cat eye on here is neutral. Alright next for our an eye on when we add a proton to it, we get the following acid. Okay. And from our list of strong acids, this is a strong acid. And like we said if we have a strong acid, it's going to have a weak conjugate. And when we have a weak conjugate that means it is neutral. So overall potassium bromide is neutral. The type of solution is neutral. So knowing that this solution is neutral, we can eliminate answer choice A as an answer because we know that in the problem it says if the ph of the solution is 8.12 and that's a basic P. H. Here are potassium bromide does not meet that. Okay, so let's move on to be Okay, so for answer choice B. We have potassium fluoride. When we dissociate potassium fluoride into its ions, we get the same, we get a potassium cat ion and a fluoride and ion. So like we just did above we're going to determine the acid and base from which these cat, this cat ion and an ion derived from. So we'll add a hydroxide to our cat ion and we'll add a proton to our an ion. So like we said, potassium hydroxide is a strong base which means it has a weak conjugate. So we know this is neutral based off of how we just solved it. In the problem above our an ion is fluoride an ion. So when we add a proton we get Hydrofluoric acid and based off of our list of strong acids and strong bases. Hydrofluoric acid is a weak acid because we have a weak acid. This means we're going to have a significant conjugate base. So we're going to have a significant conjugate, which means the type of solution is going to be basic. Okay, so that means answer choice B is a possibility but we need to see what answer choice C. Is to confirm. So we know that the type of solution for answer choice B is basic. Let's do the last one. So for answer choice C. We have potassium bromate. Okay, let's go ahead and associate it into its ions. Okay. And we're going to do the same thing. We know that the potassium hydroxide is neutral. How about our acid? We get the following acid. And on our list this is a weak acid which means we're going to have a significant conjugate. So I'll just write significant conjugate base, which means this is basic. So here we see that answer choice C. The type of solution is also basic. So which one is it? Is it going to be our potassium fluoride or are potassium bromate? So now that we know that they're both basic, we need to calculate the KB of our unknown salt and compare it to answer choice B and C. To see which one is which salt it's going to be. Okay. And so the way that we can calculate the K. B. Or the acid dissociation constant for the base is for us to figure out what is our concentration of hydroxide. Okay, so for a concentration of hydroxide, the way we get that value is it is 10 to the negative P. O. H. So in order for us to solve for the concentration of hydroxide, we need to calculate P O. H. First because we do not have that value. Okay, how do we calculate P O. H. The equation that we use to calculate P O. H. Is P O. H. Is equal to 14 minus P. H. And the problem we're told what the value of our ph is. So we have, what we need to solve for P O. H. So we have P O. H. Is equal to 14 minus 8.12. So from that we know our P O. H. Is 5.88. Okay so now we have what we need to solve for our concentration of hydroxide. So let's go ahead and plug that in. So we know our concentration of hydroxide is equal to 10 to the negative 5.88. Okay so our value then is one point times 10 to the -6. This is our concentration of hydroxide. So now that we know that we can go a step further and calculate our KB expression. Let's go ahead and write out what our equation our reaction is for assault. So for assault our reaction is our salt dissociates into a hydro ni um ion plus a hydroxide ion. And when we write a KB expression for this R. K. B. Expression is products. Overreact ints. So we have our concentration of hydroxide times our concentration of hydro ni um over our reactant which is our salt. Okay so this is our KB expression and we need to plug in our values so we know what our concentration of hydroxide is because we solved it right here and our concentration of hydroxide is going to equal our concentration of hydro ni. Um So we're just going to square this number for the numerator. So we have 1.3183 times 10 to the negative six squared. Now our concentration for our salt is going to be the malaria t minus our concentration of hydroxide and hydro ni um so we need to calculate the molar itty of our salt and we can do that because we're given that information. So we know that mill arat. E. So trying to calculate the concentration of our salt. We know malaria T is moles over leader, we know our moles is 0.87 moles based off what was given in the problem and our moles over leader we are given the volume 0.750 liters. So that means our concentration is 0.116 molar. So our concentration is going to be the difference between that. Okay, so we have 0.116 minus 1.3183 times 10 to the negative six. Okay, so r k b once we solve is 1.5 times 10 to the negative 11. And when we calculate that we can now compare this KB to our KB values for our unknowns and this KB value matches the KB value for potassium fluoride. Okay, so potassium fluoride is going to equal are unknown salt because that is the exact kB for it. So if we go up to the top, our correct answer for this problem is going to be answer choice B. That's it for this problem. I hope this was helpful

An unknown salt is either NaF, NaCl, or NaOCl. When 0.050 mol of the salt is dissolved in water to form 0.500 L of solution, the pH of the solution is 8.08. What is the identity of the salt?

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Key Concepts

pH and pOH

Salt Hydrolysis

Identifying Ions in Salts