Determine the pH of a 0.227 M C 5 H 5 N solution at 25 °C. The K b of C 5 H 5 N is 1.7 x 10 -9 .

Hey everyone, we're asked to calculate the concentration of our hydroxide ion, our ph and P O. H. For a solution of hydroxy amine. And they provided us our KB And it has a concentration of 0.40 moller first. Let's go ahead and write out our reaction. So we have our hydroxy amine and this is going to react with water. Now when this reacts with water, we end up with the conjugate acid of hydroxy amine, plus our hydroxide ion. Now let's go ahead and create our ice chart. Since everything is completely balanced out. Creating our ice chart, we were told that we had 0.40 Moeller initially of our hydroxy amine. We do not include our water in our expression since it is a liquid and we have zero of our products. Initially, our change is going to be a minus X on our reactant side and a plus X on our product side. Since we're losing reactant and gaining products at equilibrium, we have 0.40 minus X. For our react inside and an X. And an X. In our product side. Now let's go ahead and use our KB in order to determine our X. As we know our KB is equal to the concentration of our products over the concentration of our reactant. So in this case will be the concentration of the conjugate acid of our hydroxy amine times the concentration of our hydroxide ion, all divided by the concentration of our hydroxy amine Plugging in our values. We know that our KB is 1.1 times 10 to the - and this is going to be equal to X times X. All over 0.40 minus X. Now we can go ahead and check if we can omit the X. And our denominator. We can do so by taking our 0.40 and divide this by our kB of 1.1 times 10 to the negative eight. Now, if we get a value greater than 500 then we can safely omit our X and our denominator since it is negligible And in this case it is greater than 500. So we can remove our X. and our denominator. Now let's go ahead and simplify this. So we have 1.1 times 10 to the negative eight. And this is going to be equal to X squared over 0.40, multiplying both sides by 0.40. We end up with x squared is equal to 4.4 times 10 to the negative nine. Now we can take the square root of both sides. And this gets us to an ex of 6.633-5 times 10 to the - moller. Now this is going to be the concentration of our hydroxide ion and also the concentration of the conjugate acid of our hydroxy amine. Now let's go ahead and determine our P. O. H. And our ph to determine our P. O. H. We're going to take the negative log of the concentration of our hydroxide ion. So, plugging in those values, we get the negative log Of 6.63, 3 - five times 10 to the -5. This gets us to a p o. H of 4.18. Now we can use this value to determine our ph as we know, our ph is going to be equal to 14 minus our p. O. H. So, plugging in that value, we get 14 -4.18, which gets us to a ph of 9.82. And these are going to be our final answers. Now, I hope this made sense and let us know if you have any questions.