The pH of 2.65 m CH 3 NH 2(aq) is 12.54. determine the value of K b for methylamine.

Hey everyone, we're told that at 3.93 times 10 to the negative five molar solution of methyl amine, A weak organic base has a ph of 9.56. What are the KB and Pkb for this base first? Let's go ahead and write out our reaction. Since they didn't give us the formula for methyl amine. We can simply write methyl amine as B. And this is going to react with water and since we know this is a weak organic base, we're going to get our conjugate acid of methyl amine. And we can denote that by writing H. B. Plus and this will also disassociate into our hydroxide ions. Since we're looking for R K. B. And R P K B. We should first start off by finding our P. O. H. And we can find that by taking 14 and subtracting our pP So plugging in that value, we get 14 minus 9.56 which gets us to a P O. H. Of 4.44. Now to find the concentration of our hydroxide ions, we've learned that we can simply take 10 to the negative P. O. H. So plugging in those values, we get 10 to the negative 4.44 Which gets us to a concentration of 3.6308 times 10 to the -5 moller. And this is our concentration of our hydroxide ions. And as we can see above this is also the concentration of our conjugate acid of our methyl amine. Since we have a 1 to 1 ratio, solving for the concentration of our methyl amine, we can simply take our initial which was 3.93 times 10 to the negative five moller. And we can subtract our concentration of our hydroxide ions. And this is going to be 3.6308 times 10 to the -5. This gets us to a concentration of 2.99, 6 times 10 to the -6. Now to find our KB, we know that our KB is equivalent to our products over our reactant. So in this case it will be the conjugate acid of our methyl amine, times our hydroxide ions all over our methyl amine lugging those values in. We got 3.6308 times 10 to the -5 Moller. And we're going to multiply this again by 3.63 oh eight times 10 to the negative five molar. And we're going to divide this all by 2.996 times 10 to the negative six molar, Solving for RKB. We end up with a value of 4.4001 times 10 to the -4. Now to solve for P K B. All we need to do is take the negative log of our kB. So plugging those values in, we get negative log of 4.4001 times 10 to the -4. This gets us to a Pkb of 3.36. And this is going to be our final answers now. I hope that made sense and let us know if you have any questions.