The pH of a 1.00 M solution of urea, a weak organic base, is 7.050. Calculate the Ka of protonated urea.

Video transcript

Hey everyone, we were told that a 0.85 molar solution of the week based paradigm has a ph of 9.58 determine the K. A. Of the conjugate acid of paradigm First let's go ahead and write out our reaction. So we have our paradigm and this is going to react with water. Now, when this reacts with water, we get the conjugate acid of our paradigm, plus our hydroxide ion. And that's because our water donates a proton to our period. In. Now let's go ahead and create our ice chart. Initially we were told that we had 0.85 molar of our period. Ayn and water won't be included in our expression since it is a liquid. And initially we had zero of our products formed, our change is going to be a minus X on our react inside and a plus X on our product side. Since we're losing reactant and gaining products on our reactant side at equilibrium, we have 0.85 minus X. And an X. And an X in our product side. Now looking at our ice chart, we can go ahead and use this information to write out our expression for our KB. So our KB is going to be our products over our reactant. In this case we have an X. Times and X all over 0.85 minus X. But first let's go ahead and use our ph which they provided to us to determine the concentration of our hydro ni um ion. As we've learned, we know that the concentration of our hydro ni um ion is going to be 10 to the negative ph Plugging in that value. We have 10 to the negative 9.58. So this gets us to a concentration of 2.630 to 68 times 10 to the negative 10 moller. So why is this important? This is important because we're going to use this value to determine our concentration of our hydroxide ion. So using R. K. W. We know that our K. W. Is equal to the concentration of our hydro knee um ion divided by the concentration of our hydroxide ion. Now to isolate our hydroxide ion, we know that this is going to be equal to our K. W. Divided by the concentration of our hydro ni um ion. So let's go ahead and plug in these values as we know our K. W. Is one point oh times 10 to the negative 14. And we're going to go ahead and divide this by the value. We just calculated four which is 2.630 to times 10 to the negative 10 moller. So this gets us to a concentration of 3. times 10 to the -5 moller. For the concentration of our hydroxide ion. So this value that we just calculated for is also going to be known as R X. Now we can go ahead and use this information and plug it into our K. P. Expression that we wrote out earlier. So we have KB is equal to X squared. So plugging that in, we have 3.8019 times 10 to the negative five Squared divided by 0. -X. Which is 3.8019 times 10 to the -5. Now, when we calculate this out, we end up with a K. B. Of 1.7006 times 10 to the negative nine. And as we've learned we know that our K. W. Is equal to our K. A. Times our KB. So to solve for R K. A. So to solve for R K. A, we're going to take our KW and divide this by our KB. So plugging in that value, we get 1.00 times 10 to the negative 14, divided by 1.7006 times 10 to the negative nine. This gets us to a k. A. Of 5.88 times 10 to the negative six which is going to be our final answer. Now, I hope this made sense. And let us know if you have any questions