Salts containing the phosphate ion are added to municipal water supplies to prevent the corrosion of lead pipes. (a) Based on the pKa values for phosphoric acid 1pKa1 = 7.5 * 10 - 3, pKa2 = 6.2 * 10 - 8, pKa3 = 4.2 * 10 - 132 what is the Kb value for the PO43 - ion?

Video transcript

hi everyone for this problem. It reads citrate salts have medicinal use, such as treating metabolic acidosis and occasional constipation from the K. A. Values of citric acid, calculate the KB value of the citrate ion. Okay, so we want to calculate the KB value. And in the problem we're given three K s. Okay. The reason that we're given three K. S is because we're dealing with citric acid and in citric acid when it's placed in water, it will lionize in a three step manner. So this is why we have three K. A values for each of these three steps, we have a different value for the acids dissociation constant. So in order for us to calculate the KB value, we're going to need to have an equation that relates K and K B. And that equation is K W equals K. A. Times K B. Okay? And our goal here is to solve for K B. So let's go ahead and rearrange this equation. And when we rearrange it we get K. B is equal to K. W over K A. Okay, So because this is a three step process, we're going to want to choose the last K. A. Value. So we're going to write K A. Three here. Okay? And we have everything we need to plug in. So let's go ahead and plug in and solve for K P. Which is what we're being asked to solve for. So K W is a constant that we should know and that is 1.0 times 10 to the negative 14. So if you don't have that memorized, that's something you should remember is that K W is equal to one times 10 to the negative 14. Now R K A. We're going to use our K. A. Value R k A three value, which is 4.0 times 10 to the negative seven. Okay. So now that we've plugged everything in, let's go ahead and solve. And when we solve, we get KB is equal to 2.5 times to the negative eight. And this is our final answer for this problem. Okay, so that's it for this problem. I hope this is helpful.