The AIDS drug zalcitabine (also known as ddC) is a weak base with a pKb of 9.8. What percentage of the base is protonated in an aqueous zalcitabine solution containing 565 mg>L?

Video transcript

Hello. In this problem we are told that FLUoxetine is an antidepressant drug used to treat major depressive disorder and O. C. D. It is a weak base with the Mueller mass of 309.33 g per mole and a pkb of 3.90 grass. To calculate the percentage of protein database in a 450 mg per liter. A quick solution of FLUoxetine. Let's begin by calculating the concentration of our base initially which is flocks team will represent us as a capital B. We have four and 50 mg per leader converted milligrams, two g and then make use of the more mass to go from grams moles. So our milligrams cancels grams, cancels concentration initially then is 1.45 times 10 to minus three Mueller. Let's now create an ice table. So we have our base undergoing hydraulic sis so our base will accept the proton from water which acts as an acid will form the conjugate acid of our base and hydroxide ions. We have initial change in equilibrium. Initially we have 1.45 times 10 to minus three molar of our base. We'll ignore the water since it's a pure liquid and we have initially none of the conjugate acid or hydroxide in our changes minus X plus X and plus X. We combined the initial and the change to get our equilibrium, you can find the K. B. Value with all that. It's equal to the in 10 to the negative P. K. B. This is equal to 10 to the negative 3.90 Which works out to 1.25. 9 Times 10 : -4. Writing our equilibrium constant expression maybe then is equal to our product concentrations of our reacting concentration. Water being a pure liquid does not appear in our equilibrium constant expression. This then from ice table is equal to X times X over 1.45 times 10 to minus three minus X. This is equal to 1.259 Times 10 : -4. So we'll check our simplifying assumptions, see if we can eliminate the minus X. So to check our simplifying assumption and we'll take our initial concentration of our base divided by the KB. So this is 1.45 times 10 to minus three. But by 1.25, 9 times 7 -4. This works out to 11.5 which is not greater than 500. So we'll need to make use of the quadratic equation we have, then X squared is equal to 1.259 times 10 to minus four will move the denominator to the right hand side. So I applied by 1.45 times 10 to minus three minus x. We'll simplify things, move everything over to the left hand side. We'll get X squared plus 1.259 times two minus four times x minus 1. times 10 minus seven is equal to zero, solve our quadratic equation. We have X is equal to negative B plus or minus the square root of b squared minus four A. C. All over two. A plugging things in From our quadratic equation we get X is equal to negative 1.259 times 10 to minus four plus or minus square root of 1.259 times to the minus four squared minus four times A. Which is one times C. Which is negative 1.826 times 10 minus seven. All over two times a. Which is two times 1. So working out what's under the square root we get 1.259 times to the minus four plus or minus. Then eight point 639 times 10 - all over to We get two possible routes 3.696. 1 Times 10 -4 Mueller. And the other one is negative 4. 4 9 -4 Mueller. So the negative value doesn't make sense. So our X. Then is equal to the 3.6961 times 10 to minus four. Looking at our ice table, you know then that this is the concentration of our prominent form of our base. So we can calculate the percent pro nated by taking our concentration of our protein, a form of base divided by our initial concentration of the base Times 100%. This will work out too. 3.6961 times 10 to minus four moller provided by 1.4, 5 times 10 -3 Mueller, 100% percent coordinated, Works out to 25%. Thanks for watching. Hope this helped.