Morphine is a weak base. A 0.150 M solution of morphine has a pH of 10.7. What is Kb for morphine?

Video transcript

Hello, everyone today. With the following problem, morphine is a weak base. A 0.1 50 molar solution of morphine has a ph of 10.7. What is the equilibrium constant of B for morphine or the ionization constant for morphine? So we don't necessarily know the like of a formula of morphine. So we can just use B as a placeholder. So first, we want to set up an ice table. So we have B which is our weak base. It's aqueous, we add in water which is a liquid. We react that in a reversible reaction such that we get the following. We have our conjugate acid because it accepted the proton. And we have our conjugate base which is our hydroxide, which is aqueous. We don't include liquids in our equation as well. So our initial concentration of our weak base is 0.1 50 molar, we have zero for both of our products. And then since we're taken away from our reactants, we have minus X for the change and we have positive X for our products. And then our equilibrium is just our I plus. Our C. Our second step is to find the equilibrium of our expression for our KB. And it's going to be KB is equal to the products over the reactions. So for our products, we have X times X divided by 0.1 50 minus X. And that essentially would translate into X squared divided by 0.1 50 minus X. So what we need to do is to calculate X, we need to calculate the concentration of our hydroxide. So first we can calculate the POH which is 14 subtracted by the ph. So that would be 14, subtracted by 10.7 or 3.30. And then to calculate the concentration of our hydroxide, we simply have 10 rays of the negative of our POH not our P hr POH. So we have 10 raised to the power of negative 3.30. And that gives us a value of 5.0 12 times 10 to the negative fourth. And this will also be our concentration of our B plus. So to calculate KB, we will return back to our equation and we have 5.0 12 times 10 to the negative fourth squared divided by 0.15 or 0.150 subtracted by 5.0 12 times 10 to the negative fourth for a final answer of 1.680 times 10 to the negative six or enter choice C. And with that, we have solved the problem overall, I hope this helped. And until next time