The solubility-product constant for barium permanganate, Ba1MnO422, is 2.5 * 10-10. Assume that solid Ba1MnO422 is in equilibrium with a solution of KMnO4. What concentration of KMnO4 is required to establish a concentration of 2.0 * 10-8 M for the Ba2 + ion in solution?

Video transcript

Hello everyone. So in this video we're trying to determine the amount of any two S. 04 that's required to make a 3.5 times 10 to the negative three moller a G plus solution. So first things first I wanna go ahead and write out the equation for this A. G two S. +04 relating it to its K. S. P. Value. So it's going to be a G two S. 04. It's going to go ahead and associate into its ions which is two moles of a G plus and one mole of S. +042 minus. So in this problem what we're given is the concentration of R. A. G plus that is of 3.5 times 10 to the negative three molar. We are also given the K. S. P. Value which is of 1.2 times 10 to the negative five. If you're called the um equation for ksB it's going to be equal to the concentration of our two products. So first one is going to be a G plus, this coefficient in front of the A. G. Two um or a G plus and this equation will become the power now so to the power of two multiplied by the concentration of our second product. So S. 042 minus. So we're trying to solve for the concentration of S. 042 minus here, I'm going to pretend like I'm going to have this as an X. And we're basically solving for R. X. So I'll go ahead, divide both sides by this value here if we do that we can get that. The concentration of S. 042 minus is equal to 1.2 times to the negative five over the concentration of a G plus squared. So I'm gonna go ahead and find a plug in my concentration here which is given to us in the problem. So we can do that now, and that will be 1.2 times 10 to the negative 5/3 100.5 times 10 to the negative three squared. Putting this into my calculator, I get the value of 0. Moller and that's going to be the concentration of S. 042 minus. That is needed to make 3.5 times 10 to the negative three moller. A. G plus solution. So this is my final answer. Thank you all so much for watching.