The solubility product for Zn1OH22 is 3.0 * 10-16. The formation constant for the hydroxo complex, Zn1OH242 - , is 4.6 * 1017. What concentration of OH- is required to dissolve 0.015 mol of Zn1OH22 in a liter of solution?

Video transcript

Hello everyone in this video we will go ahead and calculate for the amount of hydroxide and maturity. So first we can see that were given to different molecules and its respective K. S. P or K. F value. That hints to me that when you go ahead at first route the chemical equations. So for first molecule here, a L O H three, that's going to be my starting re agent here on the left side of the equation. It's going to go ahead and associate into a L three plus and three moles of O h minus. It's given K. S. P value is 1.3 times 10 to the negative 33. As for a KF value, the formation of this um complex ion on the left side, we have RAL three plus reacting with foremost of hydroxide to go ahead and create this or form this complex ion. And it's K. F. value is of course 3.0 times 10 to the 33 power. And that is from our equation or our problem here. Alright, so we can go ahead and see that the A. L three plus will go ahead and cancel here as well as three moles over hydroxide on the second equation. Oh, just leave us with one mole of hydroxide. So adding these two equations up, we go ahead and get a L. O. H. Now, age three reacting with one mole of H R O H. Now to give us our complex ion of a L O H four - And we need a constant value. That's when KSB is multiplied by RKF value. If we put that into my calculator, I get the value of 3.9. So at equilibrium it's going to actually write this out at equilibrium. I'll just denote that as eq our moles of this. A L O H three is equal to the moles of my complex ion and that is of 0. moles. Again, that's given to us in the problem right over here. Alright, so knowing this information, let's go ahead and solve for the concentration of our complex ion. And the concentration is of course moles over leaders. Since we're given moles 0.780 moles as well as our volume solution, which is 1.5 liters. We can go ahead and just insert this into the calculator, getting the polarity of 0. Moeller again scrolling down so we can go ahead and now solve for the K value. We have the creation K equals to the concentration of our complex ion over the concentration of our hydroxide. So we have a K. Value actually of 3.9. We saw this earlier and this is equal to well we also have the concentration of our complex ion being 0.5 to moller but we do not and are solving for R O H minus concentration. So we're gonna go ahead and divide this side or both sides actually by 0.5 to moller. So we're basically rearranging the equation in black to give us that the concentration of hydroxide is equal to 0.52 molar, too, voted by 3.9. Again, I'm going to go ahead and put this into my calculator, giving me that the concentration of my hydroxide is 0.13 molar. And this right here is going to be my final answer for this problem. Thank you all so much for watching.