Pseudogout, a condition with symptoms similar to those of gout (see Problem 126), is caused by the formation of calcium diphosphate (Ca2P2O7) crystals within tendons, cartilage, and ligaments. Calcium diphosphate will precipitate out of blood plasma when diphosphate levels become abnormally high. If the calcium concentration in blood plasma is 9.2 mg>dL, and Ksp for calcium diphosphate is 8.64 * 10 - 13, what minimum concentration of diphosphate results in precipitation?

Video transcript

Hello everyone today we are being given the following example and asked to answer and solve for the minimum concentration of oxalate that will cause the formation of calcium oxalate crystals. So we're giving a little background of calcium oxalate crystals. We are told they are formed in the kidneys and are the most common form of kidney stones. Were given some more background information but the important thing to know is the normal level of calcium in the blood being between 8.6 and 10.3 mg per liter. And then we're saying if the calcium concentration in the blood is nine mg per deciliter and the K. C. K. S. P of calcium oxalate is 2.7 times 10 to the negative nine. What is the minimum concentration of this oxalic acid that will cause the formation of these crystals. And so the first thing we wanna do is you want to find the concentration of these calcium two plus ions. And so we can start by giving by getting the the concentration of regular calcium in the blood in this example And we're gonna have to convert this into polarity. And so to do that we take our nine mg per one liter. And we want to get rid of milligrams and convert to regular grams. So we're going to say that one mg is equal to 10 to the negative third grams. And they were going to say that one mole is equal to the molar mass of calcium which according to the periodic table is 40.8 g per mole. And then we have leaders that we want to eventually have our answer. And so we're going to say that one desolate er is equal to 10 to the negative one leaders. And so when our units eventually canceled out we are going to be left with 2. times 10 to the negative third modularity for calcium two plus ions. We don't want to set up an ice table but to do that we have to solve or we have to figure out what this calcium oxalate would look like once it is dissolved in water. So we have this form in the solid and we say that when we do it dissolves into calcium two plus ions as well as one oxalate to -1. And so when we have our ice table it looks a little like this. We're not worried about the solid because solid is not incorporated in our ice tables. We have an initial concentration of calcium ions which is 2.2456 times 10 to the negative third. Of course oxalate will be zero. We're gonna represent the change by saying plus X. Because we only have one of the calcium and we also have one of the Oxley as well. And so when we do the E. That's essentially I plus C. So we're gonna have two plus 2.2456 times 10 to the negative third plus or m and then for obviously we're going to have X. And the reason why we don't incorporate X. For calcium is because X. Here is much smaller than our initial concentration. So it is therefore negligible. We're gonna use our K. S. P. Equation. We're going to take A. S. P. Is equal to our calcium two plus, multiplied by our oxalate two minus R. K. S. P. As we said before is 2.7 times 10 to the negative nine. And we're gonna plug in our concentrations here 2. times 10 to the negative third. And then we're going to have X. For our oxalate When we saw for X. We're going to have 1.2 times 10 to the negative six smaller. And this is going to be our final answer. I hope this helped. And until next time.