Chapter 16 Problem 58 from the book Chemistry. The Central Signs The question states the K a constant for each cielo to is 1.1 times 10 to the negative, too. It access to calculate the concentrations of H 30 plus the Cielo to minus and h Cielo to had equal. They're real when given the initial concentration of Tzar point, sir. 1 to 5 more clarity. So the first thing we have to do is write off. Write our equation for this reaction. So we have HCL 02 It's an Aquarius in addition to water, which then creates C l o two minus plus h +30 plus right in the question acts for all the concentrations at equilibrium. So we know we had to do a nice table were the ice table just stands for initial changed and then the equilibrium So equilibrium you just add the two different things up at the initial on the change. So we first started off with initial concentration a 0.125 hilarity. We didn't have anything to start off with water and water. It does not enter change anything in our table, so I was just cross it out and then we don't have any certain concentrations of our Cielo to O r each for you. Plus, so now we talk about change. So what's actually changing in the reaction to cause our each seal of two to go to equilibrium? So for this to happen, we're actually gonna have tto lose some of our HDL or two since we don't have any starting products and they were going toe at X to both of these sides. In essence, we have that within just add these two rows up, so has their 20.125 plus and minus eggs. And then we just have X and X. Now, since we have the general basis for our equilibrium now we need to write R K expression. So we have K is equal to our products or reactant. And so our products is R C L 02 minus times are each 30 plus. And then our reactant is the H. C. Uh oh, too. And once again, water is not included because it is not a Prius. And so now we just plug in the values we have at the equilibrium So for both Cielo to minus and h the a plus that they're both ex. So I'm just going to write X squared and then for HCL 02 we have 0.125 minus x and in the question they gave us. But our K value is in its 1.1 times 10 to native to and I would just solve for X into solve for X you can use the solver function in your calculator or you consulted Algebraic Lee. But another thing to point out is that you could also there's some really good videos on how to use the solver function of finding accident year on different websites. So what we're going to do is I'm just gonna multiply my ex ever here and dio 1.1 times 10 to the negative too. Is there a point, sir? 125 minus X is he goto X squared and then multiply my oh, these two numbers out together and get 0.7 five and then minus the 1.1 times 10 to the night of two X is equal to X squared. And now I have a quadratic formula, and I would just bring it all to the same side. And so I have X squared plus 1.1 times 10 to the negative two x minus. Is there a point in Sierra +075 is equal to zero and then I would sign is equal to x mean one bee is a good 1.125 and C is equal to this value. And do the staggering I mean the project formula to suffer ex um so our ex actually ends up being seven point for five times 10 to the negative three. And I got this number by Jane the solver function in my calculator. Or like I said, you can also do a hand out by solving for the Pythagorean theorem. We're in this case are a hey is eagle toe one b is equal to 1.1 times 10 to the negative, too. And C is equal to negative. Zahra Point, Caesar's heir of 75 And in just solving for exactly. So now, since we have X now we can solve for our equilibrium. Concentrations down here and since way have excess just values. You're here than R C L 02 and HBO Plus is just 7.4 five times since a negative three. And the sinking for this one and our each Cielo to is going to be their points or one, 25 minus R x value. And I put that into my calculator end. I have the final member of 0.50 for five. So these are my final concentrations at equal there, Bram.