The acid-dissociation constant for chlorous acid 1HClO22 is 1.1 * 10-2. Calculate the concentrations of H3O+, ClO2-, and HClO2 at equilibrium if the initial concentration of HClO2 is 0.0125 M.

Video transcript

Hi everyone. This problem reads hyper brahmas acid has an acid dissociation constant of 2.8 times 10 to the negative nine if the initial concentration of hyper brahmas acid is 0.1750 moller what are the concentrations of hydro nia my on hyper bromine ion and hyper brahmas acid at equilibrium. Okay, so our goal here is to find these following concentrations at equilibrium and we're told we have hyper brahmas acid. So the first thing we're going to need to do is because we're at equilibrium we're going to need to create an ice table. Okay so let's go ahead and write out our reaction. So we have hipaa brahmas acid. Okay at equilibrium is going to produce hydro ni um ion plus our hippo bro might and ion. Okay, so we'll go ahead and draw this line here to divide our reactant from our product and we'll write out ice On the side. Okay? So our eye represents our initial concentration and we're told the initial concentration of our acid is 0.01750. Okay, so that means we have zero product and our reaction is moving to the right so we are our reactant are being consumed and our products are being produced. Okay so we have minus on the reactant side and plus on the product side and we have one mole of everything. So we're just going to have X. Okay so now we're going to for our equilibrium row, combine our I and E. Row. So for our equilibrium row we have 0. minus X. And then just X. For these two. Now for us to be able to solve for our concentrations at equilibrium, that's what the hero of our table stands for equilibrium. We need to figure out what is that value of X. Once we find our value of X. We know X. Represents our hydro knee um ion concentration and it also represents our hipaa bromide ion concentration. And then our our hypothalamus acid is represented by 0.1 750 minus X. So we need to figure out what is X. So let's go ahead and write out our K. A. Expression. Okay so R. K expression are acid dissociation, constant expression is equal to our products minus our reactant. So looking at our equation we have our hydro ni um ion concentration times are bromine ion concentration. So our products over our reactant. So our hipaa promos acid. Okay so R. K. A. Is equal to that and we know what our value of K. A. Is. It was given in the problem we're told it's 2. times 10 to the negative nine. Alright so what we're going to do now is plug in the equilibrium row of our ice table into this equilibrium expression. So we know that our concentration of hydro ni um is represented by X concentration of hyper bromide ion is represented by X. And then our hypothalamus acid is represented by 0.1750 minus X. And this is equal to R K. A. Okay so remember we said we need to be we need to solve for X. All right, so that's the goal here. So we can find out our equilibrium concentrations. Alright so we can now paying attention to our denominator here. We see we have a minus X. We can check to see if this X is negligible. If this X is negligible, we can go ahead and ignore this minus X. And it will just be 0.1750. But we first need to check is X negligible. Alright so let's write that down is X negligible. And the way we find out if X is negligible is we're going to take our initial concentration. So our initial concentration is 0.01750 and divided by RK. A. value which is 2.8 00 times 10 to the negative nine. If this value is greater than 500 then we can say X is negligible but if it's less than 500 then X is not negligible. So when we do the math it does end up being greater than 500. So yes X is negligible. So we're going to go ahead and ignore this minus or we're going to cross out the minus X. Okay so let's go ahead and simplify. So we get X squared over 0.1750 is equal to 2.800 times 10 to the negative nine. Alright so now we're solving for X. So let's simplify here. So we have X squared is equal to 0.1750 times 2.800 times 10 to the negative nine. Okay so let's simplify the right side. Okay and when we simplify and take the square root we get X. Is equal to seven times 10 to the negative six. Okay so remember we know that X. Is equal to our concentration of hydro ni um ions and our concentration of our hipaa bro. Might and I on. Okay so we know the concentration of those two. So let's go ahead and write that down. So our concentration of hydro knee um ion is equal to seven times 10 to the negative six. And our concentration of hipaa bromine ion is equal to seven times 10 to the negative six. Now what about our concentration of hypothalamus acid? Okay what is that? So we know in our table it says that its equilibrium concentration is going to be equal to 0.1750 minus X. So let's go ahead and do that. Alright so we said it's equal to 0.1750 minus X. So this is going to be equal to 0. minus. We said X is seven times 10 to the negative six. Alright, So the number we get is 0.17493. So let's go ahead and write that here 0.17 or 93. So these are our three concentrations at equilibrium. Okay. And we were able to do that by solving for X. That's it for this problem. I hope this was helpful.