Here it tells us a weak acid has a of 5.35. What is the hydronium ion concentration in a 0.10 molar solution of this weak acid? We know that we're dealing with a weak acid, and the general generic formula of a weak acid is HA. Now remember, weak acids and weak bases react with water within the solution. So this weak acid will react with water.
It is the acid, so that means water is the base. Remember, according to theory, the acid donates an . What we're going to create is . We're dealing with an ICE chart because we're dealing with a weak species. Anytime we're dealing with a weak acid or weak base, we set up an ICE chart.
Remember, in an ICE chart, we ignore solids and liquids. This water, which is a liquid, is ignored. Our initial concentration is said to be 0.10 molar. We are not given the initial concentration for our products, so they're both 0. Remember we lose reactants in order to make products.
Bring down everything. Since we're dealing with a weak acid, we want to use our acid dissociation constant or . is equal to products over reactants. Our products multiply together divided by our reactant on the bottom. Again, we ignore water because it's a liquid.
Here, the issue is we don't have , we have . So, we're going to have to convert into . Here, . We plug that value given to us of 5.35 in. That gives me .
That's my which I'm going to plug over here. At equilibrium, both my products are x. So divided by what's on the bottom which is . Here, we have this minus x. Although this is analytical chemistry, we want to be as precise as possible.
If that x variable is insignificant enough, we can ignore it. To determine if we can ignore it, we do the 5% approximation method. Now, the 5% approximation method says that if I take my initial concentration of my weak species and I divide it by its dissociation constant, which is in this case, if I divide the initial by the and the ratio gives me a value greater than 500, then I can ignore that minus x. My initial concentration is 0.10 molar. We're going to divide it by the we just found.
. When I do that, it gives me 22,387.2 as a value. That number is definitely greater than 500. According to the 5% approximation method, I can ignore that minus x there. All we do now is we solve for x.
We're going to multiply both sides by 0.10. We're going to have . We just want x, so we're going to take the square root of both sides here. So when I take the square root of both sides here, I get . When I solve for x here, this x gives me this x, which is equal to .
Remember, when we're setting up an ICE chart for a weak acid or a weak base, anytime we find x, that represents either my concentration or my concentration. Since I'm dealing with an acid here, it's going to give me the concentration, which is my hydronium ion concentration. Based on our answer, option F would be the correct choice. Just remember some of the fundamentals that we went over concerning this question.
If we're dealing with a weak acid or a weak base, in order to find hydronium ion concentration or hydroxide ion concentration, we'll have to set up some type of ice chart in order to solve for x. Once we do, we'll have that number. If we wanted to go a step further, we could have taken the negative log of this concentration, and that would have given me the pH. Here, we're not asked to find the pH. We're just asked to figure out what the concentration is of the hydronium ion. We just stop there, for x being molar.