Leah here from leah4sci.com/MCAT, and in this video we’ll look at the autoionization of water. Water is a very common and very unique molecule that you’ll study in Chemistry. If you try to understand the properties of water, one question you have to ask yourself, is water an acid or is it a base? Water or H2O is spontaneously break down to give you H+ and OH-. Now think about your acid base definitions, an acid is something that will donate an H+ in solution, well we have that right here. The arrhenius base is something that would donate an OH- in solution or the Bronsted Lowry base is something that’s negative or partially negative that can pick up an H+ in solution and we have that as well. So it’s not so much a question of, is it an acid or a base but rather when does it act like an acid and when does it act like a base? H2O is a good example of something that is Amphoteric and Amphiprotic, two words that are often confused with each other. Amphoteric tells you about a molecule that act as both an acid or acid base. But not every molecule acting as an acid or a base will accept or donate protons which brings us to the second definition of Amphiprotic. It has the word proton in it because this prefers to the molecule that can both donate and accept the proton or an H+.
Let’s take a look at what happens when we have two molecules next to each other. We’ll show the purple water molecule using one of the lone pair of electrons and Oxygen reaching for the green hydrogen on the second water molecule. Hydrogen can only have one bond so when the rear electrons grab the hydrogen, it has to let go of the other bond and those back electrons will collapse onto the green oxygen breaking the hydrogen away from the green hydrogen. We show equilibrium arrows because it’s a reversible reaction. And then we see the products where the atom is drawn exactly where they started but now the purple water molecule has the green hydrogen atom attached with the red bond.
It has just one lone pair and a quick formal charge calculation shows that it has a charge of plus one. The green water molecule is now just an Oxygen bound to a Hydrogen with its two initial green lone pairs, and now a third lone pair in black where the hydrogen broke away. A quick formal charge gives me a negative one. So which one was the acid and which one was the base? We’ll use the trick of which is more positive. We’ll pair up the purple groups and the green groups and notice that the purple groups, the water molecule on the left is neutral.
Hydronium on the right is positive. Positive is more acidic and neutral is the more negative one compare to plus one making it basic. So that means this is my base and hydronium is my conjugate acid. When comparing the green species, the one on the left is neutral, the one on the right is negative. Neutral is more positive when compare to negative one and the more positive makes it the acid. The negative Hydroxide is therefore going to be the conjugate base. But water doesn’t have to react just with another water molecule it can also react in acids and bases in solution. For example, if you dissolve a strong acid like HCl in water, it’ll break apart to give you H plus and Cl minus.
A water molecule will then use its lone electrons to reach for and grab that H+ and that will give you and H3O+. If H3O+ is a conjugate acid, then water started out as a base. Now for example if we dissolve a strong base in water like NANH2, this will break apart to give you NA+ and NH2-. The amide is a very strong base and when dissolved in water, Nitrogen will use one of its lone pairs to grab the Hydrogen off the water molecule. That will give you NH3 ammonia dissolved in solution plus OH- which is a base. If we look at the role of water in this reaction, H2O goes to OH-. If OH- is a base then in this case water is acting as an acid. So look at that, water acting as a base, give us conjugate acid, water acting as an acid give us a conjugate base. But in this video I want to look specifically at water stability to break apart.
If we look back at the initial reaction, H2O will be an equilibrium with H+ and OH- because it’s an equilibrium reaction, we need a way to calculate the ration of reactants to product. We need an equilibrium expression, so we write a Keq is equal to products over reactants. In this example, the products are H+ and OH- and the reactant is water. But don’t forget the phase of each reactant and product. Water is a liquid, H+ and OH- are dissolved in solution making them aqueous but you can only include concentrations in an equilibrium expression. Solids and liquids drop out because they equal to one and so the keq of the autoionization of water is written as the concentration of H+ times the concentration of OH- and this is called the keq of water or W simply written as kw.
The equation that you have to know is that kw is equal to the concentration of H+ times the concentration of OH-. At room temperature of 25 degrees celcius this will equal to 1 x 10 to the minus 14. One thing to keep in mind is that H+ dissolved in water will then picked up by another water molecule to give H3O+. So if you see this written as H3O+ and OH- instead of H+ it’s the same exact thing and the calculations are the same. This is a very useful equation if you’re trying to find the pH of a solution. So for example if I ask you to find the the pH of the neutral solution at 25 degrees celcius, what you have to recognize is that in a neutral solution, the concentration of acid is going to equal the concentration of base. If you have more proton, it’ll be acidic.
If you have more hydroxide, it will be basic. They have to equal each other for the solution to be neutral. And so instead of the expression kw is equal to the concentration of H+ times the concentration of OH- which is equal to one times ten to the minus fourteen. But how do you solve the equation with two unknowns?
The key here is to recognize that even though they’re unknown if they’re equal to each other, I can call the concentration of H+ x and the concentration of OH- x. And so I’m solving for x times x or simply x squared is equal to one times ten to the minus fourteen. Take the square root of both sides to isolate x and then simply find the square root of one times ten to the minus fourteen. To find the square of ten to an even power, simply divide it by two. And x which is equal to the H+ concentration which is equal to the OH- concentration is equal to 1 x 10 to the minus 7.
Another version of this equation to know is the p of this entire expression. Remember that p of anything is equal to negative log of that thing. So to take the p of this entire equation, let’s take it one at a time. The p of kw is equal to pkw, the p of H+ is equal to pH. The p of OH- is pOH. When you have multiple equation and you take the p of that expression it becomes plus. And that means pkw is equal to pH plus pOH and then the p of one times ten to the minus fourteen, we’re using the trick that I taught in the Math video series by simply taking that exponent negating it so negative becomes positive and that is equal to fourteen, and this is the second expression to know. pH plus pOH is equal to fourteen. Now this is a very very useful equation because if you’re ever given an OH minus concentration and you need pH or an H+ concentration and you need a pOH, you simply take what you have, take the p of that so you gain your pH or pOH and then your fourteen minus what you have to find the other one.
Let’s go back to our previous example and find the pH of a neutral solution. If pH is equal to negative log of the H+ concentration of negative log of 1 x 10 to the minus 7, we’ll use that trick again and that gives us pH is equal to 7. Now if we want to use this to find the pOH, we simply setup, pH plus pOH is equal to 14. Re-write this equation using what we know, 14 minus the pH equals the pOH and 14 minus 7 is equal to 7 which just goes to prove that in a neutral solution, the concentration of H+ and OH- are the same and the pH is equal to the pOH so that neither is stronger of the other because of the acid was stronger, you’ll have an acidic solution, if the base was stronger you’ll have a basic solution.
Be sure to join me in the next video where I show you how to use my pH wheel to find lots of different calculations based on one or two given values in a question. You can find this entire series along with my practice quiz and cheat sheet by visiting my website leah4sci.com/MCATAcidBase.
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