Autoionization of Water

in this video, we're gonna talk about the auto ionization of water. So water has a slight tendency toe auto ionized. And all that really means is that water can react with itself toe form ions. And those ions are gonna be hydro knee, um, cat ions, or H 30 plus, as well as hydroxide and ions or O H minus. And so recall that an ions always have a negative charge, whereas cat ions always have a positive charge. And so the water auto ionization reaction is actually a reversible reactions. So that means that the reaction can occur in both directions, and it takes place very, very, very rapidly or quickly. And so let's take a look at our example below, and what we'll see is that we've got to water molecules on the reactant side, and these water molecules are able to react with themselves. Toe form the hydro knee, um, cat ion and the hydroxide and ion. And again, this reaction can occur in both directions. It's reversible reaction, and so you can see that we've got our equilibrium arrows here Now what's important to note is that H 30 plus and O. H minus, Uh, concentrations are always gonna be very, very, very low. Very small concentrations and show. So we've drawn our equilibrium arrows here to represent that. So the top arrow here, showing the conversion of water into the ions is very small, showing that the concentrations of H 30 plus and minus are gonna be very small. And the reverse reaction arrow here, showing the conversions of these ions back into water is much larger in comparison to the top arrow showing that the concentrations of water are always gonna be much larger than the concentrations of the ions. Now, what's also important to remember from our previous chemistry courses is that in pure water, the concentrations of H 30 plus are always gonna be equal to the concentrations of O. H minus. And so this is gonna be important as we move forward into our next video. And so, uh, keeping something to remember from your previous chemistry courses is that free protons, hydrogen ions and H plus they're all essentially synonyms toe one another. And in your textbook and your professor, uh, they're probably going to use all of these terms here interchangeably with one another so it's important to keep that in mind now. Another important thing to note is that H 30 plus or this hydro knee, um, cat I end up here is commonly simplified to H plus, which again usually suggests free protons. However, free protons themselves are actually non existent and acquis systems. So whenever water is around, whenever waters around free protons are non existent, they actually exist as h 30 plus hydro knee um, ions. And so it's important to note that even though I'm going to simplify H 30 plus is H plus and your professor is going to do it and it's also in your textbooks. It's important to note that free protons are non existent and that really these h plus ions when they're in water, they're going to exist as a 30 plus. And so keeping that in mind, we can move on to our example, which shows in the alternative depiction to the water ionization uh, the same one that shown up above and so notice here that we have simplified the H 30 plus here as an H plus I on here. And so when we do that we're able to simplify this entire reaction even further and remove one of the entire water molecules. And so what you'll see is that water is ableto auto ionized and react with itself to form the hydro knee, um, Cat ion and the hydroxide and I on. And so, uh, if we apply our equilibrium constant to this reaction here, were able to get the ion constant of water or K W. And we'll talk about what that is and why that's important in our next video, so I'll see you guys in.

so because H Plus and O H minus are present in pretty much every biological solution and they participate in so many different biochemical reactions, we actually care about their concentrations and their concentrations are actually relevant to us. And so the concentrations of H plus an O. H minus can actually be determined by the equilibrium constant which were already familiar with from our previous videos, and recall that the equilibrium constant is simply the concentration of products of equilibrium over the concentration of reacting to equilibrium. And so what I want you guys to focus on in this video is actually the ion constant of water. And so it turns out that the iron constant water can be abbreviated with the symbol K W. And it's just a simple rearrangement of the equilibrium constant which were already familiar with, and the iron constant water. K W is equal to the product of the concentration of H plus times, the concentration of O H minus. So let's take a look at our example below Thio clarify the difference between equilibrium, constant and the iron constant for the auto ionization of water. Let's start with the equilibrium constant since we're already familiar with that. And so again recalled the equilibrium. Constant is simply the concentration of products equilibrium over the concentration of reacting to equilibrium. And in our previous video, we talked about how the auto ionization of water can be depicted as so and so we've got two different products here. We've got hpe plus and O H minus. And so if we go ahead and plug those in, we can put an H plus for equilibrium, concept and O H minus and are reacting is already in here. So this is our equilibrium constant for the auto ionization of water and nothing new here. We kind of already knew this from our previous videos. So how does this tie in to the K W? And so what? I want you guys to know that the K W is that the K W is equal to the concentration of H plus times, the concentration of O. H minus and that is always equal to one times 10 to the negative 14th Moeller Square. And so, if you know this, then you guys will be good in all of our practice problems. And so, uh, if you're curious about how in the world Did they get this number? And the way that they got it is by a simple algebraic rearrangement of this equation of the equilibrium constant. So we take the h 20 on the bottom and we multiply it by both on both sides of the equation just to move it up here, notice that that's exactly what we have shown here. Equilibrium, constant times, H 20 and that gives us our k W. And so, by memorizing this one number here, what that does is it saves us from having to memorize two different numbers. So we don't have to memorize equilibrium, constant or H 20 concentrations just because of the K W. So the K W is actually a good thing to help limit our memorization. So this is this green shaded region that I highlighted here is the only region you guys really need to know about K. W Now what's interesting is that K W actually varies with different conditions, and it changes with different temperatures, just like the equilibrium constant does. And so the good thing is, is that in biological systems, we always assume that the temperature is gonna be right around 298 Calvin. And so what that means is that K W is always going to be assumed to be one times 10 to the negative 14th Mueller squared in biological systems. So it's that same number here. So just by memorizing this value K w, that allows us to calculate either the H plus concentration or the O. H minus concentration when we're given the concentration of just one of these ions and again these concentrations here, we actually care about them. They're relevant to us. And so we'll get some more practice calculating these concentrations in our practice video. So I'll see you guys, then.

Calculate [H⁺] in a solution given that [OH^-] is 1.0 x 10^-10 M.

• A. 1.0 x 10^-2 M
• B. 1.0 x 10^-3 M
• C. 1.0 x 10^-4 M
• D. 1.0 x 10^-5 M

Calculate [OH^-] in a solution given that [H⁺] is 1.0 x 10^-11.8 M.

• A. 1.0 x 10^-11.8 M
• B. 1.0 x 10^-6.8 M
• C. 1.0 x 10^-4.5 M
• D. 1.0 x 10^-2.2 M

So, even in pure water, we know that water molecules have the tendency toe auto lionize and to form H three o plus ions and O H minus ions, and because water molecules have the ability to interact with each other in this kind of way, this allows for something known as proton hopping to occur. And so proton hopping is essentially when you have hydro knee um ions, or H three o plus ions and hydroxide ions or O H minus ions. That can diffuse much more rapidly than other ions in aqueous solutions or in solutions that have water in them. And the way this works is that the protons or the hydrogen Adams that are on an H three o plus or water molecule can actually hop or jump onto neighboring water molecules or O H minus ions, in order for these two ions to be able to diffuse very, very rapidly. So let's take a look at our example below to clear this idea of a proton hobby. And so over here in the image on the left we have and H three o plus ion up here, and it's surrounded by a bunch of water molecules. And so this H three o plus can donate its hydrogen to a neighboring water molecules so that it becomes an H three o plus. And it can continuously donate the hydrogen ion over long stretches toe mawr more water molecules so that the H three o plus eventually shows up in a completely different area. It's defused. And so this diffusion, this type of proton hopping is much, much faster than if this H three o plus were to try to physically diffuse and make its way over to that same area. Now, if we take a look at the image on the right, what we have is an O. H. Minus I on here, and the idea works very similarly. So we have a bunch of water molecules surrounding the O. H. Minus ion, and the water can donate a hydrogen to the O. H minus and become an O. H minus itself. And so this donation can continuously happen over long stretches so that the O. H. Minus ends up in a completely different area. And again, this is much faster. This proton hopping is much faster than the physical diffusion off this O H minus to a different location. And so other ions don't have this ability to do proton hopping. But these H three o plus no. H minus Ken. And so this concludes our lesson on the auto ionization of water, and I'll see you guys in our practice videos.

Which of the following ions is likely to diffuse the most rapidly in biological systems?

• A. Ca²⁺
• B. OH^-
• C. Mg²⁺
• D. Cl^-