Autoionization of Water - Online Tutor, Practice Problems & Exam Prep

Water autoionizes to form hydronium (H₃O⁺) and hydroxide (OH^-) ions, with their concentrations being very low. The ion constant of water (K_w) is defined as the product of these ion concentrations, equal to 1 × 10^-14 mol²/L² at 298 K. This process enables proton hopping, allowing rapid diffusion of H₃O⁺ and OH^- ions in aqueous solutions, which is crucial for various biochemical reactions.

Water Autoionization

In this video, we're going to talk about the autoionization of water. So, water has a slight tendency to autoionize, and all that really means is that water can react with itself to form ions. And those ions are going to be hydronium cations, or H₃O⁺, as well as hydroxide anions, or OH^-. Recall that anions always have a negative charge, whereas cations always have a positive charge. The water autoionization reaction is actually a reversible reaction. That means that the reaction can occur in both directions. It takes place very rapidly or quickly. Let's take a look at our example below, and what we'll see is that we've got 2 water molecules on the reactant side. These water molecules are able to react with themselves to form the hydronium cation and the hydroxide anion. This reaction can occur in both directions. It's a reversible reaction. You can see that we've got our equilibrium arrows here.

Now, what's important to note is that H₃O⁺ and OH^- concentrations are always going to be very low, very small concentrations. We've drawn our equilibrium arrows here to represent that. The top arrow here showing the conversion of water into the ions is very small, showing that the concentrations of H₃O⁺ and OH^- are going to be very small. 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 going to be much larger than the concentrations of the ions. What's also important to remember from our previous chemistry courses is that in pure water, the concentrations of H₃O⁺ are always going to be equal to the concentrations of OH^-. This is going to be important as we move forward into our next video. Something to remember from your previous chemistry courses is that free protons, hydrogen ions, and H⁺ are all essentially synonyms to one another. And in your textbook and your professor, they're probably going to use all of these terms here interchangeably with one another.

So, it's important to keep that in mind. Another important thing to note is that H₃O⁺, or this hydronium cation up here, is commonly simplified to H⁺, which again, usually suggests free protons. However, free protons themselves are actually nonexistent in aqueous systems. So whenever water is around, free protons are nonexistent. They actually exist as H₃O⁺ hydronium ions. It's important to note that even though I'm going to simplify H₃O⁺ to H⁺, and your professor's going to do it and it's also in your textbooks, free protons are nonexistent and that really these H⁺ ions when they're in water, they're going to exist as H₃O⁺. Keeping that in mind, we can move on to our example, which shows an alternative depiction of the water ionization, the same one that's shown above. Notice here that we've simplified the H₃O⁺ here as an H⁺ ion. When we do that, we're able to simplify this entire reaction even further and remove one of the entire water molecules. What you'll see is that water is able to autoionize and react with itself to form the hydronium cation and the hydroxide anion. If we apply our equilibrium constant to this reaction here, we're able to get the ion constant of water or KW, and we'll talk about what that is and why that's important in our next video. So I'll see you guys then.

Ion Constant of Water (Kw)

So because H⁺ and OH^- 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⁺ and OH^- can actually be determined by the equilibrium constant, which we're already familiar with from our previous videos. And recall that the equilibrium constant is simply the concentration of products at equilibrium over the concentration of reactants at 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 ion constant of water can be abbreviated with the symbol KW, and it's just a simple rearrangement of the equilibrium constant, which we're already familiar with. And the ion constant of water KW is equal to the product of the concentration of H⁺ times the concentration of OH^-. So let's take a look at our example below to clarify the difference between the equilibrium constant and the ion constant for the autoionization of water.

Let's start with the equilibrium constant since we're already familiar with that. And so again, recall that the equilibrium constant is simply the concentration of products at equilibrium over the concentration of reactants at equilibrium. And in our previous video, we talked about how the autoionization of water can be depicted as so. And so we've got 2 different products here. We've got H⁺ and OH^-. And so if we go ahead and plug those in, we can put in H⁺ for our equilibrium constant and OH^-. And our reactant is already in here. So this is our equilibrium constant for the autoionization of water. Nothing new here. We kinda already knew this from our previous videos. So how does this tie in to the KW?

And so what I want you guys to know that the KW is that the KW is equal to the concentration of H⁺ times the concentration of OH^-, and that is always equal to 1 times 10 to the negative 14th molar squared. And so, if you know this, then you guys will be good in all of our practice problems. And so, if you're curious about how in the world they got this number, and the the way that they got it is by a simple algebraic rearrangement of this equation, of the equilibrium constant. And so, we take the H₂O in 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 H₂O, and that gives us our KW.

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 the equilibrium constant or H₂O concentrations just because of the KW. So the KW 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 KW. Now, what's interesting is that KW actually varies with different conditions and it changes with different temperatures, just like the equilibrium constant does. And so, the good thing is that in biological systems, we always assume that the temperature is going to be right around 298 Kelvin. And so what that means is that KW is always going to be assumed to be 1 times 10 to the negative 14th molar squared in biological systems. So it's that same number here. So just by memorizing this value KW, that allows us to calculate either the H⁺ concentration or the OH^- 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

Proton Hopping

So even in pure water, we know that water molecules have the tendency to auto ionize and to form H3O+ ions and OH− 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 proton hopping to occur. And so proton hopping is essentially when you have hydronium ions or H3O+ ions and hydroxide ions, or OH− ions, that can diffuse much more rapidly than other ions in aqueous solutions, or in solutions that have water in them. And the way that this works is that the protons or the hydrogen atoms that are on an H3O+ or a water molecule can actually hop or jump onto neighboring water molecules or OH− ions in order for these 2 ions to be able to diffuse very, very rapidly.

Let's take a look at our example below to clear this idea of proton hopping. Over here in the image on the left, we have an H3O+ ion up here, and it's surrounded by a bunch of water molecules. So, this H3O+ can donate its hydrogen to a neighboring water molecule so that it becomes an H3O+, and it can continuously donate the hydrogen ion over long stretches to, more and more water molecules so that the H3O+ eventually shows up in a completely different area. It's diffused. And so, this diffusion, this type of proton hopping, is much, much faster than if this H3O+ 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 OH− ion here, and the idea works very similarly. We have a bunch of water molecules surrounding the OH− ion, and the water can donate a hydrogen to the OH− and become an OH− itself. And so, this donation can continuously happen over long stretches so that the OH− ends up in a completely different area. And again, this is much faster, this proton hopping is much faster than the physical diffusion of this OH− to a different location. And so, other ions don't have this ability to do proton hopping, but these H3O+ and OH− can.

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^-

Here’s what students ask on this topic:

What is the autoionization of water?

The autoionization of water refers to the process where water molecules react with each other to form ions. Specifically, two water molecules interact to produce a hydronium ion (H₃O⁺) and a hydroxide ion (OH^-). This reaction is reversible and occurs very rapidly. The concentrations of H₃O⁺ and OH^- in pure water are very low and equal, maintaining a balance. This process is crucial for understanding the behavior of acids and bases in aqueous solutions.

What is the ion constant of water (Kw) and its significance?

The ion constant of water (K_w) is a specific equilibrium constant for the autoionization of water. It is defined as the product of the concentrations of hydronium ions (H₃O⁺) and hydroxide ions (OH^-) in water. Mathematically, it is expressed as:

$K_w={\mathrm{[H}}_{3}O+]\times {\mathrm{[OH}}_{-}$

At 298 K, K_w is equal to 1 × 10^-14 mol²/L². This constant is essential for calculating the pH and pOH of solutions, which are critical for many biochemical reactions.

How does temperature affect the ion constant of water (Kw)?

The ion constant of water (K_w) is temperature-dependent. At 298 K, K_w is 1 × 10^-14 mol²/L². However, as the temperature increases, K_w also increases, meaning that the concentrations of H₃O⁺ and OH^- ions in water become higher. Conversely, at lower temperatures, K_w decreases. This variation is important to consider in biochemical reactions and processes that occur at different temperatures.

What is proton hopping and why is it important?

Proton hopping is a mechanism that allows hydronium ions (H₃O⁺) and hydroxide ions (OH^-) to diffuse rapidly in aqueous solutions. In this process, a proton (H⁺) can transfer from one water molecule to another, effectively 'hopping' across the solution. This rapid diffusion is much faster than the physical movement of the ions themselves. Proton hopping is crucial for many biochemical reactions, as it facilitates quick changes in pH and the efficient transport of protons in biological systems.

Why are the concentrations of H₃O⁺ and OH^- ions in pure water equal?

In pure water, the autoionization process produces equal amounts of hydronium ions (H₃O⁺) and hydroxide ions (OH^-). This is because the reaction involves the interaction of two water molecules to form one H₃O⁺ ion and one OH^- ion. Therefore, their concentrations are always equal, maintaining a neutral pH of 7 at 298 K. This balance is fundamental to the concept of pH and the behavior of acids and bases in aqueous solutions.