Auto-Ionization - Online Tutor, Practice Problems & Exam Prep

Autoionization of water occurs when water molecules react with each other, producing hydronium ions (H₃O⁺) and hydroxide ions (OH^-). This process involves one water molecule acting as an acid (donating H⁺) and another as a base (accepting H⁺). The ion product constant for water (K_w) is defined as K_w = [H₃O⁺][OH^-], with a value of 1.0 x 10^-14 at 25°C, which increases with temperature. Understanding this equilibrium is crucial for acid-base reactions and calculations in aqueous solutions.

Auto-Ionization Concept 1

Hey guys. In this new video, we're going to take a look at the autoionization of water. So, what we're going to say here is in an aqueous solution, the solvent is water, water molecules can react with each other. And we're going to say this is called the process of autoionization or self-ionization. Now, in this process, we're going to create H₃O⁺ and OH^-. Now, just realize, how does this happen? For this to occur, one of the water molecules has to act as an acid and the other one has to act as a base. So let's say that this one here acts as the acid and this here is the base. And remember, Brønsted-Lowry definitions, the acid acts as an H⁺ donor, the base acts as an H⁺ acceptor. So this base right here is going to accept an H⁺ and as a result, it's going to become H₃O⁺ Then we're going to say that the other water molecule, the one that's acting as an acid because it's giving away an H⁺, it becomes OH^-. And just also realize here that water molecules exist in liquid form but then once they become these ions, the hydronium ion and the hydroxide ion, they're going to become aqueous. So, they're no longer liquid water. And because of that, they're no longer a liquid, they're going to be aqueous. Remember, aqueous just means that the parts of the water are attracted to these particular ions. We can simplify auto ionization or self ionization by just saying that water separates into H⁺ plus OH^-. Remember, we've said this before that H⁺ is the same thing as H₃O⁺ So both are the hydronium ion. They both mean the same exact thing.

Now we're going to say here that the equilibrium equation for water is called the ion product. An ion product is simply said to be k_w. So when we're talking about the k_w for water, we're talking about the ion product of water. And we're going to say that k_w equals your hydronium ion multiplied times your hydroxide ion. And we're going to say here that at 25 degrees Celsius, k_w is 1.0×10-14. But remember, just like all k's, it's going to be temperature-dependent. If you change the temperature, you're going to change the value of the k_w. So, we're going to say increasing the temperature will increase our k_w.

Now, here I give us a bunch of different values for k_w found at various temperatures. And notice, as the temperature gradually increases, our k_w will get bigger and bigger. Now, just realize on your exam when you need to use k_w, if they don't give you a temperature, just assume that it's 25 degrees Celsius. So then k_w would be 1.0×10-14. Now, knowing this, let's take a look at this question here.

Auto-Ionization Example 1

This question states, determine the concentration of hydronium ion. Basically, find H⁺ or H₃O⁺. They both mean the same thing. For a neutral solution at 25 degrees Celsius and 50 degrees Celsius. Okay. Now, what we should realize here is what does neutral mean? Neutral means that your compound is not acidic or basic. And what it really means is that H₃O⁺ equals OH^-. They're both the same thing. And because they're equal to each other, we're going to set them both to an unknown variable. We're going to set them to x. And then what we're going to do here is we know at 25 degrees Celsius, K_w will be 1.0×10-14. At 25 degrees Celsius, that's what our K_w is. And we just said that H₃O⁺ and OH^- are equal when the solution is neutral. Times x really means x². X really means x squared. You only want to find x not x squared, so take the square root. In this case, x equals 1.0×10-7. That number right there represents my concentration of H₃O⁺ and technically because it's neutral, it also represents the concentration of OH^-. Now, if you wanted to do it at 50 degrees Celsius, we'd have to realize that since the temperature changes, K_w changes to this new number here. We're going to say 5.476×10-14, the same exact process equals x². We just want x so we're going to take the square root of both sides. When we do that, it's going to give us a final answer of x equals 2.34×10-7. Now, so remember, this is important to know because K_w equals H⁺O_H-. This equation is important because if the temperature is not given, assume that K_w equals 1.0times10to the negative14, and if you know H⁺ concentration, then you know OH- concentration because K_w will be our constant. And vice versa, if you know OH^- you can find H⁺. This is the relationship we need to understand and these are the beginning steps for us to figure out the pH and pOH of different types of aqueous solutions.

Here’s what students ask on this topic:

What is the autoionization of water?

The autoionization of water is a process where water molecules react with each other to form hydronium ions (H₃O⁺) and hydroxide ions (OH^-). In this reaction, one water molecule acts as an acid by donating a proton (H⁺), and another acts as a base by accepting the proton. The equilibrium constant for this reaction, known as the ion product of water (K_w), is given by the equation:

$K_w=\left[H_{3}O\right]\left[\mathrm{OH}\right]$

At 25°C, K_w is 1.0 x 10^-14, and it increases with temperature.

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

The ion product constant (K_w) of water is temperature-dependent. As the temperature increases, the value of K_w also increases. This is because higher temperatures provide more energy for water molecules to overcome the activation energy barrier for autoionization, leading to more frequent formation of hydronium (H₃O⁺) and hydroxide (OH^-) ions. At 25°C, K_w is 1.0 x 10^-14, but this value will be higher at elevated temperatures.

What is the significance of the ion product constant (K_w) in aqueous solutions?

The ion product constant (K_w) is crucial for understanding acid-base reactions in aqueous solutions. It defines the relationship between the concentrations of hydronium ions (H₃O⁺) and hydroxide ions (OH^-) in water. Knowing K_w allows us to calculate the pH and pOH of a solution, which are measures of its acidity and basicity, respectively. At 25°C, K_w is 1.0 x 10^-14, meaning that in pure water, [H₃O⁺] and [OH^-] are both 1.0 x 10^-7 M.

How do you calculate the pH of a solution using the ion product constant (K_w)?

To calculate the pH of a solution using the ion product constant (K_w), you first need to know the concentration of hydronium ions (H₃O⁺). The pH is then calculated using the formula:

$\mathrm{pH}=-\log \left(\right[H_{3}O\left]\right)$

Since K_w = [H₃O⁺][OH^-] and at 25°C, K_w is 1.0 x 10^-14, you can find [H₃O⁺] if you know [OH^-], and vice versa. For example, if [OH^-] is 1.0 x 10^-6 M, then [H₃O⁺] = 1.0 x 10^-8 M, and pH = 8.

What is the relationship between pH, pOH, and K_w?

The relationship between pH, pOH, and K_w is given by the equation:

$\mathrm{pH}+\mathrm{pOH}=-\log \left(K_w\right)$

At 25°C, K_w is 1.0 x 10^-14, so:

$\mathrm{pH}+\mathrm{pOH}=14$

This means that if you know either the pH or pOH of a solution, you can easily calculate the other. For example, if the pH of a solution is 5, then the pOH is 9.