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

Autoionization of water involves water molecules acting as both acids and bases, resulting in the formation of hydronium ions (H₃O⁺) and hydroxide ions (OH^-). The ionization constant of water (K_w) at 25°C is 1.0 × 10^-14, which is crucial for understanding pH and pOH relationships, expressed as pH + pOH = 14. K_w is temperature-dependent, generally increasing with temperature. This equilibrium is essential for maintaining the acidity or basicity of aqueous solutions, highlighting the amphoteric nature of water.

Auto-Ionization and Kw

Autoionization occurs when water molecules react with one another in an aqueous solution. Recall that water is amphoteric, meaning it can act as both an acid and a base. Here, one of them is going to act as a base, the other one as an acid. The acid will donate an H⁺ to the base. The basic water molecule that accepts the H⁺ becomes H₃O⁺ and the water that donated the H⁺ becomes OH^-. Associated with this reaction is K_w. K_w represents our ionization constant of water. It is an equilibrium constant, and like other equilibrium constants, it's a ratio of products over reactants. Remember, it does not take into account liquids and solids; it only concerns aqueous and gaseous compounds. In this equation, the liquids will be ignored, so the reactants on the bottom will be ignored. So K_w just equals the product of the concentrations of H₃O⁺ and OH^-: K_w is equal to 1.0 times 10 to the power of negative 14 at a temperature of 25 degrees Celsius. This fact connects us to the formula pH + pOH equals 14. Now, this whole idea of H₃O⁺ and OH^-, remember they are kind of like counterbalancing one another. If one goes up, the other goes down. This is a way of maintaining the acidity or basicity of any aqueous solution. Realize that if we're dealing with pure water, that's when their concentrations are equal to one another, and that's when we can talk about the aqueous solution being neutral. Keep this in mind; autoionization is the key to understanding the relationship between H₃O⁺, your hydronium ion concentration, with OH^-, your hydroxide ion concentration. Together, they help us to create this ionization constant expression for water, which then leads us into pH + pOH equaling 14.

Kw and Temperature

Now recall that at 25 degrees Celsius, k_w = 1.0 × 10^-14. This is a value you'll have to remember on your own. You're not going to be expected to memorize, or to be given a formula sheet with this value present. But remember k_w is an equilibrium constant and like the other equilibrium constants, it is temperature dependent. If I play around with my temperature where it strays away from 25 degrees Celsius, then the value itself will change. We're going to say the general trend is as the temperature increases, our k_w increases.

If we take a look here, we have temperatures ranging from 0 degrees Celsius all the way up to 100 degrees Celsius. And if you look, you can see that as our temperature starts to increase, going from 0 to 100, we can see that the general trend is that my k_w value is increasing. Again, at 25 degrees Celsius, k_w is equal to this value. This is what you're expected to remember on your own. If the temperature changes from 25 degrees Celsius, you'll be given that new value for k_w because it could really be any number, so it's hard for you to memorize an entire list of k_w at all these different temperatures. Okay. And remember, the general trend is as the temperature increases, our k_w generally increases as well.

Auto-Ionization Example

A particular aqueous solution at 50 degrees Celsius contains 3.7×10-4 hydronium ions. It says to calculate the hydroxide ion concentration and identify the solution as either being acidic, basic, or neutral. Alright, so hydronium ion is H₃O⁺ and they want us to find OH^-. The equation that connects them together is K_w = [H₃O⁺] × [OH^-]. Our temperature is at 50 degrees Celsius which means our K_w value changes. If you look up above you'll see that at 50 degrees Celsius K_w = 5.476 × 10^-14. Plug in our number for the hydronium ion concentration, so 3.7×10-4, and then we just have to solve for the hydroxide ion concentration. Divide both sides by 3.7×10-4, When you do that, you're going to get your hydroxide ion concentration being equal to 1.48×10-10 molar. Now, how do we determine if it's an acidic, basic, or neutral solution? Well, you can see that your hydronium ion concentration is to the negative 4, but your hydroxide is to the negative 10. Since hydronium ion concentration is greater than hydroxide ion concentration, that means that we are dealing with an acidic solution. Right? So we have both the concentration of hydroxide ion, and the fact that our solution is acidic.

Chemistry student prepared an aqueous solution at 30ºC. If the solutions contains 7.42 × 10⁻⁹ M of hydroxide ions, calculate the pH.

• A. 5.703
• B. 8.130
• C. 8.300
• D. 5.980

Calculate the K_w of pure water given the pH = 6.34.

• A. 4.57 × 10⁻⁷
• B. 6.76 × 10⁻⁴
• C. 2.09 × 10⁻¹³
• D. 4.57 × 10⁻¹⁴

Here’s what students ask on this topic:

What is the autoionization of water and how does it occur?

Autoionization of water occurs when water molecules react with each other in an aqueous solution. Water is amphoteric, meaning it can act as both an acid and a base. In this process, one water molecule donates a proton (H⁺) to another water molecule. The water molecule that accepts the proton becomes a hydronium ion (H₃O⁺), and the one that donates the proton becomes a hydroxide ion (OH^-). This reaction is represented by the equilibrium constant of water (K_w), which at 25°C is 1.0 × 10^-14. This equilibrium is crucial for understanding the pH and pOH relationships in aqueous solutions.

What is the value of the ionization constant of water (K_w) at 25°C?

The ionization constant of water (K_w) at 25°C is 1.0 × 10^-14. This value is essential for calculating the pH and pOH of aqueous solutions. The relationship between pH and pOH is given by the equation pH + pOH = 14. K_w is temperature-dependent and generally increases with increasing temperature.

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

The ionization constant of water (K_w) is temperature-dependent. As the temperature increases, the value of K_w generally increases. For example, at 25°C, K_w is 1.0 × 10^-14, but this value will change if the temperature deviates from 25°C. This trend is important to consider when studying the pH and pOH of solutions at different temperatures.

Why is the autoionization of water important for understanding pH and pOH?

The autoionization of water is crucial for understanding pH and pOH because it establishes the relationship between the concentrations of hydronium ions (H₃O⁺) and hydroxide ions (OH^-). The ionization constant of water (K_w) at 25°C is 1.0 × 10^-14, leading to the equation pH + pOH = 14. This relationship helps in determining the acidity or basicity of aqueous solutions and is fundamental in various chemical calculations.

What does it mean for water to be amphoteric in the context of autoionization?

In the context of autoionization, water being amphoteric means that it can act as both an acid and a base. During autoionization, one water molecule donates a proton (H⁺) to another water molecule. The molecule that donates the proton acts as an acid, forming a hydroxide ion (OH^-), while the molecule that accepts the proton acts as a base, forming a hydronium ion (H₃O⁺). This dual behavior is essential for the equilibrium that defines the ionization constant of water (K_w).