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

Water exhibits autoionization, where it can act as both an acid and a base due to its amphoteric nature. This process involves a water molecule donating an H⁺ ion to another, forming hydronium (H₃O⁺) and hydroxide (OH^-) ions. The ionization constant of water (K_W) is central to understanding this equilibrium, which is the product of the concentrations of H₃O⁺ and OH^- ions, excluding liquids and solids. At 25°C, K_W is:

$1.0\times {10}^{-14}$

establishing the relationship pH + pOH = 14. This balance is crucial in maintaining the acidity or basicity of a solution. It's important to note that K_W varies with temperature; it generally increases as temperature rises. Remembering the value of K_W at 25°C is essential, as it is a standard reference point in chemistry, and deviations from this temperature will result in different K_W values provided for calculations.

Auto-Ionization and Kw

Auto ionization occurs when water molecules react with one another in an aqueous solution. So here recall that water is amphoteric, meaning it can act as both an acid or a base. Here one of them is going to act as a base, the other one is going to act as an acid. The acid will donate an H⁺ to the base. The basic water molecule that accepts the H⁺ becomes H₃O⁺. The water that donated the H⁺ becomes OH^-.

Here we're going to say that 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. And remember, it does not take into account liquids and solids, it only pays attention to aqueous and gaseous compounds. Looking at this equation that we have, we're going to say that the liquids will be ignored, so the reactants on the bottom will be ignored. So K_W just equals H₃O⁺ times OH^-.

K_W is equal to 1.0×10-14 at a temperature of 25°C. This fact is what connects us to the formula of pH plus 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 one 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 an aqueous solution being neutral. So keep this in mind. Auto ionization 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 plus pOH equaling 14.

Kw and Temperature

Now recall that at 25°C, kW=1.0×10-14. This is a value you'll have to remember on your own. You're not going to be expected to be given a formula sheet with this value present. But remember, kW is an equilibrium constant and like the other equilibrium constant, it is temperature dependent.

If I play around with my temperature where it strays away from 25°C, then the value itself will change. We're going to say the general trend is as the temperature increases, our kW increases. If we take a look here, we have temperatures ranging from 0°C all the way up to 100°C. And if you look you can see that as our temperature starts to increase, going from zero to 100, we can see that the general trend is that my kW value is increasing.

Again at 25°C, kW is equal to this value. This is what you're expected to remember on your own. If the temperature changes from 25°C, you'll be given that new value for kW because it could really be any number. So it's hard for you to memorize an entire list of kW at all these different temperatures, OK? And remember the general trend is as the temperature increases, our kW generally increases as well.

Auto-Ionization Example

A particular aqueous solution at 50°C 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. All right, so hydronium ion is H₃O⁺, and they want us to find OH^-. The equation that connects them together is

k W = [ H 3 O + ] × [ OH - ]

Our temperature is at 50°C, which means our k_W value changes. If you look up above, you'll see that at 50°C k_W equals 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 acidic, basic or neutral solution? Well, you can see that your hydronium ion concentrations is to the -4, but your hydroxide is to the -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 A/C.

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:

How do you calculate kW?

To calculate kilowatts (kW), which is a unit of power, you need to know the relevant electrical values. The basic formula for calculating kilowatts in an electrical system is:

$\mathrm{Power}\left(\mathrm{kW}\right)=\mathrm{Voltage}\left(V\right)x\mathrm{Current}\left(A\right)/\mathrm{1,000}$

Here's how you can apply it:

1. Measure the voltage (V) - This is the potential difference between two points in an electrical circuit.
2. Measure the current (A) - This is the flow of electric charge through the circuit.
3. Multiply the voltage by the current to get the power in watts (W).
4. Since 1 kilowatt is equal to 1,000 watts, divide the result by 1,000 to convert watts to kilowatts.

For example, if you have a circuit with a voltage of 240 volts and a current of 10 amperes, the power would be:

$\mathrm{Power}\left(\mathrm{kW}\right)=240Vx10A/\mathrm{1,000}=2.4\mathrm{kW}$

Remember that this formula applies to direct current (DC) circuits. For alternating current (AC) circuits, especially if the load is not purely resistive (like inductive or capacitive loads), you would need to take into account the power factor as well.

How do you calculate the pH of water?

To calculate the pH of water, you need to determine the concentration of hydrogen ions (H⁺) in the solution. The pH is the negative logarithm (base 10) of this concentration. The formula to calculate pH is:

$\mathrm{pH}=-\log \left[H^{+}\right]$

Where [H⁺] is the concentration of hydrogen ions in moles per liter (M).

Pure water at 25°C has a very low concentration of hydrogen ions, about 1 x 10^-7 M. Plugging this value into the formula gives:

$\mathrm{pH}=-\log (1x{10}^{-7})=7$

Thus, the pH of pure water at 25°C is 7, which is considered neutral on the pH scale. If the concentration of hydrogen ions is higher than 1 x 10^-7 M, the pH will be lower than 7, and the water will be acidic. If the concentration is lower than 1 x 10^-7 M, the pH will be higher than 7, and the water will be basic or alkaline. Remember that pH is a logarithmic scale, so a change of one pH unit represents a tenfold change in hydrogen ion concentration.

How do you calculate the pH of water at different temperatures?

To calculate the pH of water at different temperatures, you need to understand that pH is a measure of the hydrogen ion concentration ([H⁺]) in a solution, and it's calculated using the formula:

$\mathrm{pH}=-{\log }_{10}\left[H^{+}\right]$

At 25°C (298 K), pure water has a pH of 7.0, which means the concentration of hydrogen ions is 1x10^-7 moles per liter (mol/L). However, the ion product of water (Kw), which is the product of the concentrations of hydrogen ions and hydroxide ions ([H⁺][OH^-]), changes with temperature.

At temperatures other than 25°C, you'll need the specific Kw value for that temperature. Once you have the Kw, you can calculate the concentration of hydrogen ions since for pure water [H⁺] = [OH^-] and [H⁺] = Kw. Then, you can use the pH formula to find the pH at that temperature.

Remember, as temperature increases, Kw increases, and the pH of pure water decreases, meaning it becomes less neutral. Conversely, as temperature decreases, Kw decreases, and the pH increases, making the water more neutral.