Auto-Ionization: Videos & Practice Problems

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

Autoionization of water is a fundamental process where water molecules interact with each other in an aqueous solution. Water is classified as amphoteric, meaning it can function as both an acid and a base. In this reaction, one water molecule acts as a base by accepting a proton (H⁺), while another acts as an acid by donating a proton. The result of this interaction is the formation of the hydronium ion (H₃O⁺) and the hydroxide ion (OH^-).

This reaction is associated with the ionization constant of water, denoted as K_w. K_w is an equilibrium constant that represents the ratio of the concentrations of the products (H₃O⁺ and OH^-) to the reactants. It is important to note that K_w does not include the concentrations of pure liquids and solids, focusing solely on aqueous and gaseous species. The expression for K_w can be written as:

K_w = [H₃O⁺][OH^-]

At 25 degrees Celsius, the value of K_w is 1.0 × 10^-14. This relationship is crucial as it connects to the formula pH + pOH = 14. The concentrations of H₃O⁺ and OH^- are inversely related; as the concentration of one increases, the other decreases. This balance is essential for maintaining the acidity or basicity of any aqueous solution.

In pure water, the concentrations of H₃O⁺ and OH^- are equal, leading to a neutral solution. Understanding autoionization is key to grasping the relationship between hydronium and hydroxide ions, which ultimately informs the ionization constant expression for water and the pH scale.

Kw Temperature Dependence

At 25 degrees Celsius, the ion product of water, denoted as \( K_w \), is \( 1.0 \times 10^{-14} \). This value is crucial to remember, as it serves as a reference point for understanding the behavior of water's ionization. \( K_w \) is an equilibrium constant, which means it is influenced by temperature changes. As the temperature increases, the value of \( K_w \) also tends to increase. This relationship can be observed across a range of temperatures, from 0 degrees Celsius to 100 degrees Celsius, where a clear trend shows that \( K_w \) rises with temperature.

It's important to note that if the temperature deviates from 25 degrees Celsius, you will be provided with the corresponding \( K_w \) value, as memorizing all possible values at different temperatures would be impractical. Understanding this temperature dependence of \( K_w \) is essential for grasping concepts related to acid-base chemistry and the behavior of aqueous solutions.

Auto-Ionization Example

To determine the hydroxide ion concentration in an aqueous solution at 50 degrees Celsius, we start with the known concentration of hydronium ions, which is given as \( [H_3O^+] = 3.7 \times 10^{-4} \, \text{mol/L} \). The relationship between hydronium ions and hydroxide ions is defined by the ion product of water, \( K_w \), which varies with temperature. At 50 degrees Celsius, \( K_w \) is \( 5.476 \times 10^{-14} \).

The equation connecting these concentrations is:

\[ K_w = [H_3O^+][OH^-] \]

Substituting the known values into the equation, we have:

\[ 5.476 \times 10^{-14} = (3.7 \times 10^{-4})[OH^-] \]

To find the hydroxide ion concentration, we rearrange the equation:

\[ [OH^-] = \frac{K_w}{[H_3O^+]} \]

Plugging in the values:

\[ [OH^-] = \frac{5.476 \times 10^{-14}}{3.7 \times 10^{-4}} \approx 1.48 \times 10^{-10} \, \text{mol/L} \]

Next, to classify the solution as acidic, basic, or neutral, we compare the concentrations of hydronium and hydroxide ions. Since \( [H_3O^+] = 3.7 \times 10^{-4} \) is greater than \( [OH^-] = 1.48 \times 10^{-10} \), the solution is identified as acidic. Thus, we conclude that the hydroxide ion concentration is \( 1.48 \times 10^{-10} \, \text{mol/L} \) and the 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

Answer: (A)

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

Answer: (C)

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.