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The ionization constant of water, denoted as \(K_w\), is a crucial concept in understanding the chemistry of water. Water can self-ionize into hydronium ions (\(\text{H}_3\text{O}^+\)) and hydroxide ions (\(\text{OH}^-\)). This process is an equilibrium reaction. The ionization constant \(K_w\) is the equilibrium constant for the ionization of water and is defined by the equation:

• \(K_w = [\text{H}_3\text{O}^+][\text{OH}^-]\)

In pure water, the concentrations of \([\text{H}_3\text{O}^+]\) and \([\text{OH}^-]\) are equal, which simplifies the expression for \(K_w\) as it becomes \(K_w = [\text{H}_3\text{O}^+]^2\).

This constant changes with temperature, which is why it is important to know the specific \(K_w\) value at different temperatures, such as the given \(90^{\circ} \text{C}\). Calculating \(K_w\) at this temperature involves squaring the given concentration of hydronium ions.

At \(90^{\circ} \text{C}\), if \([\text{H}_3\text{O}^+]\) is \(10^{-6}\), then \(K_w\) is calculated as \((10^{-6})^2\), resulting in \(10^{-12}\). This value represents the product of hydronium and hydroxide ion concentrations in water at this specific temperature.

Hydronium ion concentration ([\(\text{H}_3\text{O}^+\)]) is a key aspect of the water ionization process.It represents the concentration of \(\text{H}_3\text{O}^+\) ions in a solution, which is essential in determining the acidity or basicity of a solution. In pure water, this concentration is also equal to the concentration of hydroxide ions (\([\text{OH}^-]\)).

The hydronium ion concentration is crucial for calculating the ion product constant of water, \(K_w\).

• In the context of the exercise, we are given \([\text{H}_3\text{O}^+]\) as \(10^{-6}\) mole L\(^{-1}\).

This value is used to find \(K_w\) by squaring the hydronium ion concentration since in pure water, \(K_w = [\text{H}_3\text{O}^+]^2\).

Understanding hydronium ion concentration helps in predicting how acidic a solution is. The lower the concentration, the more basic the solution, whereas a higher concentration indicates acidity.

In this scenario, at a temperature of \(90^{\circ} \text{C}\), the given concentration \(10^{-6}\) leads us to calculate \(K_w\) by finding the square, which equals \(10^{-12}\). This value signifies the equilibrium state of water ionization at this temperature.

The equilibrium constant is a fundamental concept in chemistry that measures the ratio of the concentrations of the products to the reactants for a reversible reaction at equilibrium.For the ionization of water, the equilibrium constant is represented by the ion-product constant \(K_w\).

Let's break down how equilibrium constants work.

• The expression is set up by using the concentrations of the products divided by the reactants.
• This provides insight into the relative amounts of substances in the reaction when it has reached equilibrium.

At different temperatures, equilibrium constants can change, which means \(K_w\) values vary with temperature due to changes in the equilibrium position.In pure water, because the concentrations of hydronium and hydroxide ions are equivalent, \(K_w\) can be expressed simply as \([\text{H}_3\text{O}^+]^2\), which assumes a balance between ion formation and recombination.

In our case study, at \(90^{\circ} \text{C}\), this is directly applied by using the given \([\text{H}_3\text{O}^+]\) of \(10^{-6}\) mole L\(^{-1}\).The \(K_w\) is calculated as \(10^{-12}\), highlighting the dynamic nature of equilibrium constants and the way they represent the shifting balance of products and reactants in a chemical process depending on conditions like temperature.