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Ionization reactions describe the process by which a compound breaks down into ions when dissolved in water. For the hydroxide compound \( \mathrm{X} (\mathrm{OH})_3 \), the ionization reaction involves the compound dissociating into its constituent ions. Here, 100% of the first dissociation takes place to form \( \mathrm{X}^{3+} \) and hydroxide ions \( \mathrm{OH}^- \).

Subsequent dissociations might be less complete. In the case of \( \mathrm{X} (\mathrm{OH})_3 \), only about 50% of the second dissociation occurs, and the third becomes negligible. Understanding these percentages is crucial. It tells us how much of the substance splits into ions during each dissociation step. Different compounds will have different dissociation levels based on their inherent stability and the conditions of the solution.

This step-by-step ion breakdown is vital for calculating ion concentration in solution and further understanding the compound's behavior in aqueous environments.

The concentration of hydroxide ions \([\mathrm{OH}^-]\) in a solution is determined by the extent of ionization. Since \( \mathrm{X} (\mathrm{OH})_3 \) dissociates completely in its first step, every mole of it leads to the formation of three moles of hydroxide ions.

Given the concentration of \( \mathrm{X} (\mathrm{OH})_3 \) is \( 4 \times 10^{-3} \mathrm{M} \), the resultant \([\mathrm{OH}^-]\) is calculated by multiplying this concentration by three, reflecting the stoichiometry of the dissociation reaction:

• Calculate: \([\mathrm{OH}^-] = 3 \times (4 \times 10^{-3}) = 1.2 \times 10^{-2} \mathrm{M}\).

This understanding helps predict how acidic or basic a solution is, impacting pH calculations, and ultimately affecting chemical behavior in solution.

pH is a measure of how acidic or basic a solution is and is determined by the concentration of hydrogen ions \([\mathrm{H}^+]\) in the solution. However, since we often start with hydroxide ions \([\mathrm{OH}^-]\) in this context, it is useful to calculate pOH first.

The formula for pOH is given by:

• \( \mathrm{pOH} = -\log [\mathrm{OH}^-] \).

Substituting the calculated \([\mathrm{OH}^-]\) value:

• \( \mathrm{pOH} = -\log (1.2 \times 10^{-2}) \approx 1.92 \).

From here, we factor in the relationship between pH and pOH:

• \( \mathrm{pH} + \mathrm{pOH} = 14 \).

Subsequently, the pH is:

• \( \mathrm{pH} = 14 - \mathrm{pOH} \approx 12.08 \).

Understanding pH calculation helps explain why certain substances behave differently in reactions, given their acidity or basicity.

Dissociation reactions involve the process of breaking a compound into its ions. These reactions are essential for understanding chemical equilibrium in solutions as they define the extent to which a compound ionizes.

For \( \mathrm{X} (\mathrm{OH})_3 \), the dissociation into \( \mathrm{X}^{3+} \) and \( \mathrm{OH}^- \) ions highlights several crucial aspects:

• The degree of ionization, which influences how much of the compound will split into ions and establish equilibrium.
• The successive dissociation reactions, each contributing differently to the ion concentration due to varying dissociation percentages (100%, 50%, negligible).

These reactions help predict the solution's chemical properties and guide calculations regarding ion concentrations, assisting in inferring solution behavior such as conductivity, reactivity, and more. Understanding these dissociation percentages are vital for performing accurate pH or pOH calculations and anticipating the chemical interactions in aqueous solutions.