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Hydronium ions (\text{[H}_3\text{O}^+\text{]}) play a crucial role in determining the acidity of a solution. Acids release hydrogen ions (H\text{^+}) into water, which combine with water molecules to form hydronium ions. The concentration of hydronium ions directly affects the pH level of a solution.
The relationship between pH and hydronium ion concentration is expressed mathematically as: \( \text{pH} = -\text{log} \text{[H}_3\text{O}^+\text{]}.\)
To find the hydronium ion concentration when you know the pH, you can rearrange this formula:

\( \text{[H}_3\text{O}^+\text{]} = 10^{-\text{pH}}. \)

For example, if Solution X has a pH of 9.5, its hydronium ion concentration is: \( \text{[H}_3\text{O}^+\text{]}_X = 10^{-9.5}. \) For Solution Y with a pH of 7.5: \( \text{[H}_3\text{O}^+\text{]}_Y = 10^{-7.5} . \)
Lower pH indicates a higher concentration of hydronium ions, making the solution more acidic.

Understanding how to calculate pH is vital in acid-base chemistry. The pH scale ranges from 0 to 14 and measures how acidic or basic a solution is. A pH less than 7 indicates an acidic solution, while a pH greater than 7 indicates a basic solution. A pH of 7 is neutral.
You can calculate pH by determining the hydronium ion concentration using the formula: \( \text{pH} = -\text{log} \text{[H}_3\text{O}^+\text{]} . \)
For instance, in the given exercise, Solution X has a pH of 9.5, making it less acidic compared to Solution Y, which has a pH of 7.5.
Simply put, lower pH = higher acidity, and higher pH = lower acidity.

Hydroxide ions (\text{[OH}^-\text{]}) are just as important as hydronium ions in acid-base chemistry. They indicate how basic a solution is. The product of the concentrations of hydronium ions and hydroxide ions in water at 25°C is always \(10^{-14}:\)
\( \text{[H}_3\text{O}^+\text{]} \times \text{[OH}^- \text{]} = 10^{-14}\)
To find the hydroxide ion concentration, rearrange the formula:

\( \text{[OH}^- \text{]} = \frac{10^{-14}}{\text{[H}_3\text{O}^+\text{]}}.\)

For Solution X with \( \text{[H}_3\text{O}^+\text{]}_X = 10^{-9.5},\): \( \text{[OH}^- \text{]}_X = \frac{10^{-14}}{10^{-9.5}} = 10^{-4.5}.\)
For Solution Y with \( \text{[H}_3\text{O}^+\text{]}_Y = 10^{-7.5}.):\) \( \text{[OH}^- \text{]}_Y = \frac{10^{-14}}{10^{-7.5}} = 10^{-6.5}.\)

Acid-base chemistry explores the properties of acids and bases, how they interact, and how their concentrations are measured. Acids donate hydrogen ions (H\text{^+}) which combine with water to form hydronium ions (\text{H}_3\text{O}^+\text{]). Bases provide hydroxide ions (\text{OH}^-\text{]).
The pH scale is essential for understanding these interactions and determining the acidity or basicity of a solution.

Key points:

• Acids have a pH less than 7.
• Bases have a pH greater than 7.
• The pH value is inversely related to hydronium ion concentration.

Additionally, the relationship between \( \text{[H}_3\text{O}^+\text{]} \) and \( \text{[OH}^- \text{]} \) and their equilibrium (\text{10^{-14}}) in water is fundamental. By mastering these concepts, understanding acid-base reactions and calculations, such as those shown in the exercise, becomes more manageable.