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Understanding the pH scale is crucial for determining whether a solution is acidic, basic, or neutral. The pH is a logarithmic measure of the hydrogen ion concentration \( [H^+] \) in a solution. It is calculated using the formula \( pH = -\log[H^+] \). When \( [H^+] \) is known, as provided in our textbook exercise, you can easily compute the pH. For instance, if the hydrogen ion concentration is 0.0505 M, the pH is calculated as \( pH = -\log(0.0505) \), resulting in a pH less than 7, which indicates an acidic solution.

It's crucial for students to understand that a pH less than 7 is acidic, around 7 is neutral, and greater than 7 is basic. This corresponds inversely to the concentration of hydroxide ions \( [OH^-] \) in the solution, which can also be calculated using the relationship to the ion product of water. By mastering pH calculation, students can better comprehend the chemical properties of solutions and predict their behavior in various reactions.

The ion product of water (\( K_w \) is a constant at a given temperature (25掳C value of \( 1 \times 10^{-14} \) that represents the product of the molar concentrations of hydrogen \( [H^+] \) and hydroxide \( [OH^-] \) ions in water. The formula is stated as \( K_w = [H^+][OH^-] \).

This constant value allows us to solve for either ion's concentration when the other is known. In the exercise, students are shown how to manipulate this expression to find the hydroxide ion concentration given the hydrogen ion concentration. For example, if \( [H^+] = 2.5 \times 10^{-10} M \) we solve for \( [OH^-] \) by rearranging the equation to \( [OH^-] = \frac{K_w}{[H^+]} \), inserting the known values, and solving for \( [OH^-] \). This is a fundamental concept in acid-base chemistry and is essential for students to be able to shift between \( [H^+] \) and \( [OH^-] \) calculations.

The nature of a solution, whether it is acidic or basic, is determined by its pH, which is in turn dependent on the relative concentrations of hydrogen \( [H^+] \) and hydroxide \( [OH^-] \) ions.

An acidic solution has a higher concentration of hydrogen ions than hydroxide ions \( [H^+] > [OH^-] \), while a basic solution has a lower concentration of hydrogen ions than hydroxide ions \( [H^+] < [OH^-] \). When the concentrations of \( [H^+] \) and \( [OH^-] \) are equal, the solution is neutral. In our textbook problem, the nature of the solution is deduced after calculating the \( [OH^-] \) concentration. For instance, in part a, after finding \( [OH^-] = 1.98 \times 10^{-13} \), since this value is less than the given \( [H^+] \), the solution is acidic. Conversely, in part b, where \( [OH^-] > [H^+] \) the solution is basic.

It is important for students to connect the pH and \( [OH^-] \)-concentration calculations with the concept of acidity and basicity to develop a holistic understanding of chemical solutions.