The pH of a solution is \(9.5 .\) What is \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) ? What is \(\left[\mathrm{OH}^{-}\right] ?\)

Understanding the relationship between pH and pOH is essential for studying acid-base chemistry. The pH scale measures the acidity or alkalinity of a solution and ranges from 0 to 14, with 7 being neutral. A pH less than 7 indicates an acidic solution, while a pH greater than 7 signifies a basic (or alkaline) solution.

The pOH value is a similar scale that measures the concentration of hydroxide ions (\(OH^-\)). Both scales are related by the equation:
\[ pH + pOH = 14 \].
This means that if you know the pH of a solution, you can easily calculate the pOH by subtracting the pH from 14. For example, if a solution has a pH of 9.5, the pOH can be calculated as \(14 - 9.5 = 4.5\). You can then use the pOH to find the concentration of hydroxide ions, which is particularly useful when dealing with basic solutions.

The hydronium ion concentration, denoted as \( [H_3O^+] \), is a measure of the number of hydronium ions in a solution. Hydronium ions are created when an acid dissolves in water and donates a proton (\(H^+\)) to a water molecule. The concentration of \(H_3O^+\) ions determines the acidity of the solution.

To calculate the hydronium ion concentration from the pH, use the formula:
\( [H_3O^+] = 10^{-pH} \).
So for a pH of 9.5, the hydronium ion concentration would be \( 10^{-9.5} \), or approximately \(3.16 \times 10^{-10}\) M. Having a low concentration of hydronium ions, as indicated by a high pH, means the solution is basic.

In parallel to hydronium ions, the concentration of hydroxide ions, denoted as \( [OH^-] \), is crucial for understanding base strength. Hydroxide ions are present when a base dissociates in water. The higher the concentration of \(OH^-\), the more basic the solution.

To find the hydroxide ion concentration, you can use the pOH or directly calculate it if you know the \(H_3O^+\) concentration by using the ion product of water:
\( [OH^-] = \frac{1.0 \times 10^{-14}}{[H_3O^+]} \).
For a given \(H_3O^+\) concentration of \(3.16 \times 10^{-10}\) M, you find that the hydroxide ion concentration \( [OH^-] \) is \(3.16 \times 10^{-5}\) M. The higher concentration of hydroxide ions compared to hydronium ions reflects the basic nature of the solution with a pH of 9.5.

The ion product of water, also known as the water dissociation constant (\(K_w\)), is a fundamental constant at a given temperature. For standard conditions at 25°C, the ion product is \(1.0 \times 10^{-14}\). It represents the product of the molar concentrations of hydronium and hydroxide ions in pure water:
\( [H_3O^+] [OH^-] = K_w \).
This constant is the result of water autoionizing into hydronium and hydroxide ions, a process which happens in all aqueous solutions. An important point to note is that changes in the concentration of hydronium ions will inversely affect the concentration of hydroxide ions to maintain the equilibrium constant \(K_w\).

The concept of the ion product of water is essential when solving for an unknown concentration of either ion in a solution. If you are provided with one ion's concentration, you can always calculate the other ion's concentration using this constant, as shown in the previous sections.