91Ó°ÊÓ

The water ion-product constant, often symbolized as \( K_w \), is a crucial concept when dealing with ion concentration in aqueous solutions. At 25°C, pure water continuously undergoes a self-ionization process where it dissociates into equal concentrations of hydrogen ions \( \left[ \mathrm{H}^{+} \right] \) and hydroxide ions \( \left[ \mathrm{OH}^{-} \right] \). The product of these concentrations is a constant value:

• \( K_w = \left[ \mathrm{H}^{+} \right] \times \left[ \mathrm{OH}^{-} \right] = 1.0 \times 10^{-14} \text{ M}^2 \)

This constant is vital because it allows us to relate the concentration of \( \mathrm{H}^{+} \) ions and \( \mathrm{OH}^{-} \) ions in any aqueous solution. When the temperature is 25°C, the value of \( K_w \) remains the same for any solution, whether acidic or basic.
This powerful relationship means that if you know the concentration of one ion, \( \left[ \mathrm{H}^{+} \right] \) or \( \left[ \mathrm{OH}^{-} \right] \), you can easily determine the concentration of the other using the formula \( \left[ \mathrm{OH}^{-} \right] = \frac{K_w}{\left[ \mathrm{H}^{+} \right]} \). In essence, \( K_w \) is the key that maintains the balance between acidity and basicity in water.

Understanding hydrogen ion concentration \( \left[ \mathrm{H}^{+} \right] \) is essential for determining the pH and acidic nature of solutions. The acidity of a solution is directly related to how many \( \mathrm{H}^{+} \) ions it contains.
In pure water at 25°C, the concentration of \( \mathrm{H}^{+} \) ions is \( 1.0 \times 10^{-7} \text{ M} \). In solutions, however, this concentration varies leading to different pH levels.

• An increase in \( \left[ \mathrm{H}^{+} \right] \) indicates a more acidic solution.
• A decrease means a more basic or alkaline solution.

The pH scale, a logarithmic measure derived from \( \left[ \mathrm{H}^{+} \right] \), helps classify solutions as acidic, neutral, or basic:

• pH = -\( \log_{10} \left[ \mathrm{H}^{+} \right] \)
• Acidic solutions have a pH less than 7
• Neutral solutions have a pH of 7
• Basic solutions have a pH greater than 7

Therefore, knowing \( \left[ \mathrm{H}^{+} \right] \) is not just instrumental in computing the pH but is crucial in explaining the chemical nature and behavior of an aqueous solution.

Hydroxide ion concentration \( \left[ \mathrm{OH}^{-} \right] \) is pivotal when examining the basic nature of a solution. The presence of \( \mathrm{OH}^{-} \) ions indicates the capacity of a solution to neutralize acids. Just like \( \left[ \mathrm{H}^{+} \right] \), the concentration of \( \left[ \mathrm{OH}^{-} \right] \) changes depending on whether a solution is acidic or basic.

• In a basic solution, \( \left[ \mathrm{OH}^{-} \right] \) is higher than \( 1.0 \times 10^{-7} \text{ M} \).
• For acidic solutions, \( \left[ \mathrm{OH}^{-} \right] \) is lower than \( 1.0 \times 10^{-7} \text{ M} \).

Once the \( \left[ \mathrm{H}^{+} \right] \) is known, \( \left[ \mathrm{OH}^{-} \right] \) can be calculated using the formula \( \left[ \mathrm{OH}^{-} \right] = \frac{K_w}{\left[ \mathrm{H}^{+} \right]} \).
In the exercise, we found that \( \left[ \mathrm{H}^{+} \right] \) was \( 9.44 \times 10^{-11} \mathrm{M} \), leading to \( \left[ \mathrm{OH}^{-} \right] \) being approximately \( 1.06 \times 10^{-4} \mathrm{M} \).
Knowing \( \left[ \mathrm{OH}^{-} \right] \) in a solution is crucial for calculating pOH, which follows the relationship \( \text{pOH} = -\log_{10} \left[ \mathrm{OH}^{-} \right] \).
This relationship complements the pH scale and helps in deducing the overall nature of the solution.