Understanding the pH scale is key to solving this problem. The pH value indicates the acidity or alkalinity of a solution.

pH Scale Basics

• The pH scale typically ranges from 0 to 14.
• A pH of 7 is considered neutral.
• A pH less than 7 indicates an acidic solution.
• A pH greater than 7 indicates a basic (alkaline) solution.

pH and Ion Concentrations

The pH value is directly related to the concentration of hydrogen ions ($H^+$) and hydroxide ions ($OH^-$) in a solution.

• Relationship with $H^+$ Ions: pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration:

  $ pH = -\log_{10}[H^+] $

  This means that as the pH value increases, the concentration of $H^+$ ions ($[H^+]$) decreases.
• Relationship with $OH^-$ Ions: In aqueous solutions, the product of hydrogen ion and hydroxide ion concentrations is constant ($K_w = [H^+][OH^-] = 1 \times 10^{-14}$ at 25°C). This leads to the relationship:

  $ pH + pOH = 14 $

  where $pOH = -\log_{10}[OH^-]$. As the pH value increases, the pOH decreases, which in turn means the concentration of $OH^-$ ions ($[OH^-]$) increases.

Interpreting pH Increase from 7 to 14

An increase in pH from 7 to 14 signifies a shift from a neutral solution towards a highly basic (alkaline) solution.

• At pH 7 (Neutral): $[H^+] = [OH^-] = 1 \times 10^{-7}$ M.
• At pH 14 (Highly Basic): This corresponds to a pOH of 0 ($14 - 14 = 0$). Therefore, $[OH^-] = 10^0 = 1$ M, and $[H^+] = 10^{-14}$ M.

Comparing pH 7 and pH 14:

• The $H^+$ ion concentration decreases significantly (from $10^{-7}$ M to $10^{-14}$ M).
• The $OH^-$ ion concentration increases significantly (from $10^{-7}$ M to $1$ M).

Therefore, an increase in pH value from 7 to 14 represents an increase in the $OH^-$ ion concentration.