Question

What effect will decreasing the \(\left[\mathrm{H}^{+}\right]\)of a solution have on (a) \(\mathrm{pH}\), (b) \(\mathrm{pOH}\), (c) \(\left[\mathrm{OH}^{-}\right]\), and (d) \(K_{\mathrm{w}}\) ?

Short answer

Decreasing \(\backslash left[ \backslash mathrm{H}^{+} \backslash right]\) increases pH, decreases pOH, increases \(\backslash left[ \backslash mathrm{OH}^{-} \backslash right]\), and does not affect \(\backslash text{K}_{\backslash text{w}}\).

Step-by-step solution

Understanding the Relationship Between \(\backslash left[ \backslash mathrm{H}^{+} \backslash right]\) and pH

The pH of a solution is calculated using the formula \(\backslash text{pH} = -\backslash log \backslash left[ \backslash mathrm{H}^{+} \backslash right]\). Therefore, when \(\backslash left[ \backslash mathrm{H}^{+} \backslash right]\) decreases, the pH value increases.

Understanding the Relationship Between pH and pOH

The sum of pH and pOH of a solution is always equal to 14. \(\backslash text{pH} + \backslash text{pOH} = 14\). As the pH increases due to the decrease in \(\backslash left[ \backslash mathrm{H}^{+} \backslash right]\), the pOH must decrease to maintain this relationship.

Understanding the Relationship Between \(\backslash left[ \backslash mathrm{OH}^{-} \backslash right]\) and pOH

The concentration of hydroxide ions \(\backslash left[ \backslash mathrm{OH}^{-} \backslash right]\) is related to pOH by the equation \(\backslash text{pOH} = -\backslash log \backslash left[ \backslash mathrm{OH}^{-} \backslash right]\). Therefore, when pOH decreases, \(\backslash left[ \backslash mathrm{OH}^{-} \backslash right]\) must increase.

Understanding Effect on \(\backslash text{K}_{\backslash text{w}}\)

The ion-product constant for water \(\backslash text{K}_{\backslash text{w}}\) is a constant value at a given temperature \(1.0 \backslash times 10^{-14} \backslash text{ at 25} ^{\backslash text{o}} \backslash text{C}\). Changes in \(\backslash left[ \backslash mathrm{H}^{+} \backslash right]\) and \(\backslash left[ \backslash mathrm{OH}^{-} \backslash right]\) do not affect \(\backslash text{K}_{\backslash text{w}}\).

Key concepts

pH and pOH relationship

The relationship between pH and pOH is fundamental in understanding the behavior of acidic and basic solutions. They are intricately connected through the equation pH + pOH = 14. This relationship tells us that if the pH of a solution increases, the pOH must decrease and vice versa. For example, if a solution's pH is 3 (acidic), its pOH will be 11. Conversely, if the pH is 11 (basic), its pOH must be 3. This balance is crucial for maintaining the characteristics of a solution.
Understanding this concept helps in predicting changes in pH when pOH is known, and it is especially helpful in chemical titrations and other analytical methods where precision is important.

Hydrogen ion concentration

Hydrogen ion concentration \([H^+]\) dictates the acidity of a solution. It is calculated using the formula: \[\text{pH} = -\text{log}[H^+]\]. When the concentration of hydrogen ions decreases, pH increases, indicating a move toward basicity. For example, if \([H^+] = 1 \times 10^{-3}\) M, the pH will be 3 (acidic). If we reduce \([H^+]\) to \([H^+] = 1 \times 10^{-8}\) M, the pH shifts to 8 (basic).
It’s important to remember that slight changes in \([H^+]\) can significantly alter the pH, affecting the solution’s properties. This relationship is crucial for processes like enzyme activity in biochemistry, where enzymes are sensitive to pH changes.

Hydroxide ion concentration

The hydroxide ion concentration \([OH^-]\) is connected to the pOH of a solution. The formula is \[\text{pOH} = -\text{log}[OH^-]\]. When the pOH decreases, \([OH^-]\) increases. This inverse relationship works similarly to pH and \([H^+]\). For an example, if \([OH^-] = 1 \times 10^{-4}\) M, the pOH is 4, indicating a basic solution. Reducing the pOH (e.g., to 2) results in an increase in \([OH^-]\) to \([OH^-] = 1 \times 10^{-2}\) M.
Changes in \([OH^-]\) can affect the solution's reactivity and properties, important for tasks ranging from industrial chemical reactions to maintaining swimming pool water quality.

Ion-product constant for water

The ion-product constant for water \(\text{K}_w\) is a fundamental value in chemistry. At 25°C, it is always \[K_w = [H^+][OH^-] = 1.0 \times 10^{-14}\]. This constant remains unchanged regardless of the individual concentrations of \([H^+]\) or \([OH^-]\). It ensures the balance of water's ionization properties.
For instance, if \([H^+]\) decreases, \([OH^-]\) must increase to keep \[K_w\] constant. Understanding \(\text{K}_w\) is critical for predicting the behavior of aqueous solutions and for calculations involving pH and pOH in various chemical processes and solutions.