Question

What is the pH of a \(1.2 \times 10^{-4} \mathrm{M}\) solution of \(\mathrm{KOH}\) ? What is the hydronium ion concentration of the solution?

Short answer

pH is 10.08; hydronium ion concentration is \(8.32 \times 10^{-11} \mathrm{M}\).

Step-by-step solution

Understand the KOH Solution

Potassium hydroxide (KOH) is a strong base, which means it completely dissociates in water. This means the concentration of OH⁻ ions is equal to the concentration of KOH, which is \(1.2 \times 10^{-4} \mathrm{M}\).

Calculate the pOH

The pOH is calculated using the formula \(\text{pOH} = -\log[\text{OH}^-]\). Substituting the given concentration, we have:\[\text{pOH} = -\log(1.2 \times 10^{-4})\]Using a calculator, \(\text{pOH} \approx 3.92\).

Convert to pH

The relationship between pH and pOH is given by the equation \(\text{pH} + \text{pOH} = 14\). To find the pH, subtract the pOH from 14:\[\text{pH} = 14 - 3.92 = 10.08\]

Calculate Hydronium Ion Concentration

The hydronium ion concentration \([\text{H}_3\text{O}^+]\) can be found from the pH using the formula:\[[\text{H}_3\text{O}^+] = 10^{-\text{pH}}\]Substituting the pH value:\[[\text{H}_3\text{O}^+] = 10^{-10.08} \approx 8.32 \times 10^{-11} \mathrm{M}\]

Key concepts

Strong Base Dissociation

When a strong base like potassium hydroxide (KOH) is dissolved in water, it completely dissociates into its constituent ions. For KOH, this dissociation releases potassium ions (\( ext{K}^+\)) and hydroxide ions (\( ext{OH}^-\)). The process can be written as:- \( ext{KOH} \rightarrow \text{K}^+ + \text{OH}^-\)Since KOH dissociates completely, the concentration of hydroxide ions is exactly the same as the concentration of the initial KOH solution. For the given problem, this means a \(1.2 \times 10^{-4} \ \text{M}\) KOH solution has an equal concentration of \([ ext{OH}^-]\). Understanding this concept helps us calculate other parameters like pOH effectively.

pOH Calculation

The pOH of a solution measures the concentration of hydroxide ions. It is calculated using the formula:\[\text{pOH} = -\log[\text{OH}^-]\]For a solution with a hydroxide ion concentration of \(1.2 \times 10^{-4} \ \text{M}\), we plug this value into the formula: - \(\text{pOH} = -\log(1.2 \times 10^{-4})\)Doing the calculation gives us a pOH of approximately 3.92. Remember, a lower pOH indicates a higher concentration of hydroxide ions, meaning the solution is more basic. This relation between OH ion concentration and pOH is essential for understanding the acid-base balance of solutions.

Hydronium Ion Concentration

The hydronium ion concentration \([ ext{H}_3 ext{O}^+]\) in a solution is linked to pH, which is the negative logarithm of the hydrogen ion concentration. It can be calculated using pH as follows:\[[ ext{H}_3 ext{O}^+] = 10^{- ext{pH}}\]In this scenario, after determining the pOH and converting it to pH, we found the pH to be approximately 10.08. Substituting this value into the equation, we find:- \([ ext{H}_3 ext{O}^+] = 10^{-10.08} \approx 8.32 \times 10^{-11} \ \text{M}\)This low concentration of hydronium ions is typical for basic solutions, where hydroxide ions (\([ ext{OH}^-]\)) predominate.

Acid-Base Chemistry

Acid-base chemistry revolves around the interaction and balance between hydrogen ions \([ ext{H}^+]\) and hydroxide ions \([ ext{OH}^-]\). In aqueous solutions:- Acids increase \([ ext{H}^+]\)- Bases increase \([ ext{OH}^-]\)The pH scale, which ranges from 0 to 14, measures how acidic or basic a solution is. Here, acidic solutions have a pH below 7, while basic solutions have a pH above 7. The relationship between pH and pOH is expressed by the equation:- \( \text{pH} + \text{pOH} = 14 \)This relationship shows that as the pH increases (indicating a more basic solution), the pOH decreases. In our problem, the KOH solution is basic with a pH of 10.08, showing more hydroxide ions than hydronium ions. Understanding these concepts allows us to predict the behaviors and interactions of solutions in different chemical environments.