Problem 12 - Chemistry and Chemical Reactivity

Question

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

Step-by-Step Solution

Answer

The pH of the solution is 10.08, and the hydronium ion concentration is approximately \(8.32 \times 10^{-11}\; \text{M}\).

Step 1: Understand the Relationship between KOH and \\([OH^-]\\)

KOH is a strong base, meaning it completely dissociates in water to form potassium ions \([K^+]\) and hydroxide ions \([OH^-]\). Therefore, the concentration of \([OH^-]\) in the solution will be equal to the concentration of KOH, which is \(1.2 \times 10^{-4} \; \text{M}\).

Step 2: Calculate the pOH of the Solution

The pOH of a solution is calculated using the formula: \(\text{pOH} = -\log[OH^-]\). Substituting the concentration of hydroxide ions into the formula, we get \(\text{pOH} = -\log(1.2 \times 10^{-4})\approx 3.92\).

Step 3: Convert pOH to pH

The relationship between pH and pOH is given by: \(\text{pH} + \text{pOH} = 14\). Using the calculated pOH of 3.92, we find \(\text{pH} = 14 - 3.92 = 10.08\).

Step 4: Calculate the Hydronium Ion Concentration

The hydronium ion concentration \([H_3O^+]\) can be calculated from the pH using the formula: \([H_3O^+] = 10^{-\text{pH}}\). Substituting the pH value, we get \([H_3O^+] = 10^{-10.08} \approx 8.32 \times 10^{-11}\; \text{M}\).

Key Concepts

KOH dissociation

KOH, or potassium hydroxide, is known as a strong base. When dissolved in water, it undergoes a total dissociation. This means that every molecule of potassium hydroxide separates into positive potassium ions \([K^+]\) and negative hydroxide ions \([OH^-]\). This characteristic of KOH makes it very effective at increasing the concentration of hydroxide ions in a solution because there is a complete conversion without any remaining undissociated molecules.
In a 1.2 \(\times\) 10^{-4} \(\mathrm{M}\) solution of KOH, the concentration of hydroxide ions \([OH^-]\) will also be 1.2 \(\times\) 10^{-4} \(\text{M}\).
This property is a fundamental aspect to consider when carrying out pH calculations involving strong bases.

pOH calculation

The pOH value of a solution is a measure of its hydroxide ion concentration and helps in determining the basicity of the solution. It is calculated using the formula: \( ext{pOH} = -\log[OH^-]\).
For the given KOH solution, you simply input the concentration, which equates to \( ext{pOH} = -\log(1.2 \times 10^{-4})\).
This calculation results in a pOH of approximately 3.92.
A lower pOH value indicates a higher concentration of hydroxide ions, suggesting a more basic solution.
When we know the pOH, we can easily switch to pH using the relationship: \( ext{pH} + ext{pOH} = 14\).

hydronium ion concentration

After calculating pH from pOH, we focus on calculating the hydronium ion concentration, \([H_3O^+]\).
The pH of a solution is a measure of its hydrogen ion concentration, and hydronium ions are considered equivalent for this purpose.
Using the formula \[H_3O^+] = 10^{- ext{pH}}\], hydronium ions can be effectively calculated.
For example, if the pH of our solution is 10.08, then \[H_3O^+] = 10^{-10.08}\], which is approximately \((8.32 \times 10^{-11} \text{M})\).
This low concentration confirms that the solution is indeed basic, as expected since we started with a strong base.

strong base characteristics

Strong bases like KOH have distinct characteristics that define their behavior in aqueous solutions.

• Complete dissociation in water, meaning nearly all the base molecules split into cations and anions.
• High pH due to the high concentration of hydroxide ions \([OH^-]\).
• Lower pOH values indicative of a strong basic nature.
• Strong bases are good conductors of electricity in solution due to the abundance of charged ions.

These characteristics are vital in predicting and understanding how a strong base like KOH affects the pH and overall ionic composition of a solution.