Determining the pH of a 0.033 M KOH Solution: A Comprehensive Guide

KOH, also known as potassium hydroxide, is a strong base that fully dissociates in water. This article provides a detailed guide on how to determine the pH of a 0.033 M KOH solution using fundamental concepts of chemistry.

Step-by-Step Process for Calculating pH

First, let's understand the principle behind the dissociation of KOH in water. KOH completely dissociates into K and OH- ions, making it a strong base. This dissociation can be represented by the following equation:

[ text{KOH} rightarrow text{K}^ text{OH}^- ]

Since the KOH is a strong base, the concentration of OH- ions in the solution is equal to the concentration of KOH. Therefore, the concentration of OH- ions is 0.033 M.

Calculating pOH

The concentration of OH- ions can be used to calculate the pOH of the solution. The pOH is defined as the negative logarithm of the hydroxide ion concentration:

[ text{pOH} -log[text{OH}^-] ]

Substituting the concentration of OH- ions into the equation:

[ text{pOH} -log(0.033) approx 1.5 ]

Calculating pH

Once the pOH is known, the pH can be calculated using the relationship between pH and pOH. At 25°C, the sum of pH and pOH is always 14:

[ text{pH} text{pOH} 14 ]

Therefore:

[ text{pH} 14 - text{pOH} 14 - 1.5 12.5 ]

Thus, the pH of a 0.033 M KOH solution is approximately 12.5.

Alternative Methods for Calculating pH

There are alternative methods for calculating the pH of a 0.033 M KOH solution, which can be useful in different scenarios:

Alternative 1

This method involves calculating the number of moles of KOH in 1.0 L of solution and then finding the concentration of OH- ions. Here's how it works:

Calculate the moles of KOH in 1.0 L solution: Moles of KOH 1000 mL / 566 mL 0.00618 mol KOH/L KOH dissociates completely to form OH- ions, so [OH-] 0.00618 M Use the Kw equation to find [H ] [H ] [OH-] 1 × 10-14 [H ] 1 × 10-14 / 0.00618 ≈ 1.617 × 10-12 M Calculate the pH using the logarithm of [H ] pH -log[1.617 × 10-12 ≈ 11.79

Alternative 2

This method involves finding the pOH and using the relationship between pH and pOH. Here's the process:

Assuming complete dissociation, calculate the moles of hydroxide ions in the solution: Moles of OH- 0.0035 moles in 566 mL, which is equivalent to 0.0062 moles/L Calculate the pOH: pOH -log[OH-] -log(0.0062) ≈ 2.21 Calculate the pH: pH 14 - pOH 14 - 2.21 11.89 This indicates a very alkaline solution with a high concentration of hydroxide ions.

Alternative 3

This method simplifies the calculation process for competitive exams by directly finding the pOH and then the pH:

Given the concentration of KOH (0.033 M), find the concentration of OH- ions: [OH-] 0.033 M Calculate the pOH: pOH -log(0.033) -log(1.5 × 10-2) -(-2 log(1.5)) ≈ 2 - 0.176 1.824 Use the pKw equation to find the pH: pH 14 - pOH 14 - 1.824 12.176 ≈ 12.5

Conclusion

In conclusion, the pH of a 0.033 M KOH solution can be accurately determined using various methods, each offering unique advantages depending on the context and requirements. By understanding the principles of strong base dissociation and the relationship between pH and pOH, chemists and students can effectively tackle similar problems in their studies and research.