Determining Hydroxide Ion Concentration in an Aqueous Solution with pH 5

In this article, we will delve into how to determine the hydroxide ion concentration in an aqueous solution where the pH is 5. We will explore the relationship between pH, pOH, and the ion product of water (Kw). Understanding these concepts is crucial for analyzing the basic properties of aqueous solutions.

Key Concepts

Before we proceed, it’s essential to understand the key concepts involved:

pH: A measure of the concentration of hydrogen ions (H ) in a solution. pOH: A measure of the concentration of hydroxide ions (OH–) in a solution. It is related to pH by the formula pH pOH 14. Ion Product of Water (Kw): The product of the concentrations of hydrogen ions (H ) and hydroxide ions (OH–) in a solution at 25°C, which is equal to 1 x 10-14.

Calculating pH and pOH

Given that the pH of an aqueous solution is 5, we can calculate the corresponding pOH:

Calculation Steps:

Calculate pOH:

Using the relationship between pH and pOH:

pOH 14 - pH

In this case:

pOH 14 - 5 9

Calculate the Hydroxide Ion Concentration [OH–]:

The concentration of hydroxide ions can be determined using the formula:

[OH–] 10-pOH

Substituting the value of pOH:

[OH–] 10-9 M

Alternative Methods

There are two recognized methods to determine the hydroxide ion concentration, both of which are illustrated below:

Using pH and pOH:

Given:

PH 5.00

pOH 14.00 - 5.00 9.00

Therefore:

[OH–] 1 x 10-9 M

Using the Ion Product of Water (Kw):

Given:

pH 5.00

[H] 10-5 M

From the ion product of water (Kw):

Kw [H][OH–]

Therefore:

[OH–] 10-14 / 10-5 10-9 M

Miscellaneous Calculations

Here are a few additional calculations and concepts to solidify your understanding:

Using the relationship between pH and [H ]:

Given:

pH -log[H3O ] 5.6

Then:

pOH 8.4

[OH–] 10-8.4 mol L-1 3.98 x 10-9 mol L-1

General Relationship Formulae:

pH pOH 14

Given: pH 5

pOH 14 - 5 9

[OH–] 1 x 10-9 M

Another Method:

Given:

pH 5

-log[H] 5

[H] 10-5 M

From the ion product of water (Kw):

Kw [H][OH–] 1 x 10-14

Therefore:

[OH–] 1 x 10-14 / 1 x 10-5 1 x 10-9 M

Conclusion

By understanding the concepts of pH, pOH, and the ion product of water, you can accurately determine the hydroxide ion concentration in an aqueous solution with a given pH. These calculations are essential in various fields, including chemistry, environmental science, and biotechnology, where the basic properties of solutions play a crucial role.