Understanding Hydroxide Ion Concentration from pH

In chemistry, understanding the relationship between pH and hydroxide ion concentration is crucial for various applications, from environmental science to pharmaceutical research. This article will guide you through the process of calculating the hydroxide ion concentration from a given pH value, using specific examples and the relevant equations.

Introduction to pH and pOH

First, let's establish the definitions of pH and pOH. The pH of a solution is a measure of the relative acidity or basicity of that solution, defined as the negative logarithm of the hydrogen ion concentration, [H?]. On the other hand, the pOH of a solution is the negative logarithm of the hydroxide ion concentration, [OH?], and is used to represent the basicity of a solution. The relationship between these two measures can be described by the equation:

Relationship Between pH and pOH

The relationship between pH and pOH is given by:

[pH pOH 14]

This relationship is central to solving problems involving the hydroxide ion concentration of a solution.

Steps to Determine Hydroxide Ion Concentration from pH

Let's walk through the steps to find the hydroxide ion concentration of a solution with a pH of 12.8.

Step 1: Calculate the pOH

To calculate the pOH, use the equation:

[pOH 14 - pH]

For a solution with a pH of 12.8, the pOH is calculated as:

[pOH 14 - 12.8 1.2]

Step 2: Convert pOH to Hydroxide Ion Concentration

The pOH can be converted to the hydroxide ion concentration using the equation:

[[OH^-] 10^{-pOH}]

Substitute the pOH value into this equation:

[[OH^-] 10^{-1.2} approx 0.0631 M]

Thus, the hydroxide ion concentration of the solution is approximately 0.0631 M.

Alternative Methods for Calculation

While the previous method is straightforward, there are alternative ways to solve the same problem. Let's explore two different methods to find the hydroxide ion concentration for the same pH value of 12.8.

Method 1: Direct Calculation Using [H?] and [H?][OH?] (10^{-14})

If you know the hydrogen ion concentration, [H?], you can use the relationship that [H?][OH?] (10^{-14}) to find [OH?]. First, calculate [H?]:

[H^ 10^{-12.8} 1.58 times 10^{-13} M]

Then, using the relationship:

[ [OH^-] frac{10^{-14}}{H^ } frac{10^{-14}}{1.58 times 10^{-13}} approx 6.31 times 10^{-2} M ]

Method 2: Using pOH Directly

Calculate pOH using the same difference from 14:

[pOH 14 - pH 14 - 12.8 1.2]

Then calculate the hydroxide ion concentration:

[ [OH^-] 10^{-1.2} approx 6.31 times 10^{-2} M ]

Additional Example: pH of 13.20

As a further example, let's consider a solution with a pH of 13.20. Calculate the pOH:

[pOH 14 - pH 14 - 13.20 0.80]

Then, the hydroxide ion concentration is:

[ [OH^-] 10^{-0.8} 0.16 M ]

Conclusion

Understanding how to calculate the hydroxide ion concentration from a given pH is essential for chemists and researchers. By following the steps outlined in this article and applying the relevant equations, you can easily determine the hydroxide ion concentration for various solutions.