Determining the pH of a 10-8 M HCl Solution: A Comprehensive Guide

Understanding the pH of a 10-8 M HCl solution is crucial for various scientific and industrial applications. This article delves into the calculation process and provides a detailed breakdown of the steps involved to determine the pH accurately.

Introduction

Hydrochloric acid (HCl) is a strong acid that dissociates completely in water, releasing hydrogen ions (H ) and chloride ions (Cl-). The pH of a 10-8 M HCl solution represents a concentration that, while still measurable, is quite dilute. Calculating this pH requires an understanding of both HCl's dissociation and the minor contribution of hydrogen ions from water itself.

Step-by-Step Calculation

To calculate the pH of a 10-8 M HCl solution, follow these steps:

Dissociation of HCl

When HCl dissolves in water, it dissociates completely, releasing H and Cl- ions:

HCl → H Cl-

In a 10-8 M HCl solution, the concentration of H ions from HCl is:

[H ]HCl 10-8 M

Contribution from Water

Pure water has a H concentration of 10-7 M at 25°C. This minor contribution from water must be considered in the total H concentration calculation:

[H ]water 10-7 M

Total H Concentration

The total H concentration is the sum of the H ions from HCl and water:

[H ]total [H ]HCl [H ]water 10-8 M 10-7 M 1.1 times; 10-7 M

Calculating pH

The pH is defined as the negative logarithm of the hydrogen ion concentration:

pH -log[H ]

Substituting the total H concentration:

pH -log(1.1 times; 10-7) approx; 7.04

Hence, the pH of a 10-8 M HCl solution is approximately 7.04. This calculation takes into account both the H ions from HCl and the minor contribution from water.

Alternative Method

Another method involves considering the common ion effect, where the dissociation of water is suppressed by the presence of H ions from the acid:

Dissociation of Water

Water dissociates to give H and OH- ions:

H2O ? H OH-

Let [H ] from water be x. The total H concentration is [10-8 x] M, and the total OH- concentration is x M. The ionic product of water (Kw) is 10-14:

[H ][OH-] 10-14

(10-8 x)x 10-14

Solving this equation for x:

x approx; 9.5 times; 10-8

The total H concentration is:

[H ]total 10-8 9.5 times; 10-8 1.05 times; 10-7 M

Calculating pH

Using the pH formula:

pH -log(1.05 times; 10-7) approx; 6.98

This method gives a slightly lower pH of 6.98, showing the importance of considering the common ion effect in highly diluted HCl solutions.

Conclusion

The pH of a 10-8 M HCl solution can be accurately calculated by considering both the dissociation of HCl and the minor contribution of H ions from water. Understanding these calculations is vital for various applications in chemistry and related fields.