Understanding the pH of 10^-7 M HCl in Water: A Comprehensive Guide

In chemistry and environmental science, understanding the pH of solutions is fundamental. This article explains the pH of a 10^{-7} M HCl solution in water, discussing the contributions of both the acid and the autoionization of water. By delving into the details of how these components interact, we can accurately calculate the pH value and understand the underlying principles.

Introduction to pH and HCl

HCL (Hydrochloric Acid) is a strong acid, meaning it completely dissociates in water to produce H ions. When dealing with solutions of strong acids like HCl, the concentration of H ions comes almost entirely from the acid itself. However, water inherently autoionizes to produce a small concentration of H ions as well. This phenomenon is crucial for understanding the pH of the solution.

Contribution from HCl

A 10-7 M HCl solution will completely dissociate as follows:

HCl rightarrow H^ Cl^-

Therefore, a 10-7 M HCl solution contributes 10-7 M of H^ ions.

Autoionization of Water

Water autoionizes according to the following equilibrium:

H_2O rightleftharpoons H^ OH^-

At 25°C, the concentration of H^ ions from water alone is 10-7 M. This is due to the ionic product of water, [H ][OH-] 10-14.

Total Concentration of H Ions

The total concentration of H^ ions in the solution is the sum of the H^ ions from HCl and the H^ ions from the autoionization of water. Thus, we have:

[ [H^ ] [H^ ]_{HCl} [H^ ]_{water} 10^{-7}M 10^{-7}M 2times10^{-7}M ]

Calculating pH

The pH is calculated using the formula:

[ pH -log[H^ ] ]

Substituting the total concentration of H^ ions:

[ pH -log(2times10^{-7}) ]

Using properties of logarithms:

[ pH -log2 - log10^{-7} approx -0.301 - (-7) approx 6.699 ]

Therefore, the pH of a 10-7 M HCl solution in water is approximately 6.7.

Advanced Calculations

In more detailed scenarios, we need to account for both the contribution of HCl and the autoionization of water. Let's consider a hypothetical scenario where the HCl concentration is slightly different, such as 10-8 M.

Calculation with 10-8 M HCl

Following the similar process:

[ [H^ ] 10^{-8} M x ]

Where x is the H^ ions contributed by water. Using the ionic product of water:

[ [H^ ][OH^-] 10^{-14} ]

Assuming the concentration of H^ ions from water is x:

[ (10^{-8} x)times x 10^{-14} ]

Solving this quadratic equation:

[ 10^{-8}x x^2 10^{-14} ]

At low concentrations, we can approximate:

[ x^2 approx 10^{-14} Rightarrow x approx 10^{-7} ]

Then:

[ [H^ ] 10^{-8} 10^{-7} approx 10^{-7}M ]

So, the pH is:

[ pH -log(10^{-7}) approx 7 - 0.02 6.98 ]

Thus, the pH of a 10-8 M HCl solution in water is approximately 6.98, accounting for the autoionization of water.

Conclusion

Understanding the pH of 10-7 M HCl in water involves accounting for both the contribution of HCl and the autoionization of water. By considering the concentrations and the ionic product of water, we can accurately determine the pH and appreciate the interplay between these components.

FAQs

Q1: Why do we need to consider the autoionization of water when calculating pH?

A1: The autoionization of water produces a small amount of H^ ions, which must be included in the total concentration of H^ ions when calculating the pH.

Q2: What is the significance of the ionic product of water, [H^ ][OH^-] 10^-14?

A2: The ionic product of water is a constant at 25°C, reflecting the dynamic balance between H^ and OH^- ions in pure water. This product is essential for calculating the concentration of ions in dilute solutions.

Q3: How does the common ion effect influence the dissociation of HCl in water?

A3: The common ion effect acts to suppress the dissociation of water due to the presence of an excess of H^ ions from HCl. This is particularly relevant in scenarios with very low concentrations of HCl.