Calculating the pH of a 10^-7 M HCl Solution: A Comprehensive Guide

Understanding the pH of a 10^-7 M HCl solution is an essential part of chemical analysis and environmental science. This article will explore the calculation of the pH for such a solution, taking into account the dissociation of both HCl and water.

The Basics of pH Calculation

The pH of a solution is calculated using the formula:

pH -log[H]

For a HCl solution with a concentration of 10^-7 M, we initially consider the dissociation of HCl to produce H ions. However, the presence of water also contributes to the H ion concentration through its autoionization.

Calculating the pH of 10^-7 M HCl

Step 1: Calculate the H from HCl

10^-7 M HCl means 10^-7 M H ions from the acid. However, water also ionizes to contribute H ions. The autoionization of water can be expressed as:

2H2O ? H3O OH-

The ionic product of water is 10^-14. Let [H ] from water be x, then:

10^-7 x x 10^-7 x

The equation for the ionic product of water then becomes:

(10^-7 x)(x) 10^-14

10^-7x x^2 10^-14

Solving for x, we get:

x 6.1810^-8

The total [H ] from HCl and water is then:

10^-7 6.1810^-8 1.61810^-7 M

Step 2: Calculate the pH of the Solution

Using the logarithmic formula for pH:

pH -log(1.61810^-7)

This simplifies to:

pH -log(1.618) - log(10^-7) 7 - 0.21 6.79

Addition of 10^-7 M HCl to 1 L Water

Given the addition of 10^-7 moles of HCl to 1 L of water, there are two sources of H3O ions:

[OH-] x

[H3O ] 10^-7 x

The ionic product of water is still 10^-14. Setting up the equation:

(10^-7 x)(x) 10^-14

Solving this quadratic equation, the pH is approximately:

pH 7 - log(sqrt(10^-7)) ≈ 6.76

Conclusion

When calculating the pH of a 10^-7 M HCl solution, it is crucial to consider both the contribution from the HCl and the autoionization of water. Ignoring the contribution from water can lead to inaccuracies in the pH calculation.

Related Keywords: pH, HCl, ionization