What is the pH and the principal source of H3O+ ions in 1.0 * 10-10 M HCl? (Hint: The pH of an acid solution can’t exceed 7.) What is the pH of 1.0 * 10-7 M HCl?

Verified step by step guidance

Start by understanding that the pH is a measure of the concentration of hydronium ions \([\text{H}_3\text{O}^+]\) in a solution. The formula for pH is \(\text{pH} = -\log[\text{H}_3\text{O}^+]\).

For a very dilute solution of HCl, such as \(1.0 \times 10^{-10}\, \text{M}\), the concentration of \([\text{H}_3\text{O}^+]\) from the ionization of water (\(1.0 \times 10^{-7}\, \text{M}\)) is significant compared to the concentration of \([\text{H}_3\text{O}^+]\) from the acid.

Recognize that in such dilute solutions, the principal source of \([\text{H}_3\text{O}^+]\) is actually the autoionization of water, not the acid itself.

For \(1.0 \times 10^{-7}\, \text{M}\) HCl, the concentration of \([\text{H}_3\text{O}^+]\) from the acid is equal to the concentration from the autoionization of water, so the total \([\text{H}_3\text{O}^+]\) is \(2.0 \times 10^{-7}\, \text{M}\).

Calculate the pH for both solutions using the formula \(\text{pH} = -\log[\text{H}_3\text{O}^+]\), keeping in mind that the pH of an acidic solution cannot exceed 7.>

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

pH Scale

The pH scale measures the acidity or basicity of a solution, ranging from 0 to 14. A pH of 7 is neutral, while values below 7 indicate acidity and above 7 indicate basicity. The pH is calculated as the negative logarithm of the hydrogen ion concentration, pH = -log[H+]. Understanding this scale is crucial for determining the acidity of solutions like HCl.

Hydrochloric Acid (HCl) Dissociation

Hydrochloric acid (HCl) is a strong acid that completely dissociates in water to produce H3O+ ions and Cl- ions. The concentration of H3O+ ions directly influences the pH of the solution. In very dilute solutions, such as 1.0 * 10^-10 M HCl, the contribution of H3O+ from water itself (1.0 * 10^-7 M) must also be considered when calculating the overall pH.

Contributions to H3O+ Concentration

In dilute acid solutions, the concentration of H3O+ ions from the acid must be compared to the autoionization of water, which contributes 1.0 * 10^-7 M H3O+. For 1.0 * 10^-10 M HCl, the total H3O+ concentration is dominated by the water's contribution, leading to a pH that is still around 7. This concept is essential for understanding how very dilute acids behave in solution.

Recommended video:

Guided course

06:25

Hydronium Ion Concentration Example

Related Practice

Textbook Question

A 100.0 mL sample of a solution that is 0.100 M in HCl and 0.100 M in HCN is titrated with 0.100 M NaOH. Calculate the pH after the addition of the following volumes of NaOH:

(a) 0.0 mL

Textbook Question

Calculate the pH of solutions prepared by:

(d) Mixing equal volumes of 0.20 M HCl and 0.50 M HNO3.

(Assume that volumes are additive.)

Textbook Question

The acidity of lemon juice is derived primarily from citric acid (H3Cit), a triprotic acid. What are the concentrations of H3Cit, H2Cit-, HCit2-, and Cit3- in a sample of lemon juice that has a pH of 2.37 and a total concentration of the four citrate-containing species of 0.350 M?

Textbook Question

A 40.0 mL sample of a mixture of HCl and H3PO4 was titrated with 0.100 M NaOH. The first equivalence point was reached after 88.0 mL of base, and the second equivalence point was reached after 126.4 mL of base.

(e) Sketch the pH titration curve, and label the buffer regions and equivalence points.