Problem 6 Identify each of the following s... [FREE SOLUTION]

Chapter 15: Problem 6

Identify each of the following solutions that are at \(25^{\circ} \mathrm{C}\) as acidic, basic, or neutral: a. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-7} \mathrm{M}\) b. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=1.0 \times 10^{-10} \mathrm{M}\) c. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-7} \mathrm{M}\) d. \(\left[\mathrm{OH}^{-}\right]=1.0 \times 10^{-11} \mathrm{M}\) e. \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]=\left[\mathrm{OH}^{-}\right]\) f. \(\mathrm{pH}=3.0\) g. \(\mathrm{pH}=13.0\)

Short Answer

Expert verified

a. neutral, b. basic, c. neutral, d. acidic, e. neutral, f. acidic, g. basic

Step by step solution

Understand the definitions

Recall that a solution is acidic if \(\text{pH} < 7\), neutral if \(\text{pH} = 7\), and basic if \(\text{pH} > 7\) at \(25^{\text{掳}}\text{C}\). The relationship between \(\text{pH}\) and \([\text{H}_3\text{O}^+]\) is given by \(\text{pH} = -\text{log}([\text{H}_3\text{O}^+])\), and \([\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}\).

Solution (a)

For \( \text{a.} [\text{H}_3\text{O}^+] = 1.0 \times 10^{-7} \text{M} \): \( \text{pH} = -\text{log}(1.0 \times 10^{-7}) = 7 \). Since \( \text{pH} = 7 \), the solution is neutral.

Solution (b)

For \( \text{b.} [\text{H}_3\text{O}^+] = 1.0 \times 10^{-10} \text{M} \): \( \text{pH} = -\text{log}(1.0 \times 10^{-10}) = 10 \). Since \( \text{pH} = 10 \), the solution is basic.

Solution (c)

For \( \text{c.} [\text{OH}^-] = 1.0 \times 10^{-7} \text{M} \): Use the relationship \( [\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14} \). So, \( [\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-7}} = 1.0 \times 10^{-7} \text{M} \). Since \( [\text{H}_3\text{O}^+] = 1.0 \times 10^{-7} \), the solution is neutral.

Solution (d)

For \( \text{d.} [\text{OH}^-] = 1.0 \times 10^{-11} \text{M} \): Use the relationship \( [\text{H}_3\text{O}^+] = \frac{1.0 \times 10^{-14}}{1.0 \times 10^{-11}} = 1.0 \times 10^{-3} \text{M} \). \( \text{pH} = -\text{log}(1.0 \times 10^{-3}) = 3 \). Since \( \text{pH} = 3 \), the solution is acidic.

Solution (e)

For \( \text{e.} [\text{H}_3\text{O}^+] = [\text{OH}^-] \): Since \( [\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14} \) and \( [\text{H}_3\text{O}^+] = [\text{OH}^-] \), it means \( [\text{H}_3\text{O}^+]= [\text{OH}^-] = 1.0 \times 10^{-7} \text{M} \). The solution is neutral (like water).

Solution (f)

For \( \text{f.} \text{pH} = 3.0 \): Since \( \text{pH} < 7 \), the solution is acidic.

Solution (g)

For \( \text{g.} \text{pH} = 13.0 \): Since \( \text{pH} > 7 \), the solution is basic.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

pH scale

The pH scale is a measure of how acidic or basic a solution is. It ranges from 0 to 14.
Here鈥檚 how it breaks down:

Solutions with pH less than 7 are considered acidic.
Solutions with a pH of 7 are neutral.
Solutions with pH greater than 7 are basic.

The pH is calculated using the concentration of hydrogen ions in the solution: \(\text{pH} = -\text{log}([\text{H}_3\text{O}^+])\). This relationship helps determine whether a solution is acidic, neutral or basic.

Hydronium ion concentration

The hydronium ion concentration \([\text{H}_3\text{O}^+]\) is crucial in determining the pH of a solution. Hydronium ions are formed when hydrogen ions (H\textsuperscript{+}) combine with water molecules (H\textsubscript{2}O).
The concentration of hydronium ions helps us identify whether a solution is acidic or basic. For example:

If \([\text{H}_3\text{O}^+] = 1 \times 10^{-7}\text{M} \), pH = 7 and the solution is neutral.
If \([\text{H}_3\text{O}^+] = 1 \times 10^{-3}\text{M} \), pH = 3 and the solution is acidic.

Acidic and basic solutions

Acidic and basic solutions are categorized based on their pH levels:

Acidic solutions: Have a pH less than 7. They have a higher concentration of hydronium ions \([\text{H}_3\text{O}^+]\) and a lower concentration of hydroxide ions \([\text{OH}^-]\).
Basic solutions: Have a pH greater than 7. They have a higher concentration of hydroxide ions \([\text{OH}^-]\) and a lower concentration of hydronium ions \([\text{H}_3\text{O}^+]\).

Examples:

A solution with \([\text{H}_3\text{O}^+] = 1 \times 10^{-10}\text{M} \) has a pH of 10, making it basic.
A solution with a pH of 3 is acidic.

Neutral solutions

Neutral solutions have a pH of 7. This means the concentrations of hydronium ions \([\text{H}_3\text{O}^+]\) and hydroxide ions \([\text{OH}^-]\) are equal and are both \1 \times 10^{-7}\text{M}\.
At this pH level, neither acidic nor basic properties are dominant. Pure water is an example of a neutral solution. It is crucial in various chemical calculations and understanding the balance between acids and bases.

Logarithmic calculations in chemistry

In chemistry, pH calculations often involve the use of logarithms. The pH is defined as the negative logarithm of the hydronium ion concentration:
\(\text{pH} = -\text{log}([\text{H}_3\text{O}^+])\)
This relationship helps simplify the wide range of hydronium ion concentrations into a manageable scale from 0 to 14. Similarly, we can find the concentration of hydronium ions using the pH:
\([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\)
These logarithmic transformations are fundamental in acid-base chemistry.

Relationship between [H3O+] and [OH-]

The concentrations of hydronium ions \([\text{H}_3\text{O}^+]\) and hydroxide ions \([\text{OH}^-]\) in a solution are closely related by the ion product of water:
\([\text{H}_3\text{O}^+][\text{OH}^-] = 1.0 \times 10^{-14}\)
This means if one increases, the other must decrease to maintain this constant value. For instance:

If \([\text{OH}^-] = 1 \times 10^{-7}\text{M}\), then \([\text{H}_3\text{O}^+] = 1 \times 10^{-7}\text{M}\) indicating a neutral solution.
If \([\text{OH}^-] = 1 \times 10^{-11}\text{M}\), then \([\text{H}_3\text{O}^+] = 1 \times 10^{-3}\text{M}\) indicating an acidic solution.

Understanding this relationship helps in identifying the nature of the solution.

91影视

Short Answer

Step by step solution

Understand the definitions

Solution (a)

Solution (b)

Solution (c)

Solution (d)

Solution (e)

Solution (f)

Solution (g)

Key Concepts

pH scale

Hydronium ion concentration

Acidic and basic solutions

Neutral solutions

Logarithmic calculations in chemistry

Relationship between [H3O+] and [OH-]

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Making Measurements

Kinetics

Organic Chemistry

Ionic and Molecular Compounds

Nuclear Chemistry

Study anywhere. Anytime. Across all devices.