Question

Given the following \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) values, determine the pH of each solution. a. \(1.0 \times 10^{-7} \mathrm{M}\) b. \(1.0 \times 10^{-3} \mathrm{M}\) c. \(1.0 \times 10^{-12} \mathrm{M}\) d. \(1.0 \times 10^{-5} \mathrm{M}\)

Short answer

a: 7, b: 3, c: 12, d: 5

Step-by-step solution

Understand the pH Formula

The pH of a solution is determined using the formula: \[ \text{pH} = -\text{log}[\text{H}_3\text{O}^+] \]. The hydronium ion concentration, \([\text{H}_3\text{O}^+]\), is given for each solution.

Calculate pH for Part A

For the solution with \([\text{H}_3\text{O}^+] = 1.0 \times 10^{-7} \text{M}\), compute the pH as follows: \[ \text{pH} = -\text{log}(1.0 \times 10^{-7}) = 7 \].

Calculate pH for Part B

For the solution with \([\text{H}_3\text{O}^+] = 1.0 \times 10^{-3} \text{M}\), compute the pH as follows: \[ \text{pH} = -\text{log}(1.0 \times 10^{-3}) = 3 \].

Calculate pH for Part C

For the solution with \([\text{H}_3\text{O}^+] = 1.0 \times 10^{-12} \text{M}\), compute the pH as follows: \[ \text{pH} = -\text{log}(1.0 \times 10^{-12}) = 12 \].

Calculate pH for Part D

For the solution with \([\text{H}_3\text{O}^+] = 1.0 \times 10^{-5} \text{M}\), compute the pH as follows: \[ \text{pH} = -\text{log}(1.0 \times 10^{-5}) = 5 \].

Key concepts

acid-base chemistry

Acid-base chemistry is a fundamental part of understanding various chemical reactions and processes. It deals with the behavior of acids and bases in solution.
Acids are substances that donate protons (H⁺ ions) in a reaction, while bases accept protons.
When an acid dissolves in water, it forms hydronium ions \text{(\(\text{H}_3\text{O}^+\))}.
For example, when hydrochloric acid (HCl) dissolves in water, it dissociates into H⁺ and Cl⁻.
The H⁺ ion combines with a water molecule to form hydronium ion.

Understanding the concepts of acids and bases is crucial in predicting the pH of solutions and their resulting reactivity. Both concepts play a significant role in various fields like biology, medicine, and environmental science.

hydronium ion concentration

The hydronium ion concentration, \text{(\([\text{H}_3\text{O}^+]\))} is an important parameter in determining the acidity of a solution.
Hydronium ions are formed when an acid dissolves in water.
The concentration of these ions directly affects the pH of the solution. For example:

• A high \text{[\(\text{H}_3\text{O}^+\)]} denotes an acidic solution.
• A low \text{[\(\text{H}_3\text{O}^+\)]} denotes a basic solution.

Here's how the concentration of hydronium ions affects pH:

• If \text{[\(\text{H}_3\text{O}^+\)]} = 1.0 × 10⁻⁷ M, the solution is neutral with a pH of 7.
• If \text{[\(\text{H}_3\text{O}^+\)]} = 1.0 × 10⁻³ M, the solution is acidic with a pH of 3.
• If \text{[\(\text{H}_3\text{O}^+\)]} = 1.0 × 10⁻¹² M, the solution is basic with a pH of 12.

Therefore, knowing \text{[\(\text{H}_3\text{O}^+\)]} helps predict the behavior and characteristics of the solution.

logarithms in chemistry

Logarithms are an essential mathematical tool in chemistry, especially for pH calculations.
The pH of a solution is calculated using the negative logarithm (base 10) of the hydronium ion concentration: \text{\(\text{pH} = -\text{log}[\text{H}_3\text{O}^+]\)}.

Here’s why logarithms are used:

• They simplify the representation of very large or very small numbers.
  For example, \text{1.0 × 10⁻⁷} is converted to \text{7.0} in terms of pH.
• They help in easily comparing the acidity or basicity of different solutions.
  Small changes in \text{[\(\text{H}_3\text{O}^+\)]} result in more significant changes in pH values:
• For instance, moving from \text{1.0 × 10⁻⁵ M to 1.0 × 10⁻⁶ M} changes the pH from 5 to 6.

So, understanding logarithms is vital for grasping various concepts in chemistry, including pH and pOH calculations.

solution acidity

Solution acidity refers to how acidic or basic a solution is, which is determined by its pH value.
The pH scale ranges from 0 to 14.

• A pH less than 7 indicates an acidic solution.
• A pH of 7 indicates a neutral solution.
• A pH greater than 7 indicates a basic solution.

The acidity of a solution affects many chemical reactions, biological processes, and industrial applications.
For example:

• Acidic solutions can cause corrosion of metals.
• Basic solutions are important in cleaning products.
• Neutral solutions like pure water are essential for life.

Therefore, knowing the pH of a solution is crucial for many scientific and practical purposes.