Question

Make the following conversions. In each case, tell whether the solution is acidic or basic. \(\mathbf{p} \mathbf{H}$$\quad$$\left[\mathbf{H}_{3} \mathbf{O}^{*}\right]\) (a) 1.00\(\quad\)______ (b) 10.50\(\quad\)______ (c) ______\(\quad1.3 \times 10^{-3} \mathrm{M}\) (d) ______\(\quad2.3 \times 10^{-8} \mathrm{M}\)

Short answer

(a) 0.1 M, acidic; (b) \(3.16 \times 10^{-11}\) M, basic; (c) pH 2.89, acidic; (d) pH 7.64, basic.

Step-by-step solution

Understanding the pH and Hydrogen Ion Concentration Relationship

The pH of a solution is related to the concentration of hydronium ions, \([H_3O^+]\), by the equation \[pH = -\log_{10}[H_3O^+]\]. This tells us that a low pH corresponds to a high concentration of \([H_3O^+]\), while a high pH corresponds to a low concentration.

Converting pH 1.00 to Hydronium Ion Concentration

For pH 1.00, use the formula \[pH = -\log_{10}[H_3O^+]\]. Solving for \([H_3O^+]\), we have \[1 = -\log_{10}[H_3O^+]\]. Therefore, \([H_3O^+] = 10^{-1} = 0.1 \text{ M}\). Since pH 1.00 is less than 7, this solution is acidic.

Converting pH 10.50 to Hydronium Ion Concentration

For pH 10.50, we apply the same formula: \[10.50 = -\log_{10}[H_3O^+]\]. Thus, \([H_3O^+] = 10^{-10.50} \approx 3.16 \times 10^{-11} \text{ M}\). Since pH 10.50 is greater than 7, this solution is basic.

Finding pH From Hydronium Ion Concentration 1.3 x 10^{-3} M

Given \([H_3O^+] = 1.3 \times 10^{-3} \text{ M}\), find pH using the formula \[pH = -\log_{10}(1.3 \times 10^{-3})\]. Calculating, \[-\log_{10}(1.3) - (-3) \approx 2.89\]. Since 2.89 is less than 7, the solution is acidic.

Finding pH From Hydronium Ion Concentration 2.3 x 10^{-8} M

Given \([H_3O^+] = 2.3 \times 10^{-8} \text{ M}\), find pH using the formula \[pH = -\log_{10}(2.3 \times 10^{-8})\]. Calculating, \[-\log_{10}(2.3) - (-8) \approx 7.64\]. Since 7.64 is greater than 7, the solution is basic.

Key concepts

Hydronium Ion Concentration

The hydronium ion concentration is a measure of the acidity or alkalinity of a solution. When we discuss \([H_3O^+]\), we are referring to the concentration of hydronium ions present in the solution. A higher concentration of \([H_3O^+]\) indicates a more acidic solution, while a lower concentration suggests the solution is more basic.
Understanding this concept is crucial to grasping pH-related calculations effectively. Hydronium ions are formed when hydrogen ions, \( H^+ \), in a solution associate with water molecules, resulting in \( H_3O^+ \).
Knowing the hydronium concentration enables us to calculate the pH and thereby determine the nature of the solution - either acidic or basic.

Acidic and Basic Solutions

Acidic and basic solutions are essential concepts in chemistry related to pH value. A solution is classified as acidic if its pH value is less than 7. Neutral solutions have a pH of 7, typical of pure water, while solutions with a pH higher than 7 are considered basic or alkaline.

• Acidic solutions have a high concentration of hydronium ions \([H_3O^+]\).
• Basic solutions have a low concentration of hydronium ions and often a higher concentration of hydroxide ions \([OH^-]\).

Understanding whether a solution is acidic or basic is essential in various scientific fields like biology, chemistry, and environmental science. This knowledge helps in predicting the behavior of chemical reactions and processes in solutions.

Logarithmic Relationship of pH

The logarithmic scale of pH helps us manage the vast range of hydronium ion concentrations found in different solutions.
The equation \( pH = -\log_{10}[H_3O^+] \) defines this logarithmic relationship, allowing us to convert the ion concentration into a simpler scale of pH. This scale ranges from 0-14, providing an accessible way to read and understand acidity or basicity levels.
Let's break it down a bit:

• A small change in pH represents a tenfold change in the hydronium ion concentration because of the logarithmic nature.
• A decrease of 1 pH unit signifies the hydronium ion concentration increased by a factor of 10.

This relationship underscores the sensitivity of the pH scale and highlights why careful measurement and calculationare crucial in studies related to chemistry and biology.