Question

Complete the following table for a solution at \(25^{\circ} \mathrm{C}:\) \begin{tabular}{c|c|c} \(\mathrm{pH}\) & {\(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\)} & Solution is \\\ \hline\(<7\) & & \\ \hline & \(<1.0 \times 10^{-7} M\) & \\ \hline & & Neutral \end{tabular}

Short answer

Acidic solution: \([\text{H}_3\text{O}^+] > 1.0 \times 10^{-7} M\); basic solution has pH > 7.

Step-by-step solution

Understanding pH

The pH of a solution is a measure of how acidic or basic it is, calculated by the formula \(\text{pH} = -\log_{10}[\text{H}_3\text{O}^+]\). A pH less than 7 indicates an acidic solution, which means the concentration of \([\text{H}_3\text{O}^+]\) is greater than \(1.0 \times 10^{-7} M\).

Determining Hydronium Concentration

Given that \([\text{H}_3\text{O}^+] < 1.0 \times 10^{-7} M\), we can determine the pH to be greater than 7, indicating the solution is basic. As the concentration decreases below \(1.0 \times 10^{-7} M\), the solution becomes more basic.

Interpreting a Neutral Solution

A neutral solution at \(25^{\circ}C\) has a \([\text{H}_3\text{O}^+]\) of \(1.0 \times 10^{-7} M\), corresponding to a pH of 7. Hence, when a solution is neutral, it neither is acidic (pH < 7) nor basic (pH > 7).

Key concepts

Hydronium Concentration

The hydronium concentration \([ ext{H}_3 ext{O}^+]\) in a solution is crucial for determining its acidity or basicity. Hydronium ions form when hydrogen ions \( ext{H}^+ \) associate with water molecules, creating \( ext{H}_3 ext{O}^+\). The concentration of these ions provides insight into the solution's pH, which is calculated using the formula: \[ ext{pH} = -\log_{10}[ ext{H}_3 ext{O}^+]\].
When the hydronium concentration is high, specifically greater than \(1.0 \times 10^{-7} \, M\), the solution is more acidic. Conversely, when it is less than this value, the solution tends to be basic. At the standard conditions of \(25^{\circ}C\), a concentration of \(1.0 \times 10^{-7} \, M\) indicates neutrality.
Understanding the hydronium concentration helps predict changes in pH. This is vital for processes like titrations and understanding environmental changes in ecosystems.

Acidic Solution

An acidic solution is defined by a pH less than 7. This occurs when there is a higher concentration of hydronium ions compared to pure water. In more concrete terms, if \( [ ext{H}_3 ext{O}^+] > 1.0 \times 10^{-7} \, M\), the solution is acidic.
Acidic solutions have unique characteristics:

• They often have a sour taste.
• They change blue litmus paper to red.
• They can conduct electricity due to the ion presence.

The high concentration of hydronium ions is typically sourced from acids like hydrochloric acid \( ext{HCl}\) or sulfuric acid \( ext{H}_2 ext{SO}_4\), which dissociate in water to release hydrogen ions that form hydronium.

Basic Solution

A basic solution, or alkaline solution, occurs when the pH is greater than 7. This indicates a lower hydronium ion concentration, specifically less than \(1.0 \times 10^{-7} \, M\).
Common characteristics of basic solutions include:

• A bitter taste.
• The ability to turn red litmus paper to blue.
• They feel slippery to the touch, like soap.

Common bases include sodium hydroxide \( ext{NaOH}\), which dissociates in water to reduce hydronium ion concentration, making the solution basic.
Understanding the concept of basic solutions is crucial for industries like cleaning products and the culinary arts, where pH balance is vital.

Neutral Solution

A neutral solution has a perfect balance of hydronium \[ [ ext{H}_3 ext{O}^+] = 1.0 \times 10^{-7} \, M \] and hydroxide ions \[ [ ext{OH}^-] = 1.0 \times 10^{-7} \, M \]. This equilibrium results in a pH of 7.
The most common example of a neutral solution is pure water at \(25^{\circ}C\). In this state, water is neither acidic nor basic.
Neutral solutions have significant importance in biology and chemistry. For instance:

• Biological systems often operate best at neutral pH.
• Neutral pH is a standard used in various scientific analyses.

Grasping the concept of neutrality helps in the creation of buffer solutions, which resist changes in pH.