Question

When the hydronium ion concentration of a solution is \(1 \times 10^{-10}\) mole per liter, what is the \(\mathrm{pH}\) of the solution? Is the solution acidic or basic?

Short answer

The pH is 10; the solution is basic.

Step-by-step solution

Understanding the pH Definition

The pH of a solution is calculated using the formula \(\text{pH} = -\log_{10} [\text{H}_3\text{O}^+]\), where \([\text{H}_3\text{O}^+]\) is the concentration of the hydronium ions.

Substitute Hydronium Ion Concentration

Substitute the given hydronium ion concentration into the pH formula: \(\text{pH} = -\log_{10} (1 \times 10^{-10})\).

Apply the Logarithm Rule

Using the properties of logarithms, \(-\log_{10} (1 \times 10^{-10})\) becomes \(-(-10)\times \log_{10}(10)\), which simplifies to 10.

Determine Solution Nature

The pH scale ranges from 0 to 14, where a pH less than 7 indicates an acidic solution and a pH greater than 7 indicates a basic solution. Here, pH = 10, which means the solution is basic.

Key concepts

Hydronium Ion Concentration

Hydronium ions play a key role in determining the acidity of a solution. When an acid dissolves in water, it releases hydrogen ions, which combine with water molecules to form hydronium ions, denoted as \( \text{H}_3\text{O}^+ \). The concentration of these ions is crucial for calculating pH, a widely used measure of acidity or basicity.
The hydronium ion concentration is typically expressed in moles per liter. For example, if a solution has a hydronium ion concentration of \( 1 \times 10^{-10} \) mol/L, it suggests a relatively low presence of these ions, indicating a less acidic or potentially basic nature. Understanding these concentrations can help predict how a solution will behave in chemical reactions.

Acidic vs Basic Solutions

Solutions can be acidic, neutral, or basic (alkaline), which is identified through their pH value. The pH scale ranges from 0 to 14:

• A pH less than 7 indicates an acidic solution. Acidic solutions have more hydronium ions than hydroxide ions and often exhibit sour taste and corrosiveness.
• A pH of exactly 7 indicates neutrality, typical of pure water. In neutral solutions, hydronium and hydroxide ion concentrations are equal.
• A pH greater than 7 indicates a basic solution. Basic solutions have more hydroxide ions than hydronium ions, feel slippery, and are often used as cleaning agents.

In the exercise, the pH was calculated to be 10, meaning the solution is basic. Comprehending this scale is important for determining the properties and potential uses of various solutions in everyday life and industrial applications.

Logarithmic Scale in Chemistry

The pH scale is an example of a logarithmic scale used in chemistry to express the concentration of hydronium ions in a simplified manner. Logarithmic scales are helpful because they can represent a wide range of values succinctly.
The pH formula \( \text{pH} = -\log_{10} [\text{H}_3\text{O}^+] \) implies that for every unit decrease in pH, the hydronium ion concentration increases tenfold. This logarithmic relationship allows chemists to quickly compare the relative acidity of solutions without dealing with very large or small numbers.
Utilizing logarithmic scales is essential not only for calculating pH, but for other scientific fields where exponential growth or decay is observed, making them a versatile concept in understanding real-world phenomena.