Problem 9 - Chemistry and Chemical Reactivity

Question

An aqueous solution has a pH of \(3.75 .\) What is the hydronium ion concentration of the solution? Is it acidic or basic?

Step-by-Step Solution

Answer

The hydronium ion concentration is \( 1.78 \times 10^{-4} \) mol/L; the solution is acidic.

Step 1: Understanding the pH and Hydronium Ion Relationship

The pH of a solution is the negative logarithm (base 10) of the hydronium ion concentration. This relationship is expressed as \( \text{pH} = -\log[H_3O^+] \). In this exercise, we need to find \( [H_3O^+] \) given the pH is 3.75.

Step 2: Rearranging the Formula

To find the hydronium ion concentration \( [H_3O^+] \), we rearrange the formula \( \text{pH} = -\log[H_3O^+] \) to \( [H_3O^+] = 10^{-\text{pH}} \). This results directly from the definition of logarithms.

Step 3: Calculating the Hydronium Ion Concentration

Substitute the given pH value into the formula: \( [H_3O^+] = 10^{-3.75} \). Use a calculator to evaluate this expression, which results in approximately \( 1.78 \times 10^{-4} \) mol/L.

Step 4: Determining if the Solution is Acidic or Basic

A solution is acidic if its pH is less than 7, and basic if it is greater than 7. Given that the pH is 3.75, which is less than 7, the solution is therefore acidic.

Key Concepts

Hydronium Ion Concentration

Hydronium ion concentration is a fundamental concept in chemistry when discussing the acidity of solutions. The term refers to the concentration of hydronium ions, symbolized by \( [H_3O^+] \), which is a major determinant of a solution's pH. Hydronium ions form when water molecules accept a proton (H⁺), creating the formula \( H_3O^+ \).
To find the hydronium ion concentration from a known pH, we use the equation \( [H_3O^+] = 10^{-\text{pH}} \). This equation stems from the property of logarithms and the definition of pH as the negative logarithm of hydronium concentration.
For example, if a solution has a pH of 3.75, we determine its hydronium ion concentration by applying the formula \( [H_3O^+] = 10^{-3.75} \), resulting in approximately \( 1.78 \times 10^{-4} \) mol/L. This calculation illustrates how concentrations in acidic solutions are often expressed in fractions of one molar (mol/L), reflecting the presence of fewer ions compared to a neutral or basic solution.

Acidic and Basic Solutions

The classification of solutions as acidic or basic depends on their pH level. pH is a scale used to specify how acidic or basic a water-based solution is. The scale ranges from 0 to 14, where acids are characterized by a pH less than 7, and bases by a pH greater than 7.

• Solutions with pH values from 0 to 6.9 are acidic. These solutions have a higher concentration of hydronium ions.
• Solutions with pH values from 7.1 to 14 are basic (alkaline). These solutions have a lower concentration of hydronium ions compared to hydroxide ions \( [OH^-] \).
• A pH of exactly 7 denotes a neutral solution, like pure water, where the concentrations of \( H_3O^+ \) and \( OH^- \) ions are equal.

In our exercise, the solution with a pH of 3.75 clearly falls into the acidic category, as it is below 7. This implies that the presence of hydronium ions exceeds that of hydroxide ions in the solution.

Logarithmic Relationship in Chemistry

The concept of logarithms plays a significant role in chemistry, especially in pH calculations. Understanding this relationship is crucial for working with acidity and basicity.
The pH scale itself is logarithmic, meaning each step on the scale represents a tenfold change in hydronium ion concentration. For instance, a pH decrease from 4 to 3 indicates a tenfold increase in \( [H_3O^+] \).

• The pH is calculated using the formula \( \text{pH} = -\log[H_3O^+] \). This expresses how pH inversely relates to \( [H_3O^+] \).
• A lower pH means higher \( [H_3O^+] \), and vice versa.
• Logarithmic calculations convert large ranges of values into manageable numbers, simplifying the comparison of hydronium ion concentrations across different solutions.

Therefore, in chemistry, when dealing with pH, the logarithmic scale allows us to easily understand and communicate the differences in \( [H_3O^+] \) without dealing directly with cumbersome numbers.