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 \(1.78 \times 10^{-4} \ M\). The solution is acidic.

Step 1: Understand the Relationship Between pH and Hydronium Ion Concentration

The pH of a solution is calculated as the negative logarithm (base 10) of the hydronium ion concentration: \( \text{pH} = -\log [\text{H}_3\text{O}^+] \). This formula allows us to determine the concentration of hydronium ions if we know the pH.

Step 2: Rearrange the Formula to Solve for Hydronium Ion Concentration

To find the hydronium ion concentration, rearrange the pH formula to solve for \([\text{H}_3\text{O}^+]\): \([\text{H}_3\text{O}^+] = 10^{-\text{pH}}\).

Step 3: Substitute the Given pH Value

Substitute the given pH value of 3.75 into the equation: \([\text{H}_3\text{O}^+] = 10^{-3.75}\).

Step 4: Calculate the Hydronium Ion Concentration

Use a calculator to find \(10^{-3.75}\). The concentration of hydronium ions is \(1.78 \times 10^{-4}\) M.

Step 5: Determine if the Solution is Acidic or Basic

A solution is acidic if its pH is less than 7 and basic if its pH is greater than 7. Since the pH is 3.75, which is less than 7, the solution is acidic.

Key Concepts

Acidic and Basic Solutions

When discussing acids and bases, the pH scale is our main tool. This scale ranges from 0 to 14 and helps categorize solutions based on their acidity or basicity. Here’s how it works:

• A solution is considered **acidic** if its pH is less than 7. This means it has a higher concentration of hydronium ions \( ([\text{H}_3\text{O}^+]) \), which gives it its acidic properties.
• A **basic** or alkaline solution, on the other hand, has a pH greater than 7, indicating a lower concentration of hydronium ions and a higher concentration of hydroxide ions \(([\text{OH}^-]) \).
• A neutral solution has a pH of 7 with equal concentrations of hydronium and hydroxide ions.

In our example, with a pH of 3.75, it falls well into the acidic category. This means that the hydronium ion concentration is considerably higher than what you would find in a basic or neutral solution.

Chemical Calculations

Chemical calculations involving pH often require a good grasp of logarithms since pH is derived from the logarithmic scale. Here’s a simple breakdown of the steps involved:

• The primary equation showing the relationship is \( \text{pH} = -\log[\text{H}_3\text{O}^+] \).
• To find the hydronium ion concentration from a known pH, rearrange the formula: \[ [\text{H}_3\text{O}^+] = 10^{-\text{pH}} \]
• Substituting the pH value into the equation allows you to calculate the exact concentration of hydronium ions.

For example, using a calculator to evaluate \(10^{-3.75}\), we find that the hydronium ion concentration is approximately \(1.78 \times 10^{-4} \, \text{M}\). Remember, the lower the pH, the higher the concentration of hydronium ions, demonstrating an inverse relationship.

Solution pH

Understanding solution pH involves interpreting its value to understand the nature of the solution. Here’s what you need to know:

• The pH value indicates how acidic or basic a solution is.
• For this, the scale is logarithmic: each whole number change corresponds to a tenfold change in hydronium ion concentration. Thus, small pH changes can imply significant differences in acidity.
• In practical terms, a solution with a pH of 3 is ten times more acidic than a solution with a pH of 4.

The pH value of 3.75 in our example indicates that the solution is clearly more acidic than neutral water, whose pH value is 7. This measurement is valuable in various fields, such as chemistry, biology, and environmental science, as it affects chemical reactivity and biological activity in solutions.