Problem 148 - Introductory Chemistry Atoms First

Question

What is the \(\mathrm{pH}\) of a solution whose \(\mathrm{H}_{3} \mathrm{O}\) concentration is \(10^{6} \mathrm{M}\) ? Is the solution acidic or basic?

Step-by-Step Solution

Answer

The pH of the solution is 6, and since the pH is less than 7, the solution is acidic.

Step 1: Plug the H3O+ concentration into the pH formula

Use the given H3O+ concentration value: [H3O+] = \(10^6M\). Now, substitute this value into the pH formula: pH = -log10(\(10^6M\))

Step 2: Calculate the pH value

Now compute the negative logarithm of the H3O+ concentration to find the pH: pH = -log10(\(10^6\)) = -(-6) = 6

Step 3: Determine if the solution is acidic or basic

We determined the pH of the solution to be 6, which is close to neutral pH (7). According to the pH scale: - If pH < 7, the solution is acidic - If pH = 7, the solution is neutral - If pH > 7, the solution is basic Since pH 6 is less than 7, the solution is acidic.

Key Concepts

H3O+ concentration

The concentration of hydronium ions (\[ \mathrm{H}_{3} \mathrm{O}^+ \]) in a solution is a key determinant of the solution's acidity. It directly affects the pH value of the solution. The hydronium ion concentration is often expressed in terms of molarity (M), which is the number of moles of \( \mathrm{H}_{3} \mathrm{O}^+ \) ions per liter of solution.
A higher concentration of \( \mathrm{H}_{3} \mathrm{O}^+ \) indicates a more acidic solution, while a lower concentration suggests a more basic one. Understanding how to manipulate and measure this concentration allows chemists to predict and control the properties of solutions.

pH scale

The pH scale is a numerical scale ranging from 0 to 14, which helps us determine how acidic or basic a solution is. Each unit on this scale represents a tenfold difference in hydrogen ion concentration.
Here's a quick look at what different pH values imply:

• pH less than 7: The solution is acidic.
• pH equals 7: The solution is neutral, like pure water.
• pH greater than 7: The solution is basic or alkaline.

A smaller pH reflects a higher concentration of hydrogen ions and thus a more acidic solution. Conversely, a larger pH suggests fewer hydrogen ions, indicating a more basic solution.

acidic solution

An acidic solution is characterized by a high concentration of \( \mathrm{H}_{3} \mathrm{O}^+ \) ions, resulting in a pH lower than 7. These solutions tend to have a "sour" taste and can include common substances like lemon juice or vinegar.
Acids are defined by their ability to donate protons (hydrogen ions) to other substances. This proton donation is what increases the hydronium concentration in solutions, lowering the pH. The higher the concentration of these ions, the stronger the acid. Different acids vary in strength,meaning some can donate more protons or have stronger effects on pH levels.

logarithmic calculation

Logarithmic calculations are crucial in chemistry, particularly when working with the pH scale. The pH of a solution is calculated using the formula \[ \text{pH} = -\log_{10}([\text{H}_3\text{O}^+]) \] where \( [\mathrm{H}_{3} \mathrm{O}^+] \) represents the hydronium ion concentration.
This formula highlights the logarithmic nature of the pH scale, as each unit decrease represents a tenfold increase in ion concentration. Such logarithmic calculations can simplify the representation of very large or very small numbers. For instance, taking the negative logarithm of \( 10^6 \) converts a large or small exponential number into a manageable single-digit pH value. Understanding these calculations is essential for accurately measuring the acidity or basicity of a solution.