Question

A sample of coffee has a pH of 4.3. Calculate the hydronium ion concentration in this coffee. Is the coffee acidic or basic?

Short answer

The hydronium ion concentration is approximately \(5.01 \times 10^{-5}\) M, and the coffee is acidic.

Step-by-step solution

Understanding pH and Hydronium Ion Concentration

pH is a measure of the hydrogen ion concentration in a solution. The formula to calculate the hydronium ion concentration \([H_3O^+]\) from pH is given by the equation: \[ [H_3O^+] = 10^{-pH} \] This means that for any given pH, the hydronium ion concentration is calculated using the power of 10 raised to the negative of the pH value.

Calculate Hydronium Ion Concentration

We need to substitute the given pH value into the formula. The coffee has a pH of 4.3, so we calculate the hydronium ion concentration \([H_3O^+]\) as follows: \[ [H_3O^+] = 10^{-4.3} \] Use a calculator to find the result: \[ [H_3O^+] = 5.01 \times 10^{-5} \] M (molarity). This represents the concentration of hydronium ions in the coffee.

Determine if the Coffee is Acidic or Basic

A solution is considered acidic if it has a pH less than 7, and basic if the pH is greater than 7. Since the pH of the coffee is 4.3, which is less than 7, we can conclude that the coffee is acidic.

Key concepts

pH calculation

To determine the acidity or basicity of a solution, calculating its pH is essential. The pH is a scale that ranges from 0 to 14 and is used to measure the acidity or basicity of a substance. It quantifies the concentration of hydrogen ions, commonly denoted as \([H_3O^+]\), in a solution.
The formula used to find this concentration from the pH is given by: \[ [H_3O^+] = 10^{-pH} \]

In simpler terms, this formula involves raising 10 to the negative power of the value of the pH. This step converts the pH into a quantitative measure that directly correlates with the concentration of hydronium ions in the solution.

• The pH provides an inverse scale: a lower pH means a higher concentration of H extsuperscript{+} ions.
• At pH 7, the solution is neutral, such as pure water.
• A pH below 7 indicates an acidic solution, while above 7 indicates a basic solution.

acidic and basic solutions

Understanding whether a solution is acidic or basic is crucial in both everyday contexts and scientific settings. The pH scale, which goes from 0 to 14, helps identify this. It works as follows:
- **Acidic Solution**: A solution with a pH less than 7. Acids donate hydrogen ions in solutions, which increases their \([H_3O^+]\) concentration. Examples include lemon juice, vinegar, and coffee.
- **Neutral Solution**: A solution with a pH of exactly 7. Neutral solutions like pure water have a balanced concentration of hydrogen and hydroxide ions.
- **Basic Solution**: Also known as alkaline, these have a pH level greater than 7. Bases have more hydroxide ions and can accept hydrogen ions, examples include baking soda and soap.

Understanding the nature of a solution's acidity or basicity is fundamental in various fields, from environmental science to medicine. Knowing whether a solution is acidic or basic impacts aspects such as chemical reactions, digestion, and even cleaning products.

chemistry problem solving

When solving a chemistry problem, especially related to pH, it's important to follow a structured approach.
Here's how you can systematically address such problems:

• **Identify the Problem**: First, clearly understand what information is being requested. In our coffee example, you need to calculate the hydronium ion concentration and determine whether it's acidic or basic.
• **Apply Relevant Formulas**: Use the correct equations related to the problem, such as \[ [H_3O^+] = 10^{-pH} \] for finding hydrogen ion concentration.
• **Substitute Values**: Plug in the known values into the equations step by step. This careful insertion helps avoid errors and ensures precision.
• **Interpret the Results**: Understand what the calculated values mean. With a hydronium ion concentration known, you can easily decipher if the solution is acidic or basic based on its pH.

By following these steps, students can become adept at tackling chemistry problems with confidence. This approach not only aids in the current problem but builds a strong foundation for future complex chemistry challenges. This methodical pathway enhances student understanding and application of chemistry principles effectively.