Problem 25 - Chemistry Matter and Change

Question

Calculate the pH of aqueous solutions with the following \([\mathrm{H}+]\) at 298 \(\mathrm{K}\) . a. \([\mathrm{H}+]=0.0055 \mathrm{M} \quad\) b. \([\mathrm{H}+]=0.000084 \mathrm{M}\)

Step-by-Step Solution

Answer

For the aqueous solution with \([\mathrm{H}+]=0.0055\:\mathrm{M}\), the pH is approximately 2.26. For the solution with \([\mathrm{H}+]=0.000084\:\mathrm{M}\), the pH is approximately 4.08.

Step 1: Using the pH formula, we will calculate the pH for the given \([\mathrm{H}+]\) value. \(pH = -\log_{10} (\mathrm{0.0055\: M})\) Now we just plug the numbers into the formula and calculate the pH. #Step 2: Calculate the pH for \([\mathrm{H}++]=0.0055\:\mathrm{M}\)#

The pH for this solution can be calculated as follows: \(pH = -\log_{10} (\mathrm{0.0055\: M}) \approx 2.26\) #Step 3: Calculate the pH for \([\mathrm{H}+]=0.000084\:\mathrm{M}\)#

Step 2: Similarly, we will use the pH formula to calculate the pH for this given \([\mathrm{H}+]\) value. \(pH = -\log_{10} (\mathrm{0.000084\:M})\) #Step 4: Calculate the pH for \([\mathrm{H}+]=0.000084\:\mathrm{M}\)#

The pH for this solution can be calculated as follows: \(pH = -\log_{10} (\mathrm{0.000084\: M}) \approx 4.08\) Now we have calculated the pH value for both of the given \([\mathrm{H}+]\). The pH for the aqueous solution with \([\mathrm{H}+]=\mathrm{0.0055\: M}\) is approximately 2.26, and for the solution with \([\mathrm{H}+]=\mathrm{0.000084\: M}\), the pH is approximately 4.08.

Key Concepts

Aqueous Solutions

An aqueous solution is a mixture where water is the solvent. This means that substances dissolve in water, creating a homogenous mixture. They are very common in chemistry because water is an excellent solvent due to its polar nature. This allows it to dissolve many ionic compounds and molecules.
### Key Characteristics of Aqueous Solutions

• Water as solvent: Water's polarity enables it to surround and break apart ionic bonds and interact with polar molecules.
• Conductivity: Many aqueous solutions can conduct electricity, especially if they contain ions.
• pH level: Aqueous solutions can range from acidic to basic pH levels based on the dissolved substances.

The behavior of aqueous solutions is essential in many fields, such as biology, medicine, and environmental science, where the dissolution of substances in water leads to critical physiological and chemical processes.

Hydrogen Ion Concentration

Hydrogen ion concentration refers to the number of hydrogen ions (H⁺) present in a solution. This concentration determines the acidity or basicity of a solution.
### Understanding H⁺ in Solutions- **Acids and Bases**: Acids increase the hydrogen ion concentration, while bases decrease it.- **Measurement**: Concentrations are usually expressed in moles per liter (M).- **Significance**: The concentration of hydrogen ions affects the overall pH of a solution.In aqueous solutions, measuring the hydrogen ion concentration enables us to calculate the pH using the formula: \(pH = -\log_{10} [H^+]\). It serves as a vital indicator of the solution's acidity, with higher H⁺ concentrations indicating more acidic solutions.

Logarithmic Scale

The logarithmic scale is a nonlinear scale used for a wide range of scientific and mathematical applications. In the context of pH, it's used to manage the broad range of H⁺ concentrations that can occur in aqueous solutions.
### Why Use a Logarithmic Scale? The reason for utilizing a logarithmic scale in pH calculations is to transform the multitude of hydrogen ion concentrations into a more manageable range.

• **Simplification**: Converts exponential relationships into linear ones, making calculations easier.
• **Compact Representation**: Compresses the scale, so a wide range of concentrations can be represented in a shorter numerical range (0-14 for pH).
• **Intuitive Understanding**: Each unit change in pH represents a tenfold change in hydrogen ion concentration.

This use of logarithmic scale provides a simplified, yet powerful method to express and interpret acidity and basicity in aqueous solutions, which is crucial for scientific analysis and communication.