Question

A 50 liter solution contains \(8 \cdot 10^{19} \mathrm{H}^{+}\) ions. Calculate the \(\mathrm{pH}\). Is this solution acidic or basic?

Short answer

The pH is 5.57, indicating the solution is acidic.

Step-by-step solution

Understand the Relationship Between H+ Ions and pH

The pH of a solution is calculated using the formula \( \text{pH} = -\log_{10}[\text{H}^+] \). The concentration of \(\text{H}^+\) ions is needed in moles per liter (M).

Convert Ion Count to Moles per Liter

We have \(8 \cdot 10^{19}\) \(\text{H}^+\) ions in 50 liters of solution. First, convert the ion count to moles using Avogadro's number \(6.022 \cdot 10^{23}\):\[\text{Moles of } \text{H}^+ = \frac{8 \cdot 10^{19}}{6.022 \cdot 10^{23}} = 1.33 \cdot 10^{-4} \].Since this is for 50 liters, the concentration \([\text{H}^+]\) is:\[\frac{1.33 \cdot 10^{-4}}{50} = 2.66 \cdot 10^{-6} \,\text{M}\].

Calculate the pH

Use the pH formula with the concentration found:\[\text{pH} = -\log_{10}(2.66 \cdot 10^{-6}) = 5.57\].

Determine If the Solution is Acidic or Basic

A solution is acidic if its pH is less than 7, neutral at pH 7, and basic if above 7. Since the pH here is 5.57, the solution is acidic.

Key concepts

Acidic and Basic Solutions

Solutions are classified based on their pH levels. The pH scale ranges from 0 to 14 and is used to determine whether a solution is acidic, neutral, or basic.
Acidic solutions have pH values less than 7, indicating a higher concentration of hydrogen ions (H\(^+\)). Examples of common acids include vinegar and lemon juice.
Basic, or alkaline, solutions have pH values greater than 7 and contain a higher concentration of hydroxide ions (OH\(^-\)). Common bases are baking soda and soap.
A neutral solution, like pure water, has a pH of exactly 7, indicating an equal concentration of H\(^+\) and OH\(^-\) ions.
Understanding the nature of a solution through its pH is essential for chemical reactions, biological processes, and environmental sciences.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, valued at approximately \(6.022 \times 10^{23}\) particles per mole. This enormous number allows chemists to count particles at the atomic scale, converting atomic-scale measurements to macroscopic amounts.
Using Avogadro's number, we can calculate the amount of substance in moles from a given number of atoms or ions. In the exercise, \(8 \times 10^{19}\) H\(^+\) ions were converted into moles using Avogadro's number.
Importance of Avogadro's Number:

• Essential for converting between the number of particles and moles.
• Helps quantify chemical reactions and stoichiometry.
• Used in determining molar masses, concentrations, and other chemical properties.

Ion Concentration

Ion concentration is the measure of the amount of ions per unit volume in a solution, usually expressed in moles per liter (M).
Understanding ion concentration is crucial because it affects the chemical behavior and reactivity of the solution.
In the given exercise, the concentration of H\(^+\) ions was found to be \(2.66 \times 10^{-6}\) M.
Why Ion Concentration Matters:

• Determines the acidity or basicity of solutions.
• Influences electrical conductivity.
• Affects reaction rates and equilibria.

pH Scale

The pH scale is a numeric scale that extends from 0 to 14, used to specify the acidity or basicity of an aqueous solution.
Calculating pH involves the concentration of hydrogen ions, given by the formula: \(\text{pH} = -\log_{10}[\text{H}^+]\).
A solution with a pH less than 7 is acidic, exactly 7 is neutral, and greater than 7 is basic.
In the exercise, the calculated pH was 5.57, which is acidic.
The Role of the pH Scale:

• Helps in diagnosing the nature of a solution - acidic or basic.
• Crucial for environmental, biological, and industrial processes.
• Affects solubility and availability of nutrients and metals.
• Important in maintaining the pH balance in biological systems.