Calculate POH Of Sulfuric Acid Solution A Step-by-Step Guide

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Introduction

In chemistry, understanding acid-base chemistry is crucial, and one key aspect involves calculating the pOH of a solution. This article will delve into how to determine the pOH of an aqueous solution of sulfuric acid (H₂SO₄), a diprotic acid. We'll explore the concepts of acid ionization, concentration, and the relationship between pH and pOH. This detailed explanation aims to provide a comprehensive understanding, suitable for students and chemistry enthusiasts alike. Sulfuric acid (H₂SO₄) is a strong diprotic acid, meaning it can donate two protons (hydrogen ions) in aqueous solution. The complete ionization of sulfuric acid is a critical factor in determining the concentration of hydrogen ions, which subsequently affects the pOH of the solution. Understanding the behavior of acids and bases in aqueous solutions is fundamental to various chemical processes, making this a vital topic in chemistry.

Understanding Diprotic Acids

Diprotic acids, such as sulfuric acid, are capable of donating two protons (H⁺ ions) per molecule. This characteristic influences how they affect the acidity of a solution. The ionization process occurs in two steps. First, sulfuric acid donates one proton, forming the bisulfate ion (HSO₄⁻). Then, the bisulfate ion can further donate a proton, though this second ionization is not as complete as the first. The extent of ionization is critical because it determines the concentration of hydrogen ions in the solution, directly influencing the pH and, consequently, the pOH. The complete ionization of the first proton in sulfuric acid means that for every mole of H₂SO₄ dissolved, one mole of H⁺ ions is initially released. The subsequent ionization of the bisulfate ion contributes further to the H⁺ ion concentration, but to a lesser extent due to its weaker acidic nature. Accurately calculating the pOH requires considering the total concentration of hydrogen ions, which is why understanding the diprotic nature of sulfuric acid is so essential. In essence, the acid's ability to release two protons significantly impacts the solution's acidity, making it a key consideration in any acid-base calculation.

Problem Statement

We are given an aqueous solution of sulfuric acid (H₂SO₄) with a concentration of 5.0 × 10⁻³ mol/L. We assume that the acid is completely ionized in the aqueous medium. The objective is to determine the pOH of this solution. This problem combines the concepts of acid-base chemistry, ionization, and logarithmic scales to assess the acidity and basicity of a solution. The complete ionization assumption simplifies the calculation by allowing us to directly relate the concentration of sulfuric acid to the concentration of hydrogen ions. However, it's crucial to recognize that this is an approximation, as the second ionization step of sulfuric acid doesn't proceed to 100% completion. Nevertheless, for the purpose of this problem, we proceed with the assumption of complete ionization. The challenge lies in correctly applying the stoichiometric relationships and the logarithmic definitions of pH and pOH to arrive at the correct answer. This exercise is not only a test of knowledge but also of problem-solving skills in quantitative chemistry. Understanding the implications of complete ionization and its impact on ion concentrations is a fundamental aspect of mastering acid-base chemistry.

Calculation Steps

  1. Determine the concentration of H⁺ ions: Since sulfuric acid (H₂SO₄) is a diprotic acid, it donates two protons (H⁺ ions) per molecule in solution. Therefore, the concentration of H⁺ ions will be twice the concentration of the sulfuric acid. Given the concentration of H₂SO₄ is 5.0 × 10⁻³ mol/L, the concentration of H⁺ ions is:

    [H⁺] = 2 × 5.0 × 10⁻³ mol/L = 1.0 × 10⁻² mol/L

    This initial step is critical because it directly links the concentration of the acid to the concentration of the active species responsible for acidity. The diprotic nature of sulfuric acid is the key factor here, doubling the impact on the solution's acidity compared to a monoprotic acid of the same concentration. Accurately determining the [H⁺] is the foundation for all subsequent calculations, making it essential to understand the stoichiometry of the acid's ionization. This step highlights the practical significance of understanding chemical equations and their quantitative implications.

  2. Calculate the pH: The pH is the negative logarithm (base 10) of the H⁺ ion concentration:

    pH = -log₁₀[H⁺] = -log₁₀(1.0 × 10⁻²)

    The pH scale is a fundamental tool in chemistry for expressing the acidity or basicity of a solution. The logarithmic nature of the pH scale means that each unit change in pH represents a tenfold change in H⁺ ion concentration. This calculation transforms the concentration of H⁺ ions, a relatively small number, into a more manageable and intuitive pH value. The negative sign in the formula reflects the inverse relationship between H⁺ ion concentration and pH: higher concentration means lower pH and thus higher acidity. Mastering this calculation is crucial for interpreting and predicting the behavior of chemical systems.

    pH = -(-2) = 2

  3. Calculate the pOH: The pOH is related to the pH by the following equation:

    pH + pOH = 14

    This equation is derived from the ion product of water (Kw), which at 25°C is 1.0 × 10⁻¹⁴. The relationship between pH and pOH is a cornerstone of acid-base chemistry, providing a simple and direct way to convert between acidity and basicity measurements. The constant sum of 14 reflects the balance between H⁺ and OH⁻ ions in aqueous solutions, ensuring that the total ion concentration remains constant. This equation is not only a mathematical tool but also a conceptual link, helping to understand how changes in acidity directly affect basicity and vice versa.

    So, pOH = 14 - pH = 14 - 2 = 12

Answer

The pOH of the sulfuric acid solution is 12. Therefore, the correct answer is (B) 12.

This result aligns with our understanding of strong acids: they produce low pH values (highly acidic) and, consequently, high pOH values (low basicity). The calculated pOH value of 12 indicates that the solution is significantly acidic, which is expected for a solution of a strong acid like sulfuric acid. This outcome serves as a validation of our calculations and underscores the importance of understanding the properties of strong acids in determining solution acidity. This final answer not only solves the problem but also reinforces the broader context of acid-base chemistry and the practical implications of the concepts involved. The ability to accurately calculate and interpret pH and pOH values is essential for numerous applications in chemistry, biology, and environmental science.

Conclusion

In summary, we have successfully determined the pOH of a 5.0 × 10⁻³ mol/L aqueous solution of sulfuric acid, assuming complete ionization. The steps involved calculating the H⁺ ion concentration, determining the pH, and finally, finding the pOH. The key takeaway from this exercise is the importance of understanding the properties of diprotic acids and their behavior in solution. The assumption of complete ionization simplified the calculation, but it's crucial to recognize the limitations of this approximation in real-world scenarios. The pOH value of 12 indicates a highly acidic solution, consistent with the strong acid nature of sulfuric acid. This problem demonstrates the application of fundamental concepts in acid-base chemistry and reinforces the relationship between pH, pOH, and ion concentrations. Mastery of these concepts is essential for students and professionals in various scientific disciplines. Furthermore, this detailed walkthrough serves as a template for solving similar problems, emphasizing the importance of a systematic approach and attention to detail. By understanding the underlying principles and practicing problem-solving techniques, one can confidently tackle complex challenges in acid-base chemistry.

This exercise underscores the significance of a solid foundation in basic chemistry principles for solving quantitative problems. The ability to correctly apply these principles not only leads to the right answer but also fosters a deeper understanding of the chemical processes at play.