Calculating H+ Ions From Sulfuric Acid Ionization
Introduction
Understanding the behavior of acids in aqueous solutions is a fundamental concept in chemistry. Acids, such as sulfuric acid ($H_2SO_4$), dissociate in water to release hydrogen ions ($H^+), which are often simplified as $H^+$ for convenience. This article delves into calculating the number of hydrogen ions produced when 0.1 mole of sulfuric acid is completely ionized in water. We will explore the stoichiometry of the ionization process, relate moles to the number of particles using Avogadro's number, and provide a step-by-step calculation to arrive at the answer. This understanding is crucial for various applications, including pH calculations, titrations, and understanding chemical reactions in aqueous environments.
Sulfuric acid ($H_2SO_4$) is a diprotic acid, meaning it has two ionizable hydrogen atoms. When sulfuric acid dissolves in water, it undergoes a two-step ionization process. The first ionization step involves the release of one proton ($H^+$) from $H_2SO_4$, forming the bisulfate ion ($HSO_4^−$). This step is essentially complete in dilute solutions, indicating that sulfuric acid is a strong acid for its first dissociation. The second ionization step involves the dissociation of the bisulfate ion ($HSO_4^−$) into another proton ($H^+$). This second step is also significant but does not proceed to completion as readily as the first ionization. However, for the purpose of this calculation, we consider the complete ionization of sulfuric acid, which simplifies the determination of the total number of hydrogen ions produced. This assumption allows us to provide a clear and accurate estimation of the hydrogen ion concentration in the solution, which is vital for various chemical calculations and applications. We will use the concept of stoichiometry and Avogadro's number to determine the number of hydrogen ions produced from the complete ionization of 0.1 mole of sulfuric acid in water.
Understanding Avogadro's number is crucial for converting between moles, a unit of chemical quantity, and the actual number of particles (atoms, molecules, ions, etc.). Avogadro's number is defined as the number of entities in one mole of a substance, approximately $6.022 imes 10^{23}$. This constant serves as a bridge between the macroscopic world (grams, moles) and the microscopic world (atoms, molecules). In the context of this problem, it allows us to determine how many hydrogen ions are produced from a given number of moles of sulfuric acid. For instance, if we know that one molecule of sulfuric acid produces two hydrogen ions upon complete ionization, we can use Avogadro's number to calculate the total number of hydrogen ions produced by a mole of sulfuric acid molecules. This calculation is essential for determining the concentration of hydrogen ions in a solution, which is a key factor in determining the pH and reactivity of the solution. The use of Avogadro's number highlights the fundamental relationship between the quantity of a substance and the number of particles it contains, which is a cornerstone of chemical calculations.
Stoichiometry of Sulfuric Acid Ionization
To determine the number of $H^+$ ions produced, it's essential to understand the balanced chemical equation for the ionization of sulfuric acid ($H_2SO_4$) in water. Sulfuric acid is a strong acid, and it undergoes complete ionization in two steps:
ightarrow H^+ + HSO_4^-$ 2. $HSO_4^- ightarrow H^+ + SO_4^{2-}$
Combining these two steps, the overall ionization reaction is:
This equation shows that each molecule of sulfuric acid ($H_2SO_4$) produces two hydrogen ions ($H^+$) upon complete ionization. This stoichiometric relationship is the key to calculating the total number of hydrogen ions generated from a given amount of sulfuric acid. The balanced equation clearly illustrates the ratio between the reactants and products, ensuring that the number of atoms of each element is the same on both sides of the equation. In this case, one molecule of sulfuric acid yields two hydrogen ions and one sulfate ion. This 1:2:1 stoichiometry is crucial for accurately determining the quantity of hydrogen ions produced from the ionization of a specific amount of sulfuric acid. Understanding the stoichiometric relationships in chemical reactions is essential for making quantitative predictions and performing accurate calculations in chemistry.
Given that we have 0.1 mole of $H_2SO_4$, and each mole of $H_2SO_4$ produces 2 moles of $H^+$, the number of moles of $H^+$ ions produced can be calculated as follows:
Moles of $H^+$ = 0.1 mole $H_2SO_4$ × (2 moles $H^+$ / 1 mole $H_2SO_4$) = 0.2 moles $H^+$
This calculation demonstrates the direct application of stoichiometry to determine the amount of product formed from a given amount of reactant. By using the stoichiometric coefficients from the balanced chemical equation, we can accurately convert the moles of sulfuric acid to moles of hydrogen ions. This conversion is fundamental in quantitative chemistry, allowing us to predict the yield of a reaction and calculate the concentration of species in a solution. In this specific case, the calculation shows that the complete ionization of 0.1 mole of sulfuric acid results in the formation of 0.2 moles of hydrogen ions. This value is essential for the subsequent calculation of the number of individual hydrogen ions using Avogadro's number.
Calculating the Number of H+ Ions
Now that we know the number of moles of $H^+$ ions produced (0.2 moles), we can calculate the actual number of ions using Avogadro's number. Avogadro's number ($N_A$) is approximately $6.022 imes 10^{23}$ entities per mole. Therefore, the number of $H^+$ ions can be calculated as follows:
Number of $H^+$ ions = Moles of $H^+$ × Avogadro's number
Number of $H^+$ ions = 0.2 moles × $6.022 imes 10^{23}$ ions/mole
Number of $H^+$ ions = $1.2044 imes 10^{23}$
This calculation directly applies Avogadro's number to convert the number of moles of hydrogen ions into the actual number of ions. By multiplying the moles of $H^+$ by Avogadro's number, we obtain the total count of hydrogen ions produced from the ionization of 0.1 mole of sulfuric acid. This conversion is a fundamental concept in chemistry, bridging the gap between the macroscopic quantity of moles and the microscopic count of individual particles. The result, $1.2044 imes 10^{23}$ ions, represents the vast number of hydrogen ions present in the solution, which contribute to its acidic properties. This step underscores the importance of Avogadro's number as a cornerstone of quantitative chemical calculations.
To match one of the given answer choices, we can express $1.2044 imes 10^{23}$ as $2 imes 0.6022 imes 10^{23}$. This form allows for a direct comparison with the provided options and confirms the correct answer. Expressing the result in this manner demonstrates the flexibility required in scientific calculations to align with specific formats or conventions. By factoring out a 2, we emphasize that the number of hydrogen ions produced is twice a value related to Avogadro's number, highlighting the stoichiometry of the sulfuric acid ionization. This manipulation of the numerical result showcases the importance of not only arriving at the correct answer but also presenting it in a clear and comparable way.
Conclusion
In conclusion, the number of $H^+$ ions produced when 0.1 mole of sulfuric acid is completely ionized in water is $1.2044 imes 10^{23}$, which can be expressed as $2 imes 6.022 imes 10^{22}$. Therefore, the correct answer is B. $2 imes 6.022 imes 10^{23}$.
This calculation demonstrates the application of stoichiometry and Avogadro's number in determining the number of ions in a solution. Understanding these concepts is crucial for various chemical calculations and for comprehending the behavior of acids and bases in aqueous solutions. The process involves first recognizing the complete ionization of sulfuric acid, which yields two hydrogen ions per molecule, and then using this stoichiometric relationship to convert the moles of sulfuric acid to moles of hydrogen ions. Subsequently, Avogadro's number is applied to transform the moles of hydrogen ions into the actual number of ions. This systematic approach highlights the interconnectedness of fundamental chemical concepts and their practical application in quantitative analysis. By mastering these principles, one can accurately predict and interpret the behavior of chemical species in various contexts, furthering their understanding of chemistry.
The ability to calculate the number of ions in a solution is not only an academic exercise but also has practical implications in various fields. For instance, in environmental chemistry, the concentration of hydrogen ions (pH) determines the acidity of water bodies, which in turn affects aquatic life and ecosystems. In industrial chemistry, precise control over ion concentrations is crucial for various processes, such as chemical synthesis and electroplating. In medicine, the pH of body fluids is tightly regulated to maintain physiological functions, and deviations from the normal range can indicate various medical conditions. Therefore, a solid understanding of these calculations is essential for professionals in diverse fields, enabling them to make informed decisions and solve real-world problems. The concepts discussed in this article serve as a foundation for further exploration of acid-base chemistry and its applications.
Answer
B. $2 imes 6.022 imes 10^{23}$
