An Aqueous Solution Has A Hydrogen Ion Contamination Of 1.15x10^-2M (1)What Is The Hydroxide Ion Concentration
Understanding the relationship between hydrogen ion (H⁺) concentration and hydroxide ion (OH⁻) concentration in aqueous solutions is fundamental in chemistry, especially in the context of acids, bases, and pH calculations. In this article, we will explore how to determine the hydroxide ion concentration when given the hydrogen ion concentration, using principles rooted in the ion product constant of water (Kw). We will delve into the concepts of pH, pOH, and the equilibrium of water autoionization, providing an in-depth explanation suitable for students, educators, and chemistry enthusiasts alike.
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Understanding Aqueous Solutions and Ion Concentrations
What Are Aqueous Solutions?
An aqueous solution is a solution where water (H₂O) acts as the solvent. These solutions are ubiquitous in chemistry because water is a universal solvent, capable of dissolving many substances, including salts, acids, and bases. The behavior of ions in aqueous solutions is vital for understanding phenomena such as acidity, alkalinity, and chemical reactivity.Hydrogen Ions and Hydroxide Ions in Water
In pure water and aqueous solutions, water molecules undergo a process called autoionization:\[ \text{H}_2\text{O} \leftrightarrow \text{H}^+ + \text{OH}^- \]
This equilibrium results in a small but significant concentration of hydrogen ions (H⁺) and hydroxide ions (OH⁻) in water, both typically around 10⁻⁷ M at 25°C.
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Given Data: Hydrogen Ion Concentration
The problem states:
> An aqueous solution has a hydrogen ion contamination of 1.15×10⁻² M.
This indicates that the H⁺ concentration in the solution is \( [\text{H}^+] = 1.15 \times 10^{-2} \, \text{M} \).
What does this tell us?
- The solution is acidic because the H⁺ concentration is higher than the neutral value of \( 1 \times 10^{-7} \) M.
- To find the hydroxide ion concentration, we need to understand the relationship governed by Kw.
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The Ion Product of Water (Kw) and Its Significance
Definition of Kw
At 25°C, the ion product constant of water (Kw) is:\[ K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \]
This constant reflects the equilibrium between water molecules dissociating into H⁺ and OH⁻ ions.
Implication for pH and pOH
- pH is defined as:
- pOH is:
- The relationship between pH and pOH is:
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Calculating the Hydroxide Ion Concentration
Given \( [\text{H}^+] = 1.15 \times 10^{-2} \, \text{M} \), we can determine \( [\text{OH}^-] \) using the Kw relationship:
\[ [\text{OH}^-] = \frac{K_w}{[\text{H}^+]} \]
Substituting the known values:
\[ [\text{OH}^-] = \frac{1.0 \times 10^{-14}}{1.15 \times 10^{-2}} \]
Calculating this:
\[ [\text{OH}^-] = \frac{1.0 \times 10^{-14}}{1.15 \times 10^{-2}} \approx 8.70 \times 10^{-13} \, \text{M} \]
This extremely low hydroxide ion concentration confirms the solution's acidity.
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Step-by-Step Calculation Summary
- Identify the hydrogen ion concentration: \( [\text{H}^+] = 1.15 \times 10^{-2} \, \text{M} \).
- Recall Kw at 25°C: \( 1.0 \times 10^{-14} \).
- Calculate hydroxide ion concentration:
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Understanding pH and pOH in This Context
Calculating pH
Using the definition:\[ \text{pH} = -\log [\text{H}^+] \]
\[ \text{pH} = -\log (1.15 \times 10^{-2}) \]
\[ \text{pH} \approx -(\log 1.15 + \log 10^{-2}) \]
\[ \text{pH} \approx -(0.0607 - 2) = 1.939 \]
This indicates a strongly acidic solution.
Calculating pOH
Using the relation:\[ \text{pOH} = 14 - \text{pH} = 14 - 1.939 \approx 12.061 \]
Alternatively:
\[ \text{pOH} = -\log [\text{OH}^-] \]
\[ \text{pOH} = -\log (8.70 \times 10^{-13}) \]
\[ \text{pOH} \approx 12.06 \]
This confirms the hydroxide ion concentration's consistency with the pOH.
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Key Points for Chemistry Students and Enthusiasts
- The relationship between H⁺ and OH⁻ concentrations in water is inversely proportional, governed by Kw.
- Acidic solutions have high H⁺ concentrations and correspondingly low OH⁻ concentrations.
- The pH scale provides an intuitive measure of acidity; values below 7 indicate acidity, above 7 indicate alkalinity.
- Precise calculations of ion concentrations are crucial in various applications, including titrations, buffer solutions, and biochemical processes.
Practical Applications and Implications
In Laboratory Settings
Knowing how to calculate hydroxide ion concentration from hydrogen ion contamination helps chemists:- Determine the acidity or alkalinity of a solution.
- Prepare solutions with desired pH levels.
- Understand the behavior of acids and bases in reactions.
In Industry and Environmental Science
Accurate ion concentration measurements are vital for:- Water treatment processes.
- Monitoring environmental water quality.
- Designing pharmaceuticals and biochemical solutions.
In Educational Contexts
Students learning about acids and bases can reinforce their understanding of equilibrium principles and the pH scale through such calculations.---
Summary
- The given hydrogen ion concentration in the aqueous solution is \( 1.15 \times 10^{-2} \, \text{M} \).
- Using the water ion product constant \( K_w = 1.0 \times 10^{-14} \), the hydroxide ion concentration is approximately \( 8.70 \times 10^{-13} \, \text{M} \).
- The solution is highly acidic, with a pH of approximately 1.94.
- Understanding these calculations enhances comprehension of acid-base chemistry and solution behavior.
Conclusion
Determining the hydroxide ion concentration from hydrogen ion contamination is straightforward once the fundamental principles of water autoionization and the ion product constant are understood. Such calculations are essential in various scientific and industrial applications, emphasizing the importance of mastering pH and ion concentration concepts. Whether you're a student, researcher, or industry professional, knowing how to navigate these calculations enables accurate analysis and effective solution design in aqueous chemistry.
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Keywords: aqueous solution, hydrogen ion concentration, hydroxide ion concentration, pH, pOH, Kw, acid-base chemistry, water autoionization, solution chemistry, ion concentrations, pH calculation
