If The Concentration Of H3O+ In An Aqueous Solution Is 7.6 10-9 M, The Concentration Of OH- Is .A)
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Understanding the Relationship Between H3O+ and OH- in Aqueous Solutions
In aqueous chemistry, the concentrations of hydronium ions (H3O+) and hydroxide ions (OH-) are fundamental to understanding the acidity, alkalinity, and overall pH of a solution. These ions are connected through the concept of water autoionization and the water dissociation constant, Kw. When given the concentration of one ion, we can determine the concentration of the other, which is essential for various applications, including titrations, environmental analysis, and biochemical processes.
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What Is the Water Dissociation Constant (Kw)?
The water dissociation constant, symbolized as Kw, is an equilibrium constant that describes the extent to which water dissociates into H3O+ and OH- ions:
\[ \mathrm{H_2O} \rightleftharpoons \mathrm{H^+} + \mathrm{OH^-} \]
Since H+ in aqueous solutions exists primarily as H3O+, the reaction is often written as:
\[ \mathrm{H2O} \leftrightarrow \mathrm{H3O^+} + \mathrm{OH^-} \]
At 25°C, Kw is a constant value:
\[ Kw = [\mathrm{H3O^+}] \times [\mathrm{OH^-}] = 1.0 \times 10^{-14} \]
This means that at this temperature, the product of the concentrations of H3O+ and OH- ions in pure water is always \(1.0 \times 10^{-14}\).
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Calculating the Concentration of OH-
Given the concentration of H3O+ ions:
\[ [\mathrm{H_3O^+}] = 7.6 \times 10^{-9} \text{ M} \]
To find the concentration of OH- ions:
\[ [\mathrm{OH^-}] = \frac{Kw}{[\mathrm{H3O^+}]} \]
Substituting the known values:
\[ [\mathrm{OH^-}] = \frac{1.0 \times 10^{-14}}{7.6 \times 10^{-9}} \]
Calculating:
\[ [\mathrm{OH^-}] = \frac{1.0 \times 10^{-14}}{7.6 \times 10^{-9}} = \frac{1.0}{7.6} \times 10^{-14 + 9} \]
\[ [\mathrm{OH^-}] = 0.1316 \times 10^{-5} \]
\[ [\mathrm{OH^-}] \approx 1.32 \times 10^{-6} \text{ M} \]
Thus, the concentration of hydroxide ions in the solution is approximately 1.32 × 10⁻⁶ M.
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Understanding pH and pOH in This Context
The pH and pOH are logarithmic measures of the H3O+ and OH- concentrations, respectively. They provide insight into the acidity or alkalinity of a solution.
Calculating pH:
\[ \text{pH} = -\log [\mathrm{H_3O^+}] \]
Substituting:
\[ \text{pH} = -\log (7.6 \times 10^{-9}) \]
\[ \text{pH} = -(\log 7.6 + \log 10^{-9}) \]
\[ \text{pH} = -(0.8808 - 9) \]
\[ \text{pH} = 9 - 0.8808 = 8.1192 \]
Approximately, the pH is 8.12, indicating a slightly basic solution.
Calculating pOH:
\[ \text{pOH} = -\log [\mathrm{OH^-}] \]
\[ \text{pOH} = -\log (1.32 \times 10^{-6}) \]
\[ \text{pOH} = -( \log 1.32 + \log 10^{-6} ) \]
\[ \text{pOH} = - (0.1206 - 6) \]
\[ \text{pOH} = 6 - 0.1206 = 5.8794 \]
The pOH is approximately 5.88.
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Implications of the Calculated OH- Concentration
Knowing the hydroxide ion concentration has several important implications:
- pH and pOH Relationship: The sum of pH and pOH in aqueous solutions at 25°C is always approximately 14, aligning with the calculations above.
- Acidity or Basicity: Since the pH is above 7, the solution is basic, consistent with the low H3O+ concentration.
- Buffer Capacity: Such calculations are critical when designing buffer solutions that maintain pH stability.
- Environmental and Biological Relevance: The pH of natural waters and biological fluids influences chemical reactions, enzyme activity, and overall health.
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Additional Considerations in Acid-Base Chemistry
Temperature Dependence of Kw
It’s essential to recognize that Kw is temperature-dependent. While 1.0 × 10⁻¹⁴ is valid at 25°C, at higher temperatures, Kw increases, affecting ion concentrations and pH calculations.
Significance of Ion Concentrations
- Dilute Solutions: The calculated concentrations are very low, characteristic of dilute solutions.
- Real-World Applications: Accurate ion concentrations are vital in pharmaceuticals, environmental monitoring, and industrial processes.
Limitations and Assumptions
- Calculations assume ideal behavior and pure water conditions.
- Deviations may occur in complex solutions due to activity coefficients and other ionic interactions.
Conclusion
In summary, given the H3O+ concentration of \(7.6 \times 10^{-9}\) M in an aqueous solution, the hydroxide ion concentration is approximately 1.32 × 10⁻⁶ M. This calculation hinges on the fundamental water dissociation constant, Kw, and provides insights into the solution’s pH, pOH, and overall acidity or alkalinity. Understanding these relationships is crucial for chemists, environmental scientists, and biochemists working with aqueous systems. Accurate ion concentration calculations enable better control and prediction of chemical behaviors across various scientific and industrial fields.
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Meta Description:
Learn how to determine the hydroxide ion concentration in an aqueous solution when given the hydronium ion concentration. This comprehensive guide covers water ionization, Kw, pH, pOH, and practical applications.
