Chapter 15: Problem 77
A detergent solution has a pH of \(11.63\) at \(25^{\circ} \mathrm{C}\). What is the hydroxide-ion concentration?
Short Answer
Expert verified
The hydroxide-ion concentration is approximately \(4.27 \times 10^{-3}\) M.
Step by step solution
01
Recall the pH and pOH relationship
The pH and pOH of a solution are related by the equation: \( \text{pH} + \text{pOH} = 14 \). This is a fundamental concept when dealing with pH and pOH in aqueous solutions.
02
Calculate the pOH
Since we know the pH is \( 11.63 \), we use the relationship from Step 1 to find the pOH: \( \text{pOH} = 14 - \text{pH} = 14 - 11.63 = 2.37 \).
03
Convert pOH to hydroxide-ion concentration
The hydroxide-ion concentration \([OH^-]\) can be found using the formula: \([OH^-] = 10^{-\text{pOH}}\). Substitute the pOH value calculated in Step 2: \([OH^-] = 10^{-2.37} \).
04
Calculate the numerical value
Using a calculator, compute \( 10^{-2.37} \) to find the hydroxide-ion concentration: \([OH^-] \approx 4.27 \times 10^{-3} \text{ M} \).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Hydroxide-ion Concentration
Understanding hydroxide-ion concentration is key to grasping the chemistry of solutions. In any aqueous solution, water can dissociate into hydrogen ions \( (H^+) \) and hydroxide ions \( (OH^-) \).
The concentration of these ions can tell us a lot about the acidity or basicity of the solution. For basic solutions, where the pH is above 7, the hydroxide-ion concentration is higher than the hydrogen-ion concentration. To find the hydroxide-ion concentration, we often rely on the relationship between pH and pOH, where knowing the pOH can directly lead us to the concentration of \( OH^- \) ions. The lower the pOH, the higher the hydroxide-ion concentration, indicating a stronger base.
The concentration itself is expressed in moles per liter (Molarity), and can be calculated using the equation:
The concentration of these ions can tell us a lot about the acidity or basicity of the solution. For basic solutions, where the pH is above 7, the hydroxide-ion concentration is higher than the hydrogen-ion concentration. To find the hydroxide-ion concentration, we often rely on the relationship between pH and pOH, where knowing the pOH can directly lead us to the concentration of \( OH^- \) ions. The lower the pOH, the higher the hydroxide-ion concentration, indicating a stronger base.
The concentration itself is expressed in moles per liter (Molarity), and can be calculated using the equation:
- \([OH^-] = 10^{-\text{pOH}}\)
pOH Calculation
Calculating pOH is an essential step to understand a solution's basicity. It directly relates to the pH and provides a route to finding the hydroxide-ion concentration. In our exercise, we began with a known pH of a detergent solution, which is 11.63.
From the fundamental relationship:
This calculation is straightforward but crucial as it directly sets the stage to calculate the concentration of \( OH^- \) ions. Having a low pOH value like 2.37 suggests the solution is quite basic, as evidenced by the relatively high hydroxide-ion concentration.
From the fundamental relationship:
- \( \text{pH} + \text{pOH} = 14 \)
This calculation is straightforward but crucial as it directly sets the stage to calculate the concentration of \( OH^- \) ions. Having a low pOH value like 2.37 suggests the solution is quite basic, as evidenced by the relatively high hydroxide-ion concentration.
Aqueous Solutions Chemistry
Aqueous solutions chemistry revolves around interactions between solutes and water. An aqueous solution is formed when a substance dissolves in water, becoming either acidic or basic. The pH scale measures how acidic or basic a solution is, with acids having a pH less than 7 and bases having a pH greater than 7.
Water dissociates slightly to produce \( H^+ \) and \( OH^- \) ions. The degree of this dissociation alters the pH and pOH, which are interconnected:
Understanding these concepts of aqueous solutions chemistry provides a solid foundation for solving problems involving acidity and basicity, enabling us to explore further into how substances interact in water.
Water dissociates slightly to produce \( H^+ \) and \( OH^- \) ions. The degree of this dissociation alters the pH and pOH, which are interconnected:
- At 25°C, \( \text{pH} + \text{pOH} = 14 \).
Understanding these concepts of aqueous solutions chemistry provides a solid foundation for solving problems involving acidity and basicity, enabling us to explore further into how substances interact in water.