/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 77 A detergent solution has a pH of... [FREE SOLUTION] | 91Ó°ÊÓ

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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:
  • \([OH^-] = 10^{-\text{pOH}}\)
This formula allows us to convert a pOH value directly into the hydroxide-ion concentration, giving insight into the solution's basicity.
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:
  • \( \text{pH} + \text{pOH} = 14 \)
we can determine the pOH value by rearranging to \( \text{pOH} = 14 - \text{pH} \). Inserting our pH value, we find \( \text{pOH} = 14 - 11.63 = 2.37 \).

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:
  • At 25°C, \( \text{pH} + \text{pOH} = 14 \).
This relationship helps us calculate unknown values based on given information. When a solution forms, solutes can affect the balance of \( H^+ \) and \( OH^- \) ions, shifting the pH and pOH accordingly.

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.

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Most popular questions from this chapter

In the following reaction, identify the Lewis acid. $$ \begin{aligned} &\mathrm{Fe}^{3+}(a q)+6 \mathrm{CN}^{-}(a q) \rightleftharpoons \mathrm{Fe}(\mathrm{CN})_{6}^{3-}(a q) \\ &\text { b. } \mathrm{Fe}(\mathrm{CN})_{6}{ }^{3-} \end{aligned} $$ a. \(\mathrm{CN}^{-}\) c. \(\mathrm{H}^{+}\) d. \(\mathrm{Fe}^{3+}\) e. \(\mathrm{OH}^{-}\)

Explain how sodium hydroxide dissolves grease and hair from a stopped drain.

A \(2.500\) -g sample of a mixture of sodium carbonate and sodium chloride is dissolved in \(25.00 \mathrm{~mL}\) of \(0.798 \mathrm{M} \mathrm{HCl}\). Some acid remains after the treatment of the sample. a. Write the net ionic equation for the complete reaction of sodium carbonate with hydrochloric acid. b. If \(28.7 \mathrm{~mL}\) of \(0.108 M \mathrm{NaOH}\) were required to titrate the excess hydrochloric acid, how many moles of sodium carbonate were present in the original sample? C. What is the percent composition of the original sample?

Pure liquid ammonia ionizes in a way similar to that of Water. a. Write the equilibrium reaction of liquid ammonia. b. Will sodium amide, \(\mathrm{NaNH}_{2}\), be an acid or a base in liquid ammonia? Why? c. Ammonium chloride can be used to titrate sodium amide in liquid ammonia. Write the chemical equation for the titration of sodium amide with ammonium chloride in liquid ammonia.

Aluminum chloride, \(\mathrm{AlCl}_{3}\), reacts with trimethylamine, \(\mathrm{N}\left(\mathrm{CH}_{3}\right)_{3} .\) What would you guess to be the product of this reaction? Explain why you think so. Describe the reaction in terms of one of the acid-base concepts. Write an appropriate equation to go with this description. Which substance is the acid according to this acid-base concept? Explain.

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