/*! 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 60 Consider a beaker containing a s... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 17: Problem 60

Consider a beaker containing a saturated solution of \(\mathrm{PbI}_{2}\) in equilibrium with undissolved \(\mathrm{PbI}_{2}(s) .\) Now solid KI is added to this solution. (a) Will the amount of solid \(\mathrm{PbI}_{2}\) at the bottom of the beaker increase, decrease, or remain the same? (b) Will the concentration of \(\mathrm{Pb}^{2+}\) ions in solution increase or decrease? (c) Will the concentration of I \(^{-}\) ions in solution increase or decrease?

Short Answer

Expert verified
(a) The amount of solid \(PbI_{2}\) at the bottom of the beaker will increase, because the equilibrium shifts to the left due to the increased I鈦� ion concentration from the added KI. (b) The concentration of \(Pb^{2+}\) ions in the solution will decrease as the equilibrium shifts to the left. (c) The concentration of I鈦� ions in the solution will initially increase due to the addition of KI but may decrease as more solid \(PbI_{2}\) forms; however, the final concentration might still be higher than the initial one.

Step by step solution

01

Write the equation for the system

The system is given by the equilibrium between solid PbI鈧� and its ions in water: \[PbI_{2}(s) \rightleftharpoons Pb^{2+}(aq) + 2 I^{-}(aq)\]
02

Write the equation for the addition of KI

Adding solid KI to the solution implies the dissolution of KI in water: \[KI(s) \rightarrow K^{+}(aq) + I^{-}(aq)\]
03

Apply the principle of Le Ch芒telier

The principle of Le Ch芒telier states that when a system in equilibrium is subjected to a change, the system will adjust the positions of the equilibrium to counteract the change. In this case, the addition of KI increases the concentration of I鈦� ions.
04

Analyze the effect on the amount of solid PbI2

As the concentration of I鈦� ions increases, the equilibrium for the PbI鈧� system will shift to the left to counteract the change, according to Le Ch芒telier's principle. This means more solid PbI鈧� will be formed, so (a) the amount of solid PbI鈧� at the bottom of the beaker will increase.
05

Analyze the effect on the concentration of Pb虏鈦� ions

Since the system is shifting to the left, due to the increased I鈦� ion concentration from the added KI, the concentration of Pb虏鈦� ions will decrease to maintain the equilibrium. So, (b) the concentration of Pb虏鈦� ions in the solution will decrease.
06

Analyze the effect on the concentration of I鈦� ions

Initially, the concentration of I鈦� ions will increase due to the addition of KI. However, as the system tries to counteract this change, the equilibrium shifts to the left, promoting the formation of solid PbI鈧� by consuming I鈦� ions. Therefore, (c) the concentration of I鈦� ions in the solution will increase initially, and then likely decrease as more solid PbI鈧� forms but may still be higher than the initial concentration.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Equilibrium
Chemical equilibrium occurs when a reversible reaction in a closed system reaches a point where the rates of the forward and reverse reactions are equal. At this stage, the concentrations of reactants and products remain constant over time. This concept is crucial for understanding how chemical reactions behave under different conditions.
When we talk about the equilibrium between solid PbI鈧� and its ions in a solution, we refer to the dynamic balance described by the equation: \[PbI_{2}(s) \rightleftharpoons Pb^{2+}(aq) + 2 I^{-}(aq)\] This shows us how solid lead(II) iodide (PbI鈧�) can dissolve into its constituent ions and how these ions can recombine to form the solid. The equilibrium can shift to the left or right if conditions change.
According to Le Ch芒telier's Principle, if a change is applied to a system at equilibrium, the system adjusts to minimize that change, restoring equilibrium at a new position.
Solubility Product
The solubility product, often represented as \(K_{sp}\), is a constant for a given compound that reflects its solubility at a particular temperature. For PbI鈧�, its solubility product expression is: \[K_{sp} = [Pb^{2+}][I^{-}]^2\] This equation indicates that in a saturated solution, the product of the concentrations of the ions (\(Pb^{2+}\) and \(I^{-}\)) at equilibrium will remain consistent as long as temperature does not change.
When KI is added to the equilibrium system, it affects the solubility product by increasing the concentration of \(I^{-}\).
According to Le Ch芒telier's Principle, the system reacts to the increased ionic concentration by shifting the equilibrium to the left, increasing the formation of PbI鈧� solid to restore the equilibrium balance. As a result, the apparent solubility of PbI鈧� is reduced in the solution.
Ion Concentration
Ion concentration can drastically impact the position of equilibrium in a chemical system. In a solution containing PbI鈧�, the concentration of its ions \(Pb^{2+}\) and \(I^{-}\) in equilibrium are crucial to maintaining balance. When excess \(I^{-}\) ions are introduced by adding KI, this changes the initial concentration balance.
The excess \(I^{-}\) initially leads to a higher ion concentration in the solution, but the system will try to restore equilibrium by shifting to the left, thus forming more solid PbI鈧�. Consequently, the concentration of\(Pb^{2+}\) ions decreases because fewer lead ions are available in the solution.
This behavior emphasizes the relationship between solubility and ion concentration. Understanding how ion concentration affects equilibrium enables us to predict and manipulate the solubility and reaction outcomes in chemical processes.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose you want to do a physiological experiment that calls for a pH 6.50 buffer. You find that the organism with which you are working is not sensitive to the weak acid \(\mathrm{H}_{2} \mathrm{~A}\left(K_{a 1}=2 \times 10^{-2} ; K_{a 2}=5.0 \times 10^{-7}\right)\) or its sodium salts. You have available a \(1.0 \mathrm{M}\) solution of this acid and a 1.0 \(M\) solution of \(\mathrm{NaOH}\). How much of the \(\mathrm{NaOH}\) solution should be added to \(1.0 \mathrm{~L}\) of the acid to give a buffer at \(\mathrm{pH}\) 6.50? (Ignore any volume change.)

Baking soda (sodium bicarbonate, \(\mathrm{NaHCO}_{3}\) ) reacts with acids in foods to form carbonic acid \(\left(\mathrm{H}_{2} \mathrm{CO}_{3}\right),\) which in turn decomposes to water and carbon dioxide gas. In a cake batter, the \(\mathrm{CO}_{2}(g)\) forms bubbles and causes the cake to rise. \((\mathbf{a})\) A rule of thumb in baking is that \(1 / 2\) teaspoon of baking soda is neutralized by one cup of sour milk. The acid component in sour milk is lactic acid, \(\mathrm{CH}_{3} \mathrm{CH}(\mathrm{OH}) \mathrm{COOH}\). Write the chemical equation for this neutralization reaction. (b) The density of baking soda is \(2.16 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the concentration of lactic acid in one cup of sour milk (assuming the rule of thumb applies), in units of mol/L. (One cup \(=236.6 \mathrm{~mL}=48\) teaspoons \() .(\mathbf{c})\) If \(1 / 2\) teaspoon of baking soda is indeed completely neutralized by the lactic acid in sour milk, calculate the volume of carbon dioxide gas that would be produced at a pressure of \(101.3 \mathrm{kPa}\), in an oven set to \(177^{\circ} \mathrm{C}\).

Predict whether the equivalence point of each of the following titrations is below, above, or at pH 7: (a) \(\mathrm{NaHCO}_{3}\) titrated with \(\mathrm{NaOH},(\mathbf{b}) \mathrm{NH}_{3}\) titrated with \(\mathrm{HCl},\) (c) KOH titrated with HBr.

A buffer, consisting of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-},\) helps control the pH of physiological fluids. Many carbonated soft drinks also use this buffer system. What is the \(\mathrm{pH}\) of a soft drink in which the major buffer ingredients are \(10.0 \mathrm{~g}\) of \(\mathrm{KH}_{2} \mathrm{PO}_{4}\) and \(10.0 \mathrm{~g}\) of \(\mathrm{K}_{2} \mathrm{HPO}_{4}\) per \(0.500 \mathrm{~L}\) of solution?

Suggest how the cations in each of the following solution mixtures can be separated: (a) \(\mathrm{Na}^{+}\) and \(\mathrm{Cd}^{2+},(\mathbf{b}) \mathrm{Cu}^{2+}\) and \(\mathrm{Mg}^{2+},(\mathbf{c}) \mathrm{Pb}^{2+}\) and \(\mathrm{Al}^{3+},(\mathbf{d}) \mathrm{Ag}^{+}\) and \(\mathrm{Hg}^{2+} .\)
See all solutions

Recommended explanations on Chemistry Textbooks

Physical Chemistry

Read Explanation

Chemistry Branches

Read Explanation

Organic Chemistry

Read Explanation

Inorganic Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Reactions

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.