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Chapter 17: Problem 73

A solution contains \(2.0 \times 10^{-4} \mathrm{MAg}^{+}\)and \(1.5 \times 10^{-3} \mathrm{M} \mathrm{Pb}^{2+}\). If \(\mathrm{NaI}\) is added, will \(\mathrm{AgI}^{\mathrm{I}}\left(K_{4 p}=8.3 \times 10^{-17}\right)\) or \(\mathrm{PbI}_{2}\) \(\left(K_{\text {sp }}=7.9 \times 10^{-9}\right)\) precipitate first? Specify the concentration of \(I^{-}\)needed to begin precipitation.

Short Answer

Expert verified
AgI will precipitate first, and the concentration of I鈦� needed to begin precipitation is \(4.15 \times 10^{-13}\ \mathrm{M}\).

Step by step solution

01

Write the solubility product expressions for AgI and PbI鈧�

The solubility product expressions for the ionic compounds AgI and PbI鈧� are given by: \(K_{4p}(AgI) = [Ag^+][I^-] \) \(K_{sp}(PbI_2) = [Pb^{2+}][I^-]^2\) Where [Ag鈦篯, [I鈦籡, and [Pb虏鈦篯 are the molar concentrations of the respective ions in the solution.
02

Substitute the given values and solve for [I鈦籡

In order to determine the concentration of I鈦� needed to begin precipitation, substitute the known values of K鈧勨倸, K鈧涒倸, [Ag鈦篯, and [Pb虏鈦篯 into the solubility product expressions and solve for [I鈦籡: For AgI: \(K_{4p} = [Ag^+][I^-]\) \(8.3 \times 10^{-17} = (2.0 \times 10^{-4})[I^-]\) \([I^-] = \frac{8.3 \times 10^{-17}}{2.0 \times 10^{-4}} = 4.15 \times 10^{-13}\ \mathrm{M}\) For PbI鈧�: \(K_{sp} = [Pb^{2+}][I^-]^2\) \(7.9 \times 10^{-9} = (1.5 \times 10^{-3})[I^-]^2\) \([I^-] = \sqrt{\frac{7.9 \times 10^{-9}}{1.5 \times 10^{-3}}} = 7.25 \times 10^{-4}\ \mathrm{M}\)
03

Compare the [I鈦籡 values and determine which compound will precipitate first

Now that we have calculated the concentrations of I鈦� required to begin precipitation for AgI and PbI鈧�, we can compare these values to determine which compound will precipitate first: [I鈦籡 needed for AgI precipitation: \(4.15 \times 10^{-13}\ \mathrm{M}\) [I鈦籡 needed for PbI鈧� precipitation: \(7.25 \times 10^{-4}\ \mathrm{M}\) Since the concentration of I鈦� required to begin precipitation of AgI is much smaller than that required for PbI鈧�, AgI will precipitate first.
04

Specify the concentration of I鈦� needed to begin precipitation

The concentration of I鈦� needed to begin precipitation in this case is the one required for AgI precipitation, as it precipitates first: [I鈦籡 needed for precipitation: \(4.15 \times 10^{-13}\ \mathrm{M}\)

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Key Concepts

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

Precipitation Reactions
When a solution reaches a point where a particular ionic compound exceeds its solubility limit, it forms a precipitate 鈥� a solid that separates from the solution. Such reactions, known as precipitation reactions, are pivotal in the field of chemistry as they are instrumental in the separation and analysis of compounds.

In our exercise, when NaI is added to a solution containing Ag+ and Pb2+ ions, an equilibrium competition begins to assess which compound, AgI or PbI2, will precipitate first. The outcome is fundamentally determined by the respective solubility product constants for these compounds. To predict the precipitate, we calculate the concentration of I鈭� ions required to initiate the formation of each solid, which depends on the initial ion concentrations and the solubility product constants.
Ionic Equilibrium
Ionic equilibrium unfolds when there is a balance between the forward and reverse processes of ion formation and deposition in solution. It's a state of dynamic balance where the rate of the forward reaction 鈥� dissolving solid into ions 鈥� equals the rate of the reverse reaction 鈥� reformation of the solid from its ions. This balance defines the solubility of a substance in a solution at specific conditions.

For the solubility equilibrium of sparingly soluble ionic compounds like AgI and PbI2, the product of the molar concentrations of the ions at equilibrium is a constant, known as the solubility product constant, at a given temperature. The solubility product is crucial in solving problems where we need to understand when a precipitate will start to form as exemplified in the step-by-step solution provided for our exercise.
Ksp (Solubility Product Constant)
The Ksp, or Solubility Product Constant, quantifies the solubility of ionic compounds in a solution. It is defined for a saturated solution in equilibrium and varies with the temperature. A key aspect to note is that Ksp values are unique for different substances at a given temperature.

In the textbook exercise, the calculation involving Ksp serves as the underpinning for determining which compound 鈥� AgI or PbI2 鈥� will precipitate first. The Ksp values allow us to compute the concentrations at which the respective ions will start to combine and form a solid precipitate. Intuitively, lower Ksp values generally suggest lower solubility and an increased likelihood of precipitation under a set of concentration conditions, explaining why AgI, with a lower Ksp, precipitates before PbI2 in the given solution.

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Most popular questions from this chapter

(a) If the molar solubility of \(\mathrm{CaF}_{2}\) at \(35^{\circ} \mathrm{C}\) is \(1.24 \times 10^{-3} \mathrm{~mol} / \mathrm{L}\), what is \(K_{\text {sp }}\) at this temperature? (b) It is found that \(1.1 \times 10^{-2} \mathrm{~g} \mathrm{SrF}_{2}\) dissolves per \(100 \mathrm{~mL}\) of aqueous solution at \(25^{\circ} \mathrm{C}\). Calculate the solubility product for \(\mathrm{SrF}_{2}\). (c) The \(K_{\text {pp }}\) of \(\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2}\) at \(25^{\circ} \mathrm{C}\) is \(6.0 \times 10^{-10}\). What is the molar solubility of \(\mathrm{Ba}\left(\mathrm{IO}_{3}\right)_{2}\) ?

\mathrm{~A}\( biochemist needs \)750 \mathrm{~mL}\( of an acetic acid-sodium acetate buffer with pH 4.50. Solid sodium acetate ( \)\left.\mathrm{CH}_{3} \mathrm{COONa}\right)\( and glacial acetic acid \)\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\( are available. Glacial acetic acid is \)99 \% \mathrm{CH}_{3} \mathrm{COOH}\( by mass and has a density of \)1.05 \mathrm{~g} / \mathrm{ml}\(. If the buffer is to be \)0.15 \mathrm{M}\( in \)\mathrm{CH}_{3} \mathrm{COOH}\(, how many grams of \)\mathrm{CH}_{4} \mathrm{COONa}$ and how many milliliters of glacial acetic acid must be used?

Rainwater is acidic because \(\mathrm{CO}_{2}(\mathrm{~g})\) dissolves in the water, creating carbonic acid, \(\mathrm{H}_{2} \mathrm{CO}_{5}\). If the rainwater is toe acidic, it will react with limestone and seashells (which are principally made of calcium carbonate, \(\mathrm{CaCO}_{3}\) ). Calculate the concentrations of carbonic acid, bicarbonate ion \(\left(\mathrm{HCO}_{3}{ }^{-}\right)\)and carbonate ion \(\left(\mathrm{CO}_{3}^{2-}\right)\) that are in a raindrop that has a \(\mathrm{pH}\) of \(5.60\), assuming that the sum of all three species in the raindrop is \(1.0 \times 10^{-5} \mathrm{M} .\)

You are asked to prepare a pH \(=3.00\) buffer solution starting from \(1.25 \mathrm{~L}\) of a \(1.00 \mathrm{M}\) solution of hydrofluoric acid (HF) and any amount you need of sodium fluoride (NaF). (a) What is the \(\mathrm{pH}\) of the hydrofluoric acid solution prior to adding sodium fluoride? (b) How many grams of sodium fluoride should be added to prepare the buffer solution? Neglect the small volume change that occurs when the sodium fluoride is added.

Derive an equation similar to the Henderson-Hasselbalch equation relating the pOH of a buffer to the \(\mathrm{p} K_{b}\) of its base component.
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