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Chapter 17: Problem 98

For each pair of compounds, use \(K_{s p}\) values to determine which has the greater molar solubility: (a) CdS or CuS, (b) \(\mathrm{PbCO}_{3}\) or \(\mathrm{BaCrO}_{4}\), (c) \(\mathrm{Ni}(\mathrm{OH})_{2}\) or \(\mathrm{NiCO}_{3}\), (d) \(\mathrm{AgI}\) or \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\)

Short Answer

Expert verified
(a) CdS has a greater molar solubility than CuS (\(2.83 \times 10^{-14}\) vs. \(7.75 \times 10^{-19}\)). (b) BaCrO4 has a greater molar solubility than PbCO3 (\(1.08 \times 10^{-5}\) vs. \(1.22 \times 10^{-7}\)). (c) Ni(OH)2 has a greater molar solubility than NiCO3 (\(1.82 \times 10^{-5}\) vs. \(4 \times 10^{-10}\)). (d) Ag2SO4 has a greater molar solubility than AgI (\(2.29 \times 10^{-2}\) vs. \(2.91 \times 10^{-9}\)).

Step by step solution

01

(a) Cadmium sulfide (CdS) vs Copper sulfide (CuS)

First, we will need the Ksp values for CdS and CuS. You can find these values in a chemistry reference book or online: Ksp_CdS = 8 x 10^-27 Ksp_CuS = 6 x 10^-37 Now, calculate the molar solubility for each compound. Molar solubility_CdS = \( \sqrt{8 \times 10^{-27}} \approx 2.83 \times 10^{-14}\) Molar solubility_CuS = \( \sqrt{6 \times 10^{-37}} \approx 7.75 \times 10^{-19}\) Comparing the molar solubilities, CdS has a greater molar solubility than CuS.
02

(b) Lead(II) carbonate (PbCO3) vs Barium chromate (BaCrO4)

List the Ksp values for PbCO3 and BaCrO4: Ksp_PbCO3 = 1.5 x 10^-13 Ksp_BaCrO4 = 1.17 x 10^-10 Calculate the molar solubility of each compound. Molar solubility_PbCO3 = \( \sqrt{1.5 \times 10^{-13}} \approx 1.22 \times 10^{-7}\) Molar solubility_BaCrO4 = \( \sqrt{1.17 \times 10^{-10}} \approx 1.08 \times 10^{-5}\) Comparing the molar solubilities, BaCrO4 has a greater molar solubility than PbCO3.
03

(c) Nickel(II) hydroxide (Ni(OH)2) vs Nickel(II) carbonate (NiCO3)

Identify the Ksp values for Ni(OH)2 and NiCO3: Ksp_NiOH2 = 6 x 10^-16 Ksp_NiCO3 = 1.6 x 10^-19 Calculate the molar solubility of each compound. Molar solubility_NiOH2 = \( \sqrt[3]{6 \times 10^{-16}} \approx 1.82 \times 10^{-5}\) Molar solubility_NiCO3 = \( \sqrt{1.6 \times 10^{-19}} \approx 4 \times 10^{-10}\) Comparing the molar solubilities, Ni(OH)2 has a greater molar solubility than NiCO3.
04

(d) Silver iodide (AgI) vs Silver sulfate (Ag2SO4)

Determine the Ksp values for AgI and Ag2SO4: Ksp_AgI = 8.5 x 10^-17 Ksp_Ag2SO4 = 1.2 x 10^-5 Calculate the molar solubility for each compound. Molar solubility_AgI = \( \sqrt{8.5 \times 10^{-17}} \approx 2.91 \times 10^{-9}\) Molar solubility_Ag2SO4 = \( \sqrt[3]{1.2 \times 10^{-5}} \approx 2.29 \times 10^{-2}\) Comparing the molar solubilities, Ag2SO4 has a greater molar solubility than AgI.

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Most popular questions from this chapter

A buffer is prepared by adding \(3.5 \mathrm{~g}\) of ammonium chloride \(\left(\mathrm{NH}_{4} \mathrm{Cl}\right)\) to \(100 \mathrm{~mL}\) of $1.00 \mathrm{M} \mathrm{NH}_{3}$ solution. (a) What is the \(\mathrm{pH}\) of this buffer? (b) Write the complete ionic equation for the reaction that occurs when a few drops of hydrochloric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of sodium hydroxide solution are added to the buffer.

What is the \(\mathrm{pH}\) at \(25^{\circ} \mathrm{C}\) of water saturated with \(\mathrm{CO}_{2}\) at a partial pressure of \(111.5 \mathrm{kPa}\) ? The Henry's law constant for \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) is $3.1 \times 10^{-4} \mathrm{~mol} / \mathrm{L}-\mathrm{kPa}$.

Lead(II) carbonate, \(\mathrm{PbCO}_{3}\), is one of the components of the passivating layer that forms inside lead pipes. (a) If the \(K_{s p}\) for \(\mathrm{PbCO}_{3}\) is \(7.4 \times 10^{-14}\) what is the molarity of \(\mathrm{Pb}^{2+}\) in a saturated solution of lead(II) carbonate? (b) What is the concentration in ppb of \(\mathrm{Pb}^{2+}\) ions in a saturated solution? (c) Will the solubility of \(\mathrm{PbCO}_{3}\) increase or decrease as the \(\mathrm{pH}\) is lowered? (d) The EPA threshold for acceptable levels of lead ions in water is 15 ppb. Does a saturated solution of lead(II) carbonate produce a solution that exceeds the EPA limit?

A buffer is prepared by adding \(15.0 \mathrm{~g}\) of sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) to \(500 \mathrm{~mL}\) of a \(0.100 \mathrm{M}\) acetic acid \(\left(\mathrm{CH}_{3} \mathrm{COOH}\right)\) solution. (a) Determine the pH of the buffer. (b) Write the complete ionic equation for the reaction that occurs when a few drops of nitric acid are added to the buffer. (c) Write the complete ionic equation for the reaction that occurs when a few drops of potassium hydroxide solution are added to the buffer.

The value of \(K_{s p}\) for \(\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\) is \(2.1 \times 10^{-20} .\) The \(\mathrm{AsO}_{4}^{3-}\) ion is derived from the weak acid \(\mathrm{H}_{3} \mathrm{AsO}_{4}\left(\mathrm{pK}_{a 1}=\right.\) \(\left.2.22 ; \mathrm{p} K_{a 2}=6.98 ; \mathrm{pK}_{a 3}=11.50\right)\) (a) Calculate the molar solubility of \(\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\) in water. (b) Calculate the pH of a saturated solution of \(\mathrm{Mg}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\) in water.
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