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Chapter 17: Problem 69

(a) Will \(\mathrm{Ca}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathrm{pH}\) of a \(0.050 \mathrm{M}\) solution of \(\mathrm{CaCl}_{2}\) is adjusted to \(8.0 ?(\mathbf{b})\) Will \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) precipitate when \(100 \mathrm{~mL}\) of \(0.050 \mathrm{M} \mathrm{AgNO}_{3}\) is mixed with \(10 \mathrm{~mL}\) of $5.0 \times 10^{-2} \mathrm{M} \mathrm{Na}_{2} \mathrm{SO}_{4}$ solution?

Short Answer

Expert verified
In summary, \( Ca(OH)_2 \) will not precipitate from a 0.050 M solution of \( CaCl_2 \) when the pH is adjusted to 8.0 because the reaction quotient (Q) is much less than the solubility product constant (Ksp). Similarly, \( Ag_2SO_4 \) will not precipitate when 100 mL of 0.050 M \( AgNO_3 \) is mixed with 10 mL of \( 5.0 \times 10^{-2} M \, Na_2SO_4 \) solution, as Q is less than Ksp in this case as well.

Step by step solution

01

Calculate the concentration of OH- ions

The pH of the solution is given as 8.0, so we can find the concentration of OH- ions using the following relation: pOH = 14 - pH Therefore, pOH = 14 - 8 = 6 By definition, pOH = -log10[OH-]. So, we can calculate the concentration of OH- ions as: [OH-] = 10^(-pOH) = 10^(-6) = 1.0 * 10^(-6) M
02

Calculate the reaction quotient, Q

Now, we'll calculate the reaction quotient, Q, for the reaction: Ca(OH)2(s) <=> Ca2+(aq) + 2OH-(aq) In this case, Q = [Ca2+][OH-]^2, where [Ca2+] is the concentration of Ca2+ ions and [OH-] is the concentration of OH- ions. Given that [Ca2+] = 0.050 M (from the CaCl2 solution) and [OH-] = 1 * 10^(-6) M (from the pH), we can calculate Q as: Q = (0.050)(1.0 * 10^(-6))^2 = 5.0 * 10^(-13)
03

Compare Q to the solubility product constant, Ksp

The solubility product constant, Ksp, for Ca(OH)2 is 6.5 * 10^(-6). Let's compare Q to Ksp to determine if Ca(OH)2 will precipitate from the solution. Since Q (5.0 * 10^(-13)) is much less than Ksp (6.5 * 10^(-6)), no precipitate will form. Therefore, Ca(OH)2 will not precipitate from the solution when the pH is adjusted to 8.0. (b) Will Ag2SO4 precipitate when 100 mL of 0.050 M AgNO3 is mixed with 10 mL of 5.0 * 10^(-2) M Na2SO4 solution?
04

Calculate the concentrations of Ag+ and SO4 2- ions

We can find the concentrations of Ag+ and SO4 2- ions after mixing the solutions as follows: [Ag+] = (0.050 M * 100 mL) / (100 mL + 10 mL) = 0.0455 M [SO4 2-] = (5.0 * 10^(-2) M * 10 mL) / (100 mL + 10 mL) = 4.55 * 10^(-3) M
05

Calculate the reaction quotient, Q

Now, we'll calculate the reaction quotient, Q, for the reaction: Ag2SO4(s) <=> 2Ag+(aq) + SO4 2-(aq) In this case, Q = [Ag+]^2[SO4 2-], so we can calculate Q as: Q = (0.0455)^2(4.55 * 10^(-3)) = 9.38 * 10^(-6)
06

Compare Q to the solubility product constant, Ksp

The solubility product constant, Ksp, for Ag2SO4 is 1.2 * 10^(-5). Let's compare Q to Ksp to determine if Ag2SO4 will precipitate from the solutions. Since Q (9.38 * 10^(-6)) is less than Ksp (1.2 * 10^(-5)), no precipitate will form. Therefore, Ag2SO4 will not precipitate when the given solutions are mixed.

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Most popular questions from this chapter

(a) What is the ratio of \(\mathrm{HCO}_{3}^{-}\) to $\mathrm{H}_{2} \mathrm{CO}_{3}\( in blood of \)\mathrm{pH} 7.4$ ? (b) What is the ratio of \(\mathrm{HCO}_{3}^{-}\) to $\mathrm{H}_{2} \mathrm{CO}_{3}\( in an exhausted marathon runner whose blood \)\mathrm{pH}$ is \(7.1 ?\)

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.)

Compare the titration of a strong, monoprotic acid with a strong base to the titration of a weak, monoprotic acid with a strong base. Assume the strong and weak acid solutions initially have the same concentrations. Indicate whether the following statements are true or false. (a) More base is required to reach the equivalence point for the strong acid than the weak acid. \((\mathbf{b})\) The \(\mathrm{pH}\) at the beginning of the titration is lower for the weak acid than the strong acid. \((\mathbf{c})\) The \(\mathrm{pH}\) at the equivalence point is 7 no matter which acid is titrated.

Consider the titration of \(30.0 \mathrm{~mL}\) of $0.050 \mathrm{M} \mathrm{NH}_{3}\( with \)0.025 M$ HCl. Calculate the pH after the following volumes of titrant have been added: $(\mathbf{a}) 0 \mathrm{~mL},(\mathbf{b}) 20.0 \mathrm{~mL},\( (c) 59.0 \)\mathrm{mL},(\mathbf{d}) 60.0 \mathrm{~mL},(\mathbf{e}) 61.0 \mathrm{~mL},(\mathbf{f}) 65.0 \mathrm{~mL} .$

What is the \(\mathrm{pH}\) of a solution made by mixing \(0.40 \mathrm{~mol}\) \(\mathrm{NaOH}, 0.25 \mathrm{~mol} \mathrm{Na}_{2} \mathrm{HPO}_{4}\), and \(0.30 \mathrm{~mol} \mathrm{H}_{3} \mathrm{PO}_{4}\) with water and diluting to \(2.00 \mathrm{~L} ?\)
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