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Chapter 17: Problem 70

(a) Will \(\mathrm{Co}(\mathrm{OH})_{2}\) precipitate from solution if the \(\mathbf{p H}\) of a 0.020 M solution of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2}\) is adjusted to 8.5? (b) Will \(\mathrm{AgIO}_{3}\) precipitate when 20 mL of 0.010 M \(\mathrm{AglO}_{3}\) is mixed with 10 mL of 0.015 \(M \mathrm{NaIO}_{3}\)? ( \(K_{s p}\) of \(\mathrm{AgIO}_{3}\) is \(3.1 \times 10^{8}\))?

Short Answer

Expert verified
(a) After calculating the hydroxide ion concentration [OH⁻] and the concentration of \(\mathrm{Co^{2+}}\) ions, the ion product \(Q\) is found to be smaller than the \(K_{sp}\) for \(\mathrm{Co}(\mathrm{OH})_{2}\). Therefore, \(\mathrm{Co}(\mathrm{OH})_{2}\) will not precipitate at pH 8.5. (b) After mixing the solutions and calculating the new concentrations of \(\mathrm{Ag^{+}}\) and \(\mathrm{IO_{3}^{-}}\), the ion product \(Q\) is found to be smaller than the \(K_{sp}\) for \(\mathrm{AgIO}_{3}\). Therefore, \(\mathrm{AgIO}_{3}\) will not precipitate under these conditions.

Step by step solution

01

Calculate the hydroxide ion concentration from the given pH

The given pH of the solution is 8.5. To find the hydroxide ion concentration [OH⁻], use the relationship between pH and pOH: \(pOH = 14 - pH\) Calculate the pOH and find the [OH⁻] using: \([OH^-] = 10^{-pOH}\)
02

Find the concentration of \(\mathrm{Co^{2+}}\) ions

Since it is a 0.020 M solution of \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2},\) the concentration of \(\mathrm{Co^{2+}}\) ions in the solution is 0.020 M.
03

Calculate the ion product \(Q\) and compare it to \(K_{s p}\)

The ion product \(Q\) is calculated as follows: \(Q = [\mathrm{Co^{2+}}][\mathrm{OH^-]}^2\) If \(Q > K_{s p}\), precipitation will occur. (b) Precipitation of \(\mathrm{AgIO}_{3}\)
04

Calculate the concentrations after mixing the solutions

After mixing 20 mL of 0.010 M \(\mathrm{AgIO}_{3}\) with 10 mL of 0.015 M \(\mathrm{NaIO}_{3}\), calculate the new concentrations by finding the moles of each ion and divide by the total volume.
05

Calculate the ion product \(Q\) and compare it to \(K_{s p}\)

Similar to the previous case, calculate the ion product \(Q\) as follows: \(Q = [\mathrm{Ag^{+}}][\mathrm{IO_{3}^{-}}]\) If \(Q > K_{s p}\), precipitation will occur.

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Most popular questions from this chapter

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either M \(^{+}\) or \(A^{-} .(\mathbf{b})\) Common ions alter the equilibrium constant for the reaction of an ionic solid with water. (c) The common-ion effect does not apply to unusual ions like \(\mathrm{SO}_{3}^{2-}\) . (d) The solubility of a salt MA is affected equally by the addition of either \(\mathrm{A}^{-}\) or a noncommon ion.

A buffer is prepared by adding 20.0 g of sodium acetate \(\left(\mathrm{CH}_{3} \mathrm{COONa}\right)\) to 500 \(\mathrm{mL}\) of a 0.150 \(\mathrm{M}\) 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 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.

Lead(II) carbonate, 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? \((\boldsymbol{d} )\)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 solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is 0.010\(M\) in \(\mathrm{Ba}^{2+}(a q)\) and 0.010\(M\) in \(\mathrm{Sr}^{2+}(a q) .\) (a) What concentration of \(\mathrm{SO}_{4}^{2-}\) is necessary to begin precipitation? (Neglect volume changes. \(\mathrm{BaSO}_{4} : K_{s p}=1.1 \times 10^{-10} ; \mathrm{SrSO}_{4}\): \(K_{s p}=3.2 \times 10^{-7} . )\) (b) Which cation precipitates first? (c) What is the concentration of \(\mathrm{SO}_{4}^{2-}(a q)\) when the second cation begins to precipitate?

(a) Calculate the \(\mathrm{pH}\) of a buffer that is 0.105 \(\mathrm{M}\) in \(\mathrm{NaHCO}_{3}\) and 0.125 \(\mathrm{M}\) in \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) . (b) Calculate the pH of a solution formed by mixing 65 \(\mathrm{mL}\) of 0.20 \(\mathrm{M} \mathrm{NaHCO}_{3}\) with 75 \(\mathrm{mL}\) of 0.15 \(\mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} .\)
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