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Chapter 17: Problem 74

A solution of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is added dropwise to a solution that is \(0.010 \mathrm{M}\) in \(\mathrm{Ba}^{2+}(a q)\) and $0.010 \mathrm{M}\( in \)\mathrm{Sr}^{2+}(a q) .(\mathbf{a}) \mathrm{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?

Short Answer

Expert verified
(a) The necessary concentration of $\mathrm{SO}_{4}^{2-}$ to begin precipitation is \(1.1\times10^{-9}\,M\). (b) $\mathrm{Ba}^{2+}$ will precipitate first. (c) The concentration of $\mathrm{SO}_{4}^{2-}$ needed for the second cation, $\mathrm{Sr}^{2+}$, to precipitate is \(3.2\times10^{-6}\,M\).

Step by step solution

01

Write solubility product expressions.

The solubility products expressions can be written as: For BaSO4: \[K_{sp}(BaSO_4) = [Ba^{2+}][SO_4^{2-}]\] For SrSO4: \[K_{sp}(SrSO_4) = [Sr^{2+}][SO_4^{2-}]\]
02

Find saturation concentrations for each cation.

The concentration of Ba^2+ and Sr^2+ ions are both given as 0.010 M. Now, let's solve for the saturation concentration of SO4^2- for each cation using the solubility products: For Ba^2+: \[[SO_4^{2-}]_{sat}(Ba^{2+}) = \frac{K_{sp}(BaSO_4)}{[Ba^{2+}]} = \frac{1.1\times10^{-10}}{0.010} = 1.1\times10^{-9}\,M\] For Sr^2+: \[[SO_4^{2-}]_{sat}(Sr^{2+}) = \frac{K_{sp}(SrSO_4)}{[Sr^{2+}]} = \frac{3.2\times10^{-7}}{0.010} = 3.2\times10^{-6}\,M\]
03

Determine which cation precipitates first.

Since we are looking for the minimum concentration of SO4^2- to start precipitation, we should compare the saturation concentrations calculated in step 2. The cation with the lower saturation concentration will precipitate first: \(1.1\times10^{-9}\,M < 3.2\times10^{-6}\,M\), therefore Ba^2+ will precipitate first. Answer (b): Ba^2+ will precipitate first.
04

Calculate the concentration of SO4^2- when the second cation begins to precipitate.

After Ba^2+ has precipitated, it is now out of the solution and does not affect the solution anymore. The concentration of SO4^2- required to make Sr^2+ precipitate can be found using the saturation concentration we calculated for Sr^2+: Answer (c): The concentration of SO4^2- when the second cation (Sr^2+) begins to precipitate is \(3.2\times10^{-6}\,M\). In summary: (a) The necessary concentration of sulfate ions to begin precipitation is \(1.1\times10^{-9}\,M\). (b) Ba^2+ will precipitate first. (c) The concentration of sulfate ions needed for the second cation, Sr^2+, to precipitate is \(3.2\times10^{-6}\,M\).

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Most popular questions from this chapter

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HA. (a) How many moles of HA have been added at the equivalence point? (b) What is the predominant form of B at the equivalence point? (a) Is the \(\mathrm{pH} 7\), less than 7 , or more than 7 at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

The value of \(K_{s p}\) for \(\mathrm{Cd}(\mathrm{OH})_{2}\) is $2.5 \times 10^{-14} .(\mathbf{a})$ What is the molar solubility of \(\mathrm{Cd}(\mathrm{OH})_{2} ?(\mathbf{b})\) The solubility of \(\mathrm{Cd}(\mathrm{OH})_{2}\) can be increased through formation of the complex ion \(\mathrm{CdBr}_{4}^{2-}\left(K_{f}=5 \times 10^{3}\right) .\) If solid \(\mathrm{Cd}(\mathrm{OH})_{2}\) is added to a NaBr solution, what is the initial concentration of NaBr needed to increase the molar solubility of \(\mathrm{Cd}(\mathrm{OH})_{2}\) to $1.0 \times 10^{-3} \mathrm{~mol} / \mathrm{L} ?$

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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 \(2.00 \mathrm{~L} ?\)

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.
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