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Chapter 18: Problem 10

A 725 mL sample of a saturated aqueous solution of calcium oxalate, \(\mathrm{CaC}_{2} \mathrm{O}_{4},\) at \(95^{\circ} \mathrm{C}\) is cooled to \(13^{\circ} \mathrm{C}\). How many milligrams of calcium oxalate will precipitate? For \(\mathrm{CaC}_{2} \mathrm{O}_{4}, K_{\mathrm{sp}}=1.2 \times 10^{-8}\) at \(95^{\circ} \mathrm{C}\) and \(2.7 \times 10^{-9}\) at \(13^{\circ} \mathrm{C}\).

Short Answer

Expert verified
To find the short answer, follow the calculations set out in the steps. The final result will be the amount in milligrams of calcium oxalate that precipitates when cooled to \(13^{\circ} C\).

Step by step solution

01

Calculate the molar solubility at \(95^{\circ} C\)

The solubility product constant, \(K_{sp}\), at \(95^{\circ} C\) is given as \(1.2 \times 10^{-8}\). Since the equation for calcium oxalate, \(CaC_{2}O_{4}\), can be written as \(CaC_{2}O_{4} ⇌ Ca^{2+} + C_{2}O_{4}^{2-}\), we know that the \(K_{sp}\) expression is \(K_{sp} = [Ca^{2+}][C_{2}O_{4}^{2-}]\). Because calcium oxalate is a 1:1 salt, the molar solubility at \(95^{\circ} C\) can be represented by \(s\) and so \(K_{sp}\) can be expressed as \(s^{2}\). Solving for \(s\), we get \(s = \sqrt{K_{sp}} = \sqrt{1.2 \times 10^{-8}}\).
02

Calculate the molar solubility at \(13^{\circ} C\)

We repeat the step for temperature \(13^{\circ} C\) where \(K_{sp}\) is given as \(2.7 \times 10^{-9}\). Thus, \(s = \sqrt{K_{sp}} = \sqrt{2.7 \times 10^{-9}}\).
03

Calculate the difference in molar solubility

The difference in molar solubility will give us the amount of \(CaC_{2}O_{4}\) that precipitates out when cooled to \(13^{\circ} C\). It's calculated as: \(\Delta s = s_{95} - s_{13}\).
04

Convert molar solubility to mass

Calculate the milligrams of \(CaC_{2}O_{4}\) that precipitates out by converting the molar solubility difference (\(\Delta s\)) into grams using its molar weight (one mole of \(CaC_{2}O_{4}\) has a weight of \(128.1g\)) and then into milligrams. Multiply this with the volume of the solution in litres to get the total milligrams that precipitate.

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Most popular questions from this chapter

Which of the following has the highest molar solubility? (a) \(\mathrm{MgF}_{2}, K_{\mathrm{sp}}=3.7 \times 10^{-8}\) \(\mathrm{MgCO}_{3}\), \(K_{\mathrm{sp}}=3.5 \times 10^{-8} ;(\mathrm{c}) \mathrm{Mg}_{3}\left(\mathrm{PO}_{4}\right)_{2}, K_{\mathrm{sp}}=1 \times 10^{-25}\); (d) \(\mathrm{Li}_{3} \mathrm{PO}_{4}, K_{\mathrm{sp}}=3.2 \times 10^{-9}\).

The slightly soluble solute \(\mathrm{Ag}_{2} \mathrm{CrO}_{4}\) is most soluble in (a) pure water; (b) \(0.10 \mathrm{M} \mathrm{K}_{2} \mathrm{CrO}_{4} ;\) (c) \(0.25 \mathrm{M} \mathrm{KNO}_{3}\); (d) \(0.40 \mathrm{M} \mathrm{AgNO}_{3}\).

All but two of the following solutions yield a precipitate when the solution is also made \(2.00 \mathrm{M}\) in \(\mathrm{NH}_{3}\). Those two are (a) \(\mathrm{MgCl}_{2}(\mathrm{aq}) ;\) (b) \(\mathrm{FeCl}_{3}(\mathrm{aq})\); (c) \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(\mathrm{aq}) ;(\mathrm{d}) \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(\mathrm{aq})\); (e) \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(\mathrm{aq})\).

Write net ionic equations for each of the following observations. (a) When concentrated \(\mathrm{CaCl}_{2}(\mathrm{aq})\) is added to \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq}),\) a white precipitate forms that is \(38.7 \%\) Ca by mass. (b) When a piece of dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) is placed in a clear dilute solution of limewater \(\left[\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\right]\), bubbles of gas evolve. At first, a white precipitate forms, but then it redissolves.

A solution is \(0.010 \mathrm{M}\) in both \(\mathrm{CrO}_{4}^{2-}\) and \(\mathrm{SO}_{4}^{2-}\). To this solution, \(0.50 \mathrm{M} \mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}(\text { aq })\) is slowly added. (a) Which anion will precipitate first from solution? (b) What is \(\left[\mathrm{Pb}^{2+}\right]\) at the point at which the second anion begins to precipitate? (c) Are the two anions effectively separated by this fractional precipitation?
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