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Chapter 18: Problem 73

The chief compound in marble is \(\mathrm{CaCO}_{3}\). Marble has been widely used for statues and ornamental work on buildings. However, marble is readily attacked by acids. Determine the solubility of marble (that is, \(\left.\left[\mathrm{Ca}^{2+}\right] \text { in a saturated solution }\right)\) in (a) normal rainwater of \(\mathrm{pH}=5.6 ;\) (b) acid rainwater of \(\mathrm{pH}=4.20 .\) Assume that the overall reaction that occurs is \(\mathrm{CaCO}_{3}(\mathrm{s})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \rightleftharpoons\) \(\mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1)\)

Short Answer

Expert verified
The solubility of marble (concentration of Ca2+ ions) in normal and acid rainwater is \(10^{-5.6}\) and \(10^{-4.2}\) respectively.

Step by step solution

01

- Understanding pH

Firstly, it's important to understand that pH is a scale used to measure the acidity or basicity of a solution. It is defined as the negative logarithm (base 10) of the concentration of H3O+ ions. Therefore, the formula to calculate the concentration of H3O+ ions in a solution is given by: \[ \mathrm{[H_{3}O^{+}]} = 10^{-\mathrm{pH}}]. \]
02

-Calculating [H3O+] for normal and acid rainwater

Working out the H3O+ ion concentration in normal rainwater (pH 5.6) and acid rainwater (pH 4.2) using the aforementioned formula gives us: \n For normal rainwater: \[ [\mathrm{H_{3}O^{+}}] = 10^{-5.6} \] and for acid rainwater: \[ [\mathrm{H_{3}O^{+}}] = 10^{-4.2} \]
03

- Understanding the reaction and the equilibrium constant

Next, we have to understand the reaction under consideration. The reaction is: \[ \mathrm{CaCO_{3}(s)} + \mathrm{H_{3}O^{+}(aq)} \Rightarrow \mathrm{Ca^{2+}(aq)} + \mathrm{HCO_{3}^{-}(aq)} + \mathrm{H_{2}O(l)} \] The equilibrium constant expression for the reaction is then: \[ \mathrm{K = [Ca^{2+}]} \] because the concentration of solid calcium carbonate does not appear in the equilibrium constant expression, and we've assumed that [H2O] remains constant.
04

- Calculating the concentration of Ca2+ ions

The equilibrium constant for this particular reaction is the same as the concentration of the marble (Ca2+ ions) in the solution. Assuming that the reaction goes to completion, the [Ca2+] is equal to [H3O+]. Thus, for normal rainwater: \[ [Ca^{2+}] = 10^{-5.6} \], and for acid rainwater: \[ [Ca^{2+}] = 10^{-4.2} \]

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Most popular questions from this chapter

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?

The addition of \(\mathrm{HCl}(\mathrm{aq})\) to a solution containing several different cations produces a white precipitate. The filtrate is removed and treated with \(\mathrm{H}_{2} \mathrm{S}(\mathrm{aq})\) in 0.3 M HCl. No precipitate forms. Which of the following conclusions is (are) valid? Explain. (a) \(\mathrm{Ag}^{+}\) or \(\mathrm{Hg}_{2}^{2+}\) (or both) is probably present. (b) \(\mathrm{Mg}^{2+}\) is probably not present. (c) \(\mathrm{Pb}^{2+}\) is probably not present. (d) \(\mathrm{Fe}^{2+}\) is probably not present.

In a solution that is \(0.0500 \mathrm{M}\) in \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{3-}\) and \(0.80 \mathrm{M}\) in free \(\mathrm{CN}^{-}\), the concentration of \(\mathrm{Cu}^{+}\) is \(6.1 \times 10^{-32} \mathrm{M}\) Calculate \(K_{\mathrm{f}}\) of \(\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{3-}\). \(\mathrm{Cu}^{+}(\mathrm{aq})+4 \mathrm{CN}^{-}(\mathrm{aq}) \rightleftharpoons\left[\mathrm{Cu}(\mathrm{CN})_{4}\right]^{3-}(\mathrm{aq}) \quad K_{\mathrm{f}}=?\)

A \(250 \mathrm{mL}\) sample of saturated \(\mathrm{CaC}_{2} \mathrm{O}_{4}(\mathrm{aq})\) requires \(4.8 \mathrm{mL}\) of \(0.00134 \mathrm{M} \mathrm{KMnO}_{4}(\mathrm{aq})\) for its titration in an acidic solution. What is the value of \(K_{\mathrm{sp}}\) for \(\mathrm{CaC}_{2} \mathrm{O}_{4}\) obtained with these data? In the titration reaction, \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\) is oxidized to \(\mathrm{CO}_{2}\) and \(\mathrm{MnO}_{4}^{-}\) is reduced to \(\mathrm{Mn}^{2+}\).

Without performing detailed calculations, indicate whether either of the following compounds is appreciably soluble in \(\mathrm{NH}_{3}(\mathrm{aq}):(\mathrm{a}) \mathrm{CuS}, K_{\mathrm{sp}}=6.3 \times 10^{-36},\)(b) \(\mathrm{CuCO}_{3}, K_{\mathrm{sp}}=1.4 \times 10^{-10} .\) Also use the fact that \(K_{\mathrm{f}}\) for \(\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}\) is \(1.1 \times 10^{13}\).
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