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Chapter 19: Problem 77

Slaked lime, \(\mathrm{Ca}(\mathrm{OH})_{2},\) is used to soften hard water by removing calcium ions from hard water through the reaction $$\begin{array}{r}\mathrm{Ca}(\mathrm{OH})_{2}(a q)+\mathrm{Ca}^{2+}(a q)+2 \mathrm{HCO}_{3}^{-}(a q) \rightarrow \\\2 \mathrm{CaCO}_{3}(s)+2 \mathrm{H}_{2} \mathrm{O}(l)\end{array}$$.Although \(\mathrm{CaCO}_{3}(s)\) is considered insoluble, some of it does dissolve in aqueous solutions. Calculate the molar solubility of \(\mathrm{CaCO}_{3}\) in water \(\left(K_{\mathrm{sp}}=8.7 \times 10^{-9}\right)\).

Short Answer

Expert verified
The molar solubility of \(\mathrm{CaCO}_3\) in water is \(9.3 \times 10^{-5}\, \mathrm{M}\).

Step by step solution

01

Write the balanced dissolution reaction of \(\mathrm{CaCO}_{3}\)

The balanced dissolution reaction for \(\mathrm{CaCO}_{3}\) can be written as: \[\mathrm{CaCO}_{3}(s) \rightleftharpoons \mathrm{Ca}^{2+}(aq) + \mathrm{CO}_{3}^{2-}(aq)\]
02

Write the \(K_{sp}\) expression

The expression for the solubility product constant, \(K_{sp}\), can be written as: \[K_{sp} = [\mathrm{Ca^{2+}}][\mathrm{CO_{3}^{2-}}]\]
03

Define the molar solubility

Let the molar solubility of \(\mathrm{CaCO}_{3}\) in water be \(S\). Then, the equilibrium concentrations of the ions are as follows: \[[\mathrm{Ca}^{2+}] = S\] \[[\mathrm{CO}_{3}^{2-}] = S\]
04

Substitute the concentrations into the \(K_{sp}\) expression

Now substitute the equilibrium concentrations of \(\mathrm{Ca}^{2+}\) and \(\mathrm{CO}_{3}^{2-}\) into the \(K_{sp}\) expression: \[K_{sp} = S \times S\]
05

Solve for molar solubility (\(S\))

Given that \(K_{sp} = 8.7 \times 10^{-9}\), we have: \[8.7 \times 10^{-9} = S^{2}\] Solving for \(S\), we get: \[S = \sqrt{8.7 \times 10^{-9}} = 9.3 \times 10^{-5}\, \text{M}\] Thus, the molar solubility of \(\mathrm{CaCO}_3\) in water is \(9.3 \times 10^{-5}\, \mathrm{M}\).

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Most popular questions from this chapter

Silicon is produced for the chemical and electronics industries by the following reactions. Give the balanced equation for each reaction. a. \(\mathrm{SiO}_{2}(s)+\mathrm{C}(s) \longrightarrow \mathrm{Si}(s)+\mathrm{CO}(g)\). b. Silicon tetrachloride is reacted with very pure magnesium, producing silicon and magnesium chloride. c. \(\mathrm{Na}_{2} \mathrm{SiF}_{6}(s)+\mathrm{Na}(s) \longrightarrow \mathrm{Si}(s)+\mathrm{NaF}(s)\).

Explain why HF is a weak acid, whereas HCl, HBr, and HI are all strong acids.

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