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Chapter 17: Problem 59

Consider a beaker containing a saturated solution of \(\mathrm{CaF}_{2}\) in equilibrium with undissolved \(\mathrm{CaF}_{2}(s)\). Solid \(\mathrm{CaCl}_{2}\) is then added to the solution. (a) Will the amount of solid \(\mathrm{CaF}_{2}\) at the bottom of the beaker increase, decrease, or remain the same? (b) Will the concentration of \(\mathrm{Ca}^{2+}\) ions in solution increase or decrease? (c) Will the concentration of \(\mathbf{F}^{-}\) ions in solution increase or decrease?

Short Answer

Expert verified
(a) The amount of solid CaF₂ will increase due to the common ion effect and equilibrium shift. (b) The concentration of Ca²⁺ ions will remain constant as the equilibrium counteracts the additional ions from CaCl₂. (c) The concentration of F⁻ ions will decrease due to the equilibrium shift favoring the formation of solid CaF₂.

Step by step solution

01

Identify the solubility product constant expression for CaF₂

CaF₂ has the formula unit: Ca²⁺ + 2F⁻. Its solubility product constant expression is given by: \[K_{sp} = [Ca^{2+}][F^{-}]^2\]
02

Write the equilibrium expressions for the addition of CaCl₂

When CaCl₂ is added to the solution, it will dissociate into its ions: Ca²⁺ and 2Cl⁻. We will not consider Cl⁻ ions in our analysis, as they don't affect the CaF₂ equilibrium. The equilibrium expressions for the addition of CaCl₂ are: Before CaCl₂ addition: \[K_{sp} = [Ca^{2+}][F^{-}]^2\] After CaCl₂ addition: \[K_{sp} = ([Ca^{2+}] + x)[F^{-}]^2\] where x is the increase in concentration of Ca²⁺ ions due to the addition of CaCl₂.
03

Consider the common ion effect on the equilibrium

Since adding CaCl₂ increases the concentration of the common ion Ca²⁺, the equilibrium will shift to the left, favoring the formation of solid CaF₂ according to Le Châtelier's principle. This means the amount of solid CaF₂ will increase, the concentration of Ca²⁺ ions in solution will remain constant, and the concentration of F⁻ ions will decrease.
04

Answer the exercise questions

(a) The amount of solid CaF₂ at the bottom of the beaker will increase due to the common ion effect and the shift in the equilibrium. (b) The concentration of Ca²⁺ ions in the solution will remain constant because the equilibrium will shift to counteract the addition of more Ca²⁺ ions from CaCl₂. (c) The concentration of F⁻ ions in the solution will decrease, as the equilibrium shift to the left due to the common ion effect will favor the formation of solid CaF₂.

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Most popular questions from this chapter

(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 \(\mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3} .\)

How many milliliters of 0.0850\(M \mathrm{NaOH}\) are required to titrate each of the following solutions to the equivalence point: (a) 40.0 \(\mathrm{mL}\) of \(0.0900 \mathrm{M} \mathrm{HNO}_{3},\) (\mathbf{b} ) 35.0 \(\mathrm{mL}\) of \(0.0850 M \mathrm{CH}_{3} \mathrm{COOH},(\mathbf{c}) 50.0 \mathrm{mL}\) of a solution that contains 1.85 \(\mathrm{g}\) of \(\mathrm{HCl}\) per liter?

(a) Write the net ionic equation for the reaction that occurs when a solution of hydrochloric acid (HCl) is mixed with a solution of sodium formate (NaCHO \(_{2} )\) . (b) Calculate the equilibrium constant for this reaction. (c) Calculate the equilibrium concentrations of \(\mathrm{Na}^{+}, \mathrm{Cl}^{-}, \mathrm{H}^{+}, \mathrm{CHO}_{2}^{-}\) and \(\mathrm{HCHO}_{2}\) when 50.0 \(\mathrm{mL}\) of 0.15 \(\mathrm{MCl}\) is mixed with 50.0 \(\mathrm{mL}\) of 0.15 \(\mathrm{MNaCHO}_{2} .\)

Calculate the \(\mathrm{pH}\) at the equivalence point in titrating 0.100 M solutions of each of the following with 0.080 \(\mathrm{M}\) NaOH: (a) hydrobromic acid (HBr), (b) chlorous acid (HClO_{2} ) , (c) benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\)

A 1.00 -L solution saturated at \(25^{\circ} \mathrm{C}\) with calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) contains 0.0061 \(\mathrm{g}\) of \(\mathrm{CaC}_{2} \mathrm{O}_{4} .\) Calculate the solubility-product constant for this salt at \(25^{\circ} \mathrm{C}\) .
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