Directions: Questions 1-3 are long free-response questions that require about 23 minutes each to answer and are worth 10 points each. Write your response in the space provided following each question. Examples and equations may be included in your responses where appropriate. For calculations, clearly show the method used and the steps involved in arriving at your answers. You must show your work to receive credit for your answer. Pay attention to significant figures. A student is tasked with determining the identity of an unknown carbonate compound with a mass of 1.89 g. The compound is first placed in water, where it dissolves completely. The \(K_{s p}\) value for several carbonate-containing compounds are given below. $$\begin{array}{|c|c|}\hline \text { Compound } & {K_{s p}} \\ \hline \text { Lithium carbonate } & {8.15 \times 10^{-4}} \\ \hline \text { Nickel (II) carbonate } & {1.42 \times 10^{-7}} \\ \hline \text { Strontium carbonate } & {5.60 \times 10^{-10}} \\ \hline\end{array}$$ (a) In order to precipitate the maximum amount of the carbonate ions from solution, which of the following should be added to the carbonate solution: \(\operatorname{LiNO}_{3}, \mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2},\) or \(\mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2} ?\) Justify your answer. (b) For the carbonate compound that contains the cation chosen in part (a), determine the concentration of each ion of that compound in solution at equilibrium. (c) When mixing the solution, should the student ensure the carbonate solution or the nitrate solution is in excess? Justify your answer. (d) After titrating sufficient solution to precipitate out all of the carbonate ions, the student filters the solution before placing it in a crucible and heating it to drive off the water. After several heatings, the final mass of the precipitate remains constant and is determined to be 2.02 g. (i) Determine the number of moles of precipitate. (ii) Determine the mass of carbonate present in the precipitate. (e) Determine the percent, by mass, of carbonate in the original sample. (f) Is the original compound most likely lithium carbonate, sodium carbonate, or potassium carbonate? Justify your answer.

Step by step solution

01

Precipitation decision

Decide which compound will yield maximum precipitation of carbonate ions. Based on the principles of solubility, the compound with the lowest solubility product constant (\(K_{s p}\)) will precipitate the most. Here, the compound with the lowest \(K_{s p}\) is Strontium carbonate (\(K_{s p} = 5.60 \times 10^{-10}\)).

02

Triangulate Ion Concentration

For determining the concentrations of each ion, consider the solubility product expression for Strontium carbonate, which is \(K_{s p} = [Sr^{2+}] [CO_{3}^{2-}]\). Given the \(K_{s p}\), solve this equation for concentration which yields that [Sr^{2+}] = [CO_{3}^{2-}] = \(7.48 \times 10^{-6} M\).

03

The excess factor

To drive out all the carbonate, sufficient amount of nitrate is needed to react with it completely. Thus, the nitrate solution should be in excess as it ensures that all the carbonate will be precipitated out.

04

Determine Moles

Given the final mass of precipitate, use the molar mass of Strontium carbonate to find the moles of precipitate which equals to \(2.02 g / 147.63 g/mol = 0.0137 mol\).

05

Calculate Carbonate Mass

The mole ratio of SrCO3 to CO3^2- is 1:1, so the moles of CO3^2- is also 0.0137. Using the molar mass of CO3^2-, find the mass of carbonate which equals to \(0.0137 mol * 60.01 g/mol = 0.822 g\).

06

Percentage of Carbonate

Compute the percentage of carbonate by mass in the original sample which equals \(0.822 g / 1.89 g *100 = 43.5%\).

07

Compound Identification

Compare the given percentage with the theoretical carbonate content in Lithium carbonate, Nickel carbonate and Strontium carbonate (which are 48.69%, 11.38%, and 46.7% respectively). The match with closest carbonate content determines the unknown compound, hence it is most likely Strontium Carbonate.

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