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Chapter 17: Problem 53

A \(1.00-\mathrm{L}\) 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 solubilityproduct constant for this salt at \(25^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The solubility product constant (Ksp) for calcium oxalate (CaC2O4) in a 1.00 L solution containing 0.0061 g of the salt at 25°C can be determined by first calculating the molar mass of CaC2O4, which is \(40.08 + (2 \times 12.01) + (4 \times 16.00)\,\text{g/mol}\). Then, find the number of moles of CaC2O4 by dividing its mass by its molar mass, followed by finding the concentration of Ca²⁺ and C₂O₄²⁻ ions in the solution, which will be equal to the concentration of CaC2O4. Finally, calculate the Ksp using the formula Ksp = [Ca²⁺][C₂O₄²⁻], which is equal to the square of the concentration of ions.

Step by step solution

01

Find the molar mass of calcium oxalate

To find the concentration of the ions in the solution, we need the molar mass of calcium oxalate (CaC2O4). The molar mass of CaC2O4 can be found by adding up the molar masses of its constituent elements: Calcium (Ca): 40.08 g/mol Carbon (C): 12.01 g/mol (there are two Carbon atoms, so multiply by 2) Oxygen (O): 16.00 g/mol (there are four Oxygen atoms, so multiply by 4) Molar mass of CaC2O4 = \(40.08 + (2 \times 12.01) + (4 \times 16.00)\)
02

Calculate the number of moles of calcium oxalate

Now that we have the molar mass of calcium oxalate, we can find the number of moles of the compound in the 1.00 L solution. Moles of CaC2O4 = mass / molar mass = \(0.0061\,\text{g} / \left( 40.08 + (2 \times 12.01) + (4 \times 16.00) \right)\,\text{g/mol}\)
03

Find the concentration of Ca²⁺ and C₂O₄²⁻ ions in the solution

Calcium oxalate (CaC2O4) dissociates into one Ca²⁺ ion and one C₂O₄²⁻ ion. Thus, the concentration of each ion will be equal to the concentration of CaC2O4 in the solution. Concentration of ions = moles / volume = moles / 1.00 L
04

Calculate the solubility product constant (Ksp)

Now we have found the concentration of each ion, we can calculate the solubility product constant (Ksp) using the following equation: Ksp = [Ca²⁺][C₂O₄²⁻] Ksp = (Concentration of ions)² Use the formula and the concentration of ions calculated in step 3 to find the Ksp.

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Most popular questions from this chapter

(a) What is the common-ion effect? (b) Give an example of a salt that can decrease the ionization of \(\mathrm{HNO}_{2}\) in solution.

In the course of various qualitative analysis procedures, the following mixtures are encountered: (a) \(\mathrm{Zn}^{2+}\) and \(\mathrm{Cd}^{2+}\) (b) \(\mathrm{Cr}(\mathrm{OH})_{3}\) and \(\mathrm{Fe}(\mathrm{OH})_{3}\) (c) \(\mathrm{Mg}^{2+}\) and \(\mathrm{K}^{+},\) (d) \(\mathrm{Ag}^{+}\) and \(\mathrm{Mn}^{2+}\). Suggest how each mixture might be separated.

A sample of \(0.1687 \mathrm{~g}\) of an unknown monoprotic acid was dissolved in \(25.0 \mathrm{~mL}\) of water and titrated with \(0.1150 \mathrm{M} \mathrm{NaOH}\). The acid required \(15.5 \mathrm{~mL}\) of base to reach the equivalence point. (a) What is the molecular weight of the acid? (b) After \(7.25 \mathrm{~mL}\) of base had been added in the titration, the \(\mathrm{pH}\) was found to be 2.85 . What is the \(K_{a}\) for the unknown acid?

A hypothetical weak acid, HA, was combined with \(\mathrm{NaOH}\) in the following proportions: \(0.20 \mathrm{~mol}\) of \(\mathrm{HA}, 0.080 \mathrm{~mol}\) of \(\mathrm{NaOH}\). The mixture was diluted to a total volume of \(1.0 \mathrm{~L}\) and the pH measured. (a) If \(\mathrm{pH}=4.80\), what is the \(\mathrm{p} K_{a}\) of the acid? (b) How many additional moles of \(\mathrm{NaOH}\) should be added to the solution to increase the \(\mathrm{pH}\) to \(5.00 ?\)

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base \(\mathrm{B}\) that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HX. (a) How many moles of \(\mathrm{HX}\) have been added at the equivalence point? (b) What is the predominant form of \(\mathrm{B}\) at the equivalence point? (c) What factor determines the \(\mathrm{pH}\) at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?
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