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Chapter 18: Problem 68

A handbook lists the solubility of \(\mathrm{CaHPO}_{4}\) as \(0.32 \mathrm{g}\) \(\mathrm{CaHPO}_{4} \cdot 2 \mathrm{H}_{2} \mathrm{O} / \mathrm{L}\) and lists \(K_{\mathrm{sp}}\) as \(1 \times 10^{-7}\). (a) Are these data consistent? (That is, are the molar solubilities the same when derived in two different ways?) (b) If there is a discrepancy, how do you account for it?

Short Answer

Expert verified
The given solubility data and solubility product constant (Ksp) are not consistent because the calculated Ksp of \(3.4 \times 10^{-6}\) based on the given solubility differs from the provided Ksp of \(1 \times 10^{-7}\). The discrepancy could be due to various factors such as different experimental conditions, rounding errors, or approximations in the calculation.

Step by step solution

01

Convert Solubility into Molarity

First, convert the given solubility from grams per liter into molarity. Molarity is defined as the number of moles of solute per liter of solvent. The molar mass of CaHPO4•2H2O is approximately \(174.2 \, \text{g/mol}\). Thus, the molar solubility is \( \frac{0.32\,g}{174.2\,g/mol}=1.84\times 10^{-3} \,mol/L.\)
02

Setup Ksp Equation

The equilibrium reaction for \( CaHPO_4 \) dissolving in water is: \(CaHPO_4 \leftrightarrow Ca^{2+} + HPO_4^{-2}\). Therefore, the expression for the solubility product constant would be \(K_{sp}=[Ca^{2+}][HPO_4^{-2}]\). Since the molarities of \(Ca^{2+}\) and \(HPO_4^{-2}\) are equal, we can simplify the equation to \(K_{sp} = (s)^2\), where \(s\) is the molar solubility.
03

Calculate and Compare with the Given Ksp

Plugging the calculated molar solubility \(s = 1.84\times 10^{-3}\) into the Ksp equation from step 2, we get \(K_{sp} = (1.84\times 10^{-3} \, mol/L )^2 = 3.4\times 10^{-6}\). This value differs from the provided \(K_{sp} = 1 \times 10^{-7}\), which indicates that the given data are not consistent.
04

Explain the Discrepancy

The discrepancy could result from the original data handbook's different experimental or environmental conditions, rounding errors, or the use of approximations in the calculation. For a detailed explanation, one should refer to the context or specific footnotes of the original data source.

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Most popular questions from this chapter

An aqueous solution that \(2.00 \mathrm{M}\) in \(\mathrm{AgNO}_{3}\) is slowly added from a buret to an aqueous solution that is \(0.0100 \mathrm{M}\) in \(\mathrm{Cl}^{-}\) and \(0.250 \mathrm{M}\) in \(\mathrm{I}^{-}\). (a) Which ion, \(\mathrm{Cl}^{-}\) or \(\mathrm{I}^{-}\), is the first to precipitate? (b) When the second ion begins to precipitate, what is the remaining concentration of the first ion? (c) Is the separation of \(\mathrm{Cl}^{-}\) and \(\mathrm{I}^{-}\) feasible by fractional precipitation in this solution?

Write net ionic equations for each of the following observations. (a) When concentrated \(\mathrm{CaCl}_{2}(\mathrm{aq})\) is added to \(\mathrm{Na}_{2} \mathrm{HPO}_{4}(\mathrm{aq}),\) a white precipitate forms that is \(38.7 \%\) Ca by mass. (b) When a piece of dry ice, \(\mathrm{CO}_{2}(\mathrm{s}),\) is placed in a clear dilute solution of limewater \(\left[\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})\right]\), bubbles of gas evolve. At first, a white precipitate forms, but then it redissolves.

Write net ionic equations for the following qualitative cation analysis procedures. (a) precipitation of \(\mathrm{PbCl}_{2}(\mathrm{s})\) from a solution containing \(\mathrm{Pb}^{2+}\) (b) dissolution of \(\mathrm{Zn}(\mathrm{OH})_{2}(\mathrm{s})\) in a solution of \(\mathrm{NaOH}(\mathrm{aq})\) (c) dissolution of \(\mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{s})\) in \(\mathrm{HCl}(\mathrm{aq})\) (d) precipitation of \(\mathrm{CuS}(\mathrm{s})\) from an acidic solution of \(\mathrm{Cu}^{2+}\) and \(\mathrm{H}_{2} \mathrm{S}\)

Will precipitation of \(\mathrm{MgF}_{2}(\mathrm{s})\) occur if a \(22.5 \mathrm{mg}\) sample of \(\mathrm{MgCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is added to \(325 \mathrm{mL}\) of \(0.035 \mathrm{M} \mathrm{KF}\) ?

Both \(\mathrm{Mg}^{2+}\) and \(\mathrm{Cu}^{2+}\) are present in the same aqueous solution. Which of the following reagents would work best in separating these ions, precipitating one and leaving the other in solution: \(\mathrm{NaOH}(\mathrm{aq}), \mathrm{HCl}(\mathrm{aq})\), \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{aq}),\) or \(\mathrm{NH}_{3}(\mathrm{aq}) ?\) Explain your choice.
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