/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 The solubility of the ionic comp... [FREE SOLUTION] | 91影视

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Chapter 16: Problem 24

The solubility of the ionic compound \(\mathrm{M}_{2} \mathrm{X}_{3}\), having a molar mass of \(288 \mathrm{~g} / \mathrm{mol}\), is \(3.60 \times 10^{-7} \mathrm{~g} / \mathrm{L}\). Calculate the \(K_{\mathrm{sp}}\) of the compound.

Short Answer

Expert verified
The solubility product constant, \(K_{sp}\), for the ionic compound \(M_{2}X_{3}\) is approximately \(1.24 \times 10^{-43}\).

Step by step solution

01

Convert solubility from g/L to mol/L

First, we need to convert the given solubility, which is expressed in g/L, to a molar solubility expressed in mol/L. To do this, we will divide the given solubility in g/L by the given molar mass of the compound. \(Molar\: solubility = \frac{Solubility\: (g/L)}{Molar\: mass\: (g/mol)}\)
02

Calculate ion concentration in the saturated solution

We will use the molar solubility to find the concentration of ions in a saturated solution of M鈧俋鈧�. Each M鈧俋鈧� unit dissociates into 2 M鈦� ions and 3 X鈦� ions. So, if 's' is the molar solubility, the resulting concentrations will be: MM: 2s XX: 3s
03

Calculate Ksp

Now that we have the ion concentrations in the saturated solution, we can calculate the Ksp using the following expression: \(K_{sp} = [M^+]^2 [X^-]^3\) Plugging in the ion concentrations (2s for M鈦� and 3s for X鈦�) into the formula and simplifying: \(K_{sp} = (2s)^2 (3s)^3\) Now we can substitute the molar solubility from Step 1 and compute the Ksp.
04

Substitute the molar solubility and simplify

Substitute the molar solubility found in Step 1 into the Ksp expression and simplify: \( K_{sp} = (2 \times (\frac{3.60 \times 10^{-7}}{288}))^2 (3 \times (\frac{3.60 \times 10^{-7}}{288}))^3 \) After substituting and solving for Ksp: \(K_{sp} \approx 1.24 \times 10^{-43}\) The solubility product constant, Ksp, for the ionic compound M鈧俋鈧� is approximately 1.24 x 10鈦烩伌鲁.

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Most popular questions from this chapter

a. Using the \(K_{\mathrm{sp}}\) value for \(\mathrm{Cu}(\mathrm{OH})_{2}\left(1.6 \times 10^{-19}\right)\) and the overall formation constant for \(\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}\left(1.0 \times 10^{13}\right)\), calculate the value for the equilibrium constant for the following reaction: \(\mathrm{Cu}(\mathrm{OH})_{2}(s)+4 \mathrm{NH}_{3}(a q) \rightleftharpoons \mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}^{2+}(a q)+2 \mathrm{OH}^{-}(a q)\) b. Use the value of the equilibrium constant you calculated in part a to calculate the solubility (in \(\mathrm{mol} / \mathrm{L}\) ) of \(\mathrm{Cu}(\mathrm{OH})_{2}\) in \(5.0 \mathrm{M}\) \(\mathrm{NH}_{3} .\) In \(5.0 \mathrm{M} \mathrm{NH}_{3}\) the concentration of \(\mathrm{OH}^{-}\) is \(0.0095 \mathrm{M} .\)

Calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) is relatively insoluble in water \(\left(K_{\mathrm{xp}}=\right.\) \(\left.2 \times 10^{-9}\right)\). However, calcium oxalate is more soluble in acidic solution. How much more soluble is calcium oxalate in \(0.10 \mathrm{M}\) \(\mathrm{H}^{+}\) than in pure water? In pure water, ignore the basic properties of \(\mathrm{C}_{2} \mathrm{O}_{4}^{2-}\)

Use the following data to calculate the \(K_{\mathrm{sp}}\) value for each solid. a. The solubility of \(\mathrm{Pb}_{3}\left(\mathrm{PO}_{4}\right)_{2}\) is \(6.2 \times 10^{-12} \mathrm{~mol} / \mathrm{L}\). b. The solubility of \(\mathrm{Li}_{2} \mathrm{CO}_{3}\) is \(7.4 \times 10^{-2} \mathrm{~mol} / \mathrm{L}\).

The copper(I) ion forms a chloride salt that has \(K_{\text {sp }}=1.2 \times 10^{-6}\). Copper(I) also forms a complex ion with \(\mathrm{Cl}^{-}\) : $$\mathrm{Cu}^{+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{CuCl}_{2}^{-}(a q) \quad K=8.7 \times 10^{4}$$ a. Calculate the solubility of copper(I) chloride in pure water. (Ignore \(\mathrm{CuCl}_{2}^{-}\) formation for part a.) b. Calculate the solubility of copper(I) chloride in \(0.10 \mathrm{M} \mathrm{NaCl}\).

Write equations for the stepwise formation of each of the following complex ions. a. \(\mathrm{Ni}(\mathrm{CN})_{4}^{2-}\) b. \(\mathrm{V}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}{ }^{3-}\)
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