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Chapter 17: Problem 51

Write the expression for the solubility-product constant for each of the following ionic compounds: $\mathrm{BaCrO}_{4}, \mathrm{CuS}, \mathrm{PbCl}_{2}\( and \)\mathrm{LaF}_{3} .$

Short Answer

Expert verified
The solubility-product constant expressions for the given ionic compounds are: - BaCrO\(_4\): \(K_\mathrm{sp} = [\mathrm{Ba^{2+}}][\mathrm{CrO_4^{2-}}]\) - CuS: \(K_\mathrm{sp} = [\mathrm{Cu^{2+}}][\mathrm{S^{2-}}]\) - PbCl\(_2\): \(K_\mathrm{sp} = [\mathrm{Pb^{2+}}][\mathrm{Cl^-}]^2\) - LaF\(_3\): \(K_\mathrm{sp} = [\mathrm{La^{3+}}][\mathrm{F^-}]^3\)

Step by step solution

01

1. Understanding solubility-product constant (K\(_{sp}\))

The solubility-product constant, K\(_{sp}\), is an equilibrium constant that measures the solubility of a sparingly soluble ionic compound in a solution. It is represented by the product of the equilibrium concentrations of the constituent ions of the ionic compound, each raised to the power of its stoichiometric coefficient.
02

2. Write the dissociation equation for BaCrO\(_4\)

First, let's write the dissociation equation for the ionic compound in water: \[ \mathrm{BaCrO_4}(s) \rightleftharpoons \mathrm{Ba^{2+}}(aq) + \mathrm{CrO_4^{2-}}(aq) \]
03

3. Write the K\(_{sp}\) expression for BaCrO\(_4\)

Now, we can write the solubility-product constant using the concentrations of the ions and their stoichiometric coefficients according to the balanced equation: \[ K_\mathrm{sp} = [\mathrm{Ba^{2+}}][\mathrm{CrO_4^{2-}}] \]
04

4. Write the dissociation equation for CuS

Let's write the dissociation equation for CuS: \[ \mathrm{CuS}(s) \rightleftharpoons \mathrm{Cu^{2+}}(aq) + \mathrm{S^{2-}}(aq) \]
05

5. Write the K\(_{sp}\) expression for CuS

The solubility-product constant for CuS can be written as: \[ K_\mathrm{sp} = [\mathrm{Cu^{2+}}][\mathrm{S^{2-}}] \]
06

6. Write the dissociation equation for PbCl\(_2\)

Now, let's write the dissociation equation for PbCl\(_2\): \[ \mathrm{PbCl_2}(s) \rightleftharpoons \mathrm{Pb^{2+}}(aq) + 2\mathrm{Cl^{-}}(aq) \]
07

7. Write the K\(_{sp}\) expression for PbCl\(_2\)

The solubility-product constant for PbCl\(_2\) can be written as: \[ K_\mathrm{sp} = [\mathrm{Pb^{2+}}][\mathrm{Cl^-}]^2 \]
08

8. Write the dissociation equation for LaF\(_3\)

Finally, let's write the dissociation equation for LaF\(_3\): \[ \mathrm{LaF_3}(s) \rightleftharpoons \mathrm{La^{3+}}(aq) + 3\mathrm{F^{-}}(aq) \]
09

9. Write the K\(_{sp}\) expression for LaF\(_3\)

The solubility-product constant for LaF\(_3\) can be written as: \[ K_\mathrm{sp} = [\mathrm{La^{3+}}][\mathrm{F^-}]^3 \]
10

Summary

We've written the solubility-product constant expressions for the given ionic compounds as follows: - BaCrO\(_4\): \(K_\mathrm{sp} = [\mathrm{Ba^{2+}}][\mathrm{CrO_4^{2-}}]\) - CuS: \(K_\mathrm{sp} = [\mathrm{Cu^{2+}}][\mathrm{S^{2-}}]\) - PbCl\(_2\): \(K_\mathrm{sp} = [\mathrm{Pb^{2+}}][\mathrm{Cl^-}]^2\) - LaF\(_3\): \(K_\mathrm{sp} = [\mathrm{La^{3+}}][\mathrm{F^-}]^3\)

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Most popular questions from this chapter

What is the \(\mathrm{pH}\) of a solution made by mixing \(0.40 \mathrm{~mol}\) \(\mathrm{NaOH}, 0.25 \mathrm{~mol} \mathrm{Na}_{2} \mathrm{HPO}_{4}\), and \(0.30 \mathrm{~mol} \mathrm{H}_{3} \mathrm{PO}_{4}\) with water and diluting to \(2.00 \mathrm{~L} ?\)

Which of the following salts will be substantially more soluble in an \(\mathrm{HNO}_{3}\) solution than in pure water: (a) \(\mathrm{BaSO}_{4}\), (b) \(\mathrm{CuS},\) (c) \(\mathrm{Cd}(\mathrm{OH})_{2}\) (d) \(\mathrm{PbF}_{2}\), (e) \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?\)

What is the \(\mathrm{pH}\) at \(25^{\circ} \mathrm{C}\) of water saturated with \(\mathrm{CO}_{2}\) at a partial pressure of \(111.5 \mathrm{kPa}\) ? The Henry's law constant for \(\mathrm{CO}_{2}\) at \(25^{\circ} \mathrm{C}\) is $3.1 \times 10^{-4} \mathrm{~mol} / \mathrm{L}-\mathrm{kPa}$.

A buffer contains 0.30 mol of propionic acid $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOH}\right)\( and \)0.25 \mathrm{~mol}$ of potassium propionate \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{COOK}\right)\) in 1.80 L. (a) What is the pH of this buffer? (b) What is the pH of the buffer after the addition of \(0.10 \mathrm{~mol}\) of \(\mathrm{NaOH}\) ? \((\mathbf{c})\) What is the \(\mathrm{pH}\) of the buffer after the addition of \(0.10 \mathrm{~mol}\) of \(\mathrm{HCl}\) ?

Equal quantities of \(0.010 \mathrm{M}\) solutions of an acid HA and a base \(\mathrm{B}\) are mixed. The \(\mathrm{pH}\) of the resulting solution is 9.2 . (a) Write the chemical equation and equilibrium-constant expression for the reaction between HA and B. (b) If \(K_{a}\) for HA is \(8.0 \times 10^{-5}\), what is the value of the equilibrium constant for the reaction between HA and B? (c) What is the value of \(K_{b}\) for \(B\) ?
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