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Chapter 16: Problem 90

If the solubility of a compound increases with increasing temperature, does \(K_{\mathrm{sp}}\) increase or decrease?

Short Answer

Expert verified
Answer: When the solubility of a compound increases with increasing temperature due to an endothermic dissolution process, the solubility product constant (\(K_{\mathrm{sp}}\)) also increases.

Step by step solution

01

Understand the terms: Solubility and Solubility Product Constant (\(K_{\mathrm{sp}}\))

Solubility is a measure of the maximum amount of a solute that can dissolve in a solvent at a given temperature. The solubility product constant (\(K_{\mathrm{sp}}\)) is the equilibrium constant for a chemical equilibrium between a solid ionic compound and its dissolved ions. Let's consider the general dissolution process for a compound with the formula \(A_xB_y\): \(A_xB_y(s) \rightleftharpoons xA^{y+}(aq) + yB^{x-}(aq)\). The \(K_{\mathrm{sp}}\) expression for this reaction is given by: \(K_{\mathrm{sp}} = [A^{y+}]^x[B^{x-}]^y\) where [ ] represents the molar concentration of the respective ions at equilibrium.
02

How solubility and \(K_{\mathrm{sp}}\) are related

The solubility of a compound is directly proportional to its \(K_{\mathrm{sp}}\) because as the solubility (amount of dissolved solute) increases, the concentrations of the dissolved ions ([A^{y+}] and [B^{x-}]) also increase, which increases the \(K_{\mathrm{sp}}\). Conversely, if solubility decreases, \(K_{\mathrm{sp}}\) decreases as well.
03

Effect of temperature on solubility and \(K_{\mathrm{sp}}\)

The relationship between solubility, \(K_{\mathrm{sp}}\), and temperature depends on the type of reaction. If the dissolution process is endothermic (absorbs heat), solubility increases with an increase in temperature due to Le Ch芒telier's Principle. Since higher solubility results in increased concentrations of the dissolved ions, \(K_{\mathrm{sp}}\) will also increase. On the other hand, if the dissolution process is exothermic (releases heat), solubility decreases with an increase in temperature, leading to a decrease in \(K_{\mathrm{sp}}\). For this exercise, the solubility of the compound increases with increasing temperature. Therefore, the dissolution process is endothermic.
04

Determine the effect of increased temperature on \(K_{\mathrm{sp}}\).

Since the solubility of the compound increases with increased temperature and the dissolution process is endothermic, \(K_{\mathrm{sp}}\) will increase as per Le Ch芒telier's Principle. The increase in solubility leads to higher dissolved ion concentrations, so \(K_{\mathrm{sp}} = [A^{y+}]^x[B^{x-}]^y\) also increases.

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Most popular questions from this chapter

Some scientists have proposed adding \(\mathrm{Fe}(\mathrm{III})\) compounds to large expanses of the open ocean to promote the growth of phytoplankton that would in turn remove \(\mathrm{CO}_{2}\) from the atmosphere through photosynthesis. Assuming the average pH of open ocean water is \(8.13,\) what is the maximum value of \(\left[\mathrm{Fe}^{3+}\right]\) in seawater if the \(K_{\mathrm{sp}}\) value of \(\mathrm{Fe}(\mathrm{OH})_{3}\) is \(1.1 \times 10^{-36} ?\)

Will lead(II) chloride precipitate if \(185 \mathrm{mL}\) of \(0.025 \mathrm{M}\) sodium chloride is added to \(235 \mathrm{mL}\) of \(0.165 M\) lead (II) perchlorate at \(25^{\circ} \mathrm{C} ?\)

What is the pH of \(1.00 M \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2} ?\)

Why is \(\mathrm{BF}_{3}\) a Lewis acid but not a Bronsted-Lowry acid?

If only \(0.160 \mathrm{g} \mathrm{Ca}(\mathrm{OH})_{2}\) dissolves in \(0.100 \mathrm{L}\) of water, what is the \(K_{\mathrm{sp}}\) value for calcium hydroxide at that temperature?
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