Question

If a solution contains either \(\mathrm{Pb}^{2+}(a q)\) or \(\mathrm{Ag}^{+}(a q),\) how can temperature be manipulated to help identify the ion in solution?

Short answer

To identify the ion in a solution containing either Ag+ or Pb2+, temperature can be manipulated based on Le Chatelier's principle and the solubility product constant (Ksp). Since the dissolution of salts containing Ag+ or Pb2+ ions is an endothermic process, increasing temperature results in increased solubility, while decreasing temperature results in decreased solubility. The key is to find a temperature at which the solubility difference between the two ions is significant, by comparing their Ksp values and temperature dependence. By cooling the solution to that specific temperature, the less soluble ion will precipitate out, allowing for identification of the ion present in the solution. This information can be found in standard chemistry textbooks or databases such as CRC Handbook of Chemistry and Physics.

Step-by-step solution

Understand Solubility Product Constant

Solubility product constant (Ksp) is an equilibrium constant that represents the solubility of a sparingly soluble salt in solution. For the reaction of a salt AxB, the equation can be represented as: \(A_x B_y (s) \rightleftharpoons xA^{y+} (aq) + yB^{x-} (aq)\) The solubility product constant (Ksp) for this reaction is given by: \(K_{sp} = [A^{y+}]^x[B^{x-}]^y\) Here, we need to look into the solubility product of two salts: PbX and AgX, where X can be any counter anion.

Le Chatelier's Principle

Le Chatelier's principle can be used to predict how the equilibrium of a system will shift when subjected to external changes such as temperature, pressure, or concentration. For our exercise, we will focus on the effect of temperature on the solubility of the two salts. According to Le Chatelier's principle, 1. If a system at equilibrium is subjected to an increase in temperature, the equilibrium will shift towards the direction that absorbs heat (endothermic) 2. If a system at equilibrium is subjected to a decrease in temperature, the equilibrium will shift towards the direction that releases heat (exothermic)

Analyze the Effect of Temperature on Solubility

For salts containing Ag+ or Pb2+ ions (in this case, AgX or PbX), dissolving the salt in water is an endothermic process. As a result, when the temperature of the solution is increased, the solubility of the salts will increase. This means that more ions will be released into the solution, increasing the concentration of the ions in the solution. Conversely, when the temperature of the solution is decreased, the solubility of the salts will decrease. This means that fewer ions will be released into the solution, decreasing the concentration of the ions in the solution. However, not all salts exhibit the same degree of temperature dependence. Some salts might have a stronger temperature dependence than others, and this difference can be used to separate different ions from a mixture.

Determine the Appropriate Temperature to Identify the Ion in Solution

To identify the ion in solution (either Ag+ or Pb2+), we need to find a temperature at which one of the ions is less soluble than the other. By cooling the solution to this specific temperature, the less soluble ion will start to precipitate out of the solution, while the more soluble ion will remain in the solution. To determine the appropriate temperature for this process, one needs to look into the Ksp values and their temperature dependence for both salts (AgX and PbX). A comparison of the Ksp values and their change with temperature will give the required information. This data is usually available in standard chemistry textbooks or databases such as CRC Handbook of Chemistry and Physics. Once you know the temperature at which the solubility difference is significant, you can reduce the temperature of the solution to that point. The less soluble ion will start to precipitate out, while the other ion remains in the solution. By analyzing the precipitate formed, you can identify the ion present in the solution.

Key concepts

Ksp (Solubility Product Constant)

The solubility product constant, or Ksp, is a crucial concept in chemistry. It helps us understand how much of a sparingly soluble salt can dissolve in a solution. Imagine a salt, say AxB, dissolving in water. It separates into its ions:

• For AxB, this would be xA^y+ and yB^x-.
• The Ksp of this reaction is represented by the equation: \[ K_{sp} = [A^{y+}]^x[B^{x-}]^y \]

This formula shows the product of the concentrations of the ions, each raised to the power of their respective coefficients in the balanced equation.
The larger the Ksp, the more soluble the compound. In our context, to identify the ions \(\mathrm{Pb}^{2+}\) or \(\mathrm{Ag}^{+}\) in a solution, we need to compare their Ksp with their solubility under varying conditions.
Understanding these values provides insight into which compound is more likely to dissolve or precipitate under different conditions.

Le Chatelier's Principle

Le Chatelier's Principle is like a guidebook for predicting changes in chemical equilibria. It tells us how changes in temperature, pressure, or concentration can shift the equilibrium. When the temperature changes, it affects equilibrium as follows:

• An increase in temperature will shift equilibrium in the direction that absorbs heat (endothermic direction).
• A decrease in temperature pushes equilibrium towards the direction that releases heat (exothermic direction).

In our exercise, we're dealing with the solubility of salts containing \(\mathrm{Ag}^{+}\) or \(\mathrm{Pb}^{2+}\). These processes are often endothermic, meaning they absorb heat as they dissolve, thereby increasing solubility with temperature.
Applying Le Chatelier’s principle, if we cool down the solution, the equilibrium shifts to the exothermic side, causing precipitation. This can be crucial in identifying ions by observing which precipitates out at different temperatures.

Temperature effect on solubility

Temperature plays a critical role in the solubility of substances. Generally:

• Endothermic dissolution means increasing temperature increases solubility.
• Conversely, decreasing temperature decreases solubility.

For salts like \(\mathrm{AgX}\) or \(\mathrm{PbX}\), these concepts are vital.
Increasing the temperature of the solution makes these salts dissolve more, releasing more ions (\(\mathrm{Ag}^{+}\) or \(\mathrm{Pb}^{2+}\)) into the solution.
However, not all salts behave identically with temperature changes. By identifying how each salt’s solubility changes with temperature, you can exploit this behavior to differentiate between the two metals. If one of these salts becomes less soluble at a specific cooler temperature, it will precipitate first, providing a means to identify the ion present. This approach requires knowledge of the Ksp values and temperature dependence of these salts, which is typically found in chemistry reference materials.