Question

The enthalpy of solution for AgNO \(_{3}\) is \(+22.8 \mathrm{kJ} / \mathrm{mol}\) . a. Write the equation that represents the dissolution of AgNO \(_{3}\) in water. b. Is the dissolution process endothermic or exothermic? Is the crystallization process endothermic or exothermic? c. As AgNO \(_{3}\) dissolves, what change occurs in the temperature of the solution? d. When the system is at equilibrium, how do the rates of dissolution and crystallization compare? e. If the solution is then heated, how will the rates of dissolution and crystallization be affected? Why? f. How will the increased temperature affect the amount of solute that can be dissolved? g. If the solution is allowed to reach equilibrium and is then cooled, how will the system be affected?

Short answer

a) \mathrm{AgNO_{3}(s)\rightarrow Ag^{+}(aq) + NO_{3}^{-}(aq)\}b) Endothermic, Exothermicc) Temperature decreasesd) Rates are equale) Both rates increase, dissolution moref) More solute dissolvesg) Solute precipitates

Step-by-step solution

Write the dissolution equation

The equation representing the dissolution of silver nitrate (AgNO \(_{3}\)) can be written as follows: \[ \mathrm{AgNO_{3}(s) \rightarrow Ag^{+}(aq) + NO_{3}^{-}(aq)} \]

Determine if dissolution is endothermic or exothermic

Given that the enthalpy of solution for AgNO \(_{3}\) is \( +22.8\ \mathrm{kJ} \ / \ \mathrm{mol}\), it means this process requires energy. Hence, the dissolution process is endothermic.

Determine if crystallization is endothermic or exothermic

The reverse of the dissolution process is crystallization. If dissolution is endothermic, then crystallization must be exothermic.

Temperature change during dissolution

Since the dissolution of AgNO \(_{3}\) is endothermic, it absorbs heat from the surroundings, causing the temperature of the solution to decrease.

Rates of dissolution and crystallization at equilibrium

At equilibrium, the rates of dissolution and crystallization are equal.

Effect of heating on the rates of dissolution and crystallization

When the solution is heated, the increased kinetic energy of the molecules typically increases both the rate of dissolution and the rate of crystallization. However, for an endothermic dissolution process like this, the rate of dissolution will increase more.

Effect of increased temperature on solubility

Increasing the temperature will generally increase the amount of AgNO \(_{3}\) that can be dissolved in water, since the dissolution process is endothermic and more heat favors dissolving.

Effect of cooling on the system

If the solution reaches equilibrium and is then cooled, the solubility of AgNO \(_{3}\) will decrease, causing some of the solute to precipitate out of the solution as the system re-establishes equilibrium.

Key concepts

Endothermic Process

An endothermic process is one that absorbs heat from the surroundings. In the context of the dissolution of AgNO \(_{3}\), the enthalpy of solution being \(+22.8 \mathrm{kJ} / \mathrm{mol}\) indicates that this process requires energy.
This means it's taking in heat as AgNO \(_{3}\) dissolves.
The main clue that shows a process is endothermic is an increase in enthalpy (positive value).
As the dissolution occurs, the temperature of the solution decreases because the process absorbs thermal energy from its environment.
This cooling effect is a direct consequence of the endothermic nature of the process.

Dissolution Equation

The dissolution equation represents the process of a solute dissolving in a solvent. For silver nitrate (AgNO \(_{3}\)), the equation can be written as follows:

\[ \mathrm{AgNO_{3}(s) \rightarrow Ag^{+}(aq) + NO_{3}^{-}(aq)} \]

This equation shows that solid AgNO \(_{3}\) dissociates into its ions (Ag\(^{+}\) and NO\(^3^{-}\)) when dissolved in water. It's fundamental to understand that the dissolution process involves breaking ionic bonds in the solid solute and forming new interactions between these ions and the water molecules. The ability to write and understand this equation is crucial for solving related problems in chemistry.

Crystallization

Crystallization is the reverse of the dissolution process. It involves the transition from a liquid or aqueous state back to a solid state.
In the case of AgNO \(_{3}\), if the dissolution process is endothermic, then the crystallization must be exothermic. This is because energy is released when the ions come together to form the solid crystal again.
Since crystallization releases heat to the surroundings, the process causes the temperature of the solution to increase.
The understanding of crystallization helps in predicting the system's behavior when conditions such as temperature are altered.

Temperature Effect on Solubility

Temperature has a significant impact on solubility, especially in endothermic processes. When the temperature increases, the kinetic energy of molecules also increases, which can lead to more solute dissolving in the solvent.
For the endothermic dissolution of AgNO \(_{3}\), increasing the temperature favors the dissolving process because it provides additional energy that aids in breaking the ionic bonds.
So, a higher temperature typically results in a greater amount of AgNO \(_{3}\) being dissolved in water. Conversely, if the solution is cooled, the solubility decreases, and precipitates might form as the dissolved ions re-crystallize.

Chemical Equilibrium

Chemical equilibrium occurs when the rates of the forward reaction (dissolution) and the reverse reaction (crystallization) are equal. At this point, the concentration of dissolved ions and the solid AgNO \(_{3}\) remain constant.
For a solution in equilibrium, heating the system increases the rates of both dissolution and crystallization, but the dissolution rate would increase more for an endothermic process.
Ultimately, this shifts the equilibrium favoring more solute in the solution.
Understanding chemical equilibrium is vital for predicting how the system will respond to changes in temperature and other conditions.