Problem 40
Question
A soluble salt, \(\mathrm{MX}_{2}\), is added to water in a beaker. The equation for the dissolving of the salt is: $$ \mathrm{MX}_{2}(s) \longrightarrow \mathrm{M}^{2+}(a q)+2 \mathrm{X}^{-}(a q) ; \quad \Delta H>0 $$ a. Immediately after the salt dissolves, is the solution warmer or colder? b. Indicate the direction of heat flow, in or out of the beaker, while the salt dissolves. c. After the salt dissolves and the water returns to room temperature, what is the value of \(q\) for the system?
Step-by-Step Solution
Verified Answer
a: Colder; b: Heat flows into the beaker; c: \(q = 0\) at equilibrium.
1Step 1: Analyzing the Enthalpy Change
The problem states that \( \Delta H > 0 \), indicating that the dissolving process is endothermic. In an endothermic reaction, the system absorbs heat from its surroundings.
2Step 2: Effect on Solution Temperature
Since the reaction is endothermic, the system absorbs heat, causing the surroundings (solution) to become colder immediately after dissolution. Thus, the solution becomes colder.
3Step 3: Determine the Direction of Heat Flow
In this endothermic process, heat flows into the system (the dissolving salt) from the surroundings (the water in the beaker). Therefore, the direction of heat flow is into the beaker.
4Step 4: Evaluating Thermal Equilibrium State
Once all the salt is dissolved and the system returns to room temperature, the system and surroundings reach thermal equilibrium. At this point, heat flow stops, and \( q = 0 \), since there is no net change in energy in the system or surroundings.
Key Concepts
Enthalpy ChangeHeat Flow DirectionThermal EquilibriumDissolution of Salts
Enthalpy Change
Enthalpy change is a fundamental concept in thermochemistry that relates to the heat absorbed or released during a chemical reaction. In the exercise, the enthalpy change (\( \Delta H \)) for the dissolution of the salt \( \text{MX}_2 \) is greater than zero. This indicates the process is endothermic.
In an endothermic reaction, the system requires energy to proceed, which it absorbs from its surroundings. This absorption results in a temperature decrease of the surrounding environment, as observed in this exercise where the solution becomes colder immediately after the salt dissolves.
Understanding \( \Delta H \) helps predict whether a reaction will require or release energy and how it will affect the temperature of the surroundings. In this case, \( \Delta H > 0 \) confirms that dissolving \( \text{MX}_2 \) is endothermic, pulling heat from the water and cooling it down.
In an endothermic reaction, the system requires energy to proceed, which it absorbs from its surroundings. This absorption results in a temperature decrease of the surrounding environment, as observed in this exercise where the solution becomes colder immediately after the salt dissolves.
Understanding \( \Delta H \) helps predict whether a reaction will require or release energy and how it will affect the temperature of the surroundings. In this case, \( \Delta H > 0 \) confirms that dissolving \( \text{MX}_2 \) is endothermic, pulling heat from the water and cooling it down.
Heat Flow Direction
The direction of heat flow is crucial in understanding endothermic and exothermic processes. During the dissolution of \( \text{MX}_2 \) in water, heat flows into the system, which consists of the salt and the surrounding water.
In an endothermic reaction, like the one in this exercise, heat is absorbed from the surroundings into the system. Therefore, as the salt dissolves, heat flows from the water into the dissolving salt.
This inward flow of heat results in a lower temperature of the surrounding solution, since energy is leaving the water to satisfy the energy requirement of the dissolution process. Recognizing the direction of heat flow aids in predicting changes in temperature and understanding the energy balance in a chemical process.
In an endothermic reaction, like the one in this exercise, heat is absorbed from the surroundings into the system. Therefore, as the salt dissolves, heat flows from the water into the dissolving salt.
This inward flow of heat results in a lower temperature of the surrounding solution, since energy is leaving the water to satisfy the energy requirement of the dissolution process. Recognizing the direction of heat flow aids in predicting changes in temperature and understanding the energy balance in a chemical process.
Thermal Equilibrium
Thermal equilibrium is the state where no net heat flow occurs between a system and its surroundings. After the salt \( \text{MX}_2 \) fully dissolves and the system returns to room temperature, thermal equilibrium is reached.
At thermal equilibrium, both the system and its surroundings stabilize at the same temperature, halting any heat transfer between them. This is why \( q = 0 \) at equilibrium, indicating no net change in energy.
In this exercise, after all the salt is dissolved and the solution temperature normalizes, the system achieves thermal equilibrium. Understanding this concept is important when studying reactions and their energy exchanges, as it assures that energy conservation principles are adhered to in chemical processes.
At thermal equilibrium, both the system and its surroundings stabilize at the same temperature, halting any heat transfer between them. This is why \( q = 0 \) at equilibrium, indicating no net change in energy.
In this exercise, after all the salt is dissolved and the solution temperature normalizes, the system achieves thermal equilibrium. Understanding this concept is important when studying reactions and their energy exchanges, as it assures that energy conservation principles are adhered to in chemical processes.
Dissolution of Salts
The dissolution of salts in water involves breaking ionic bonds and forming new interactions between salt ions and water molecules. When \( \text{MX}_2 \) dissolves, the solid \( \text{MX}_2 \) breaks into its constituent ions \( \text{M}^{2+} \) and \( 2 \text{X}^{-} \), which requires energy, hence the endothermic nature of the process.
This process depends heavily on the enthalpy of solution, which indicates whether the dissolution releases or requires heat. With \( \Delta H > 0 \), the dissolution is endothermic, absorbing heat and thus cooling the water.
Understanding how salts dissolve informs predictions about their behavior in different environments, such as temperature changes and their impact on the solvent (like water), and how equilibria are established between dissolved ions and the surrounding solution.
This process depends heavily on the enthalpy of solution, which indicates whether the dissolution releases or requires heat. With \( \Delta H > 0 \), the dissolution is endothermic, absorbing heat and thus cooling the water.
Understanding how salts dissolve informs predictions about their behavior in different environments, such as temperature changes and their impact on the solvent (like water), and how equilibria are established between dissolved ions and the surrounding solution.
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