Problem 54 - Advanced Problems in Physical Chemistry for Competitive Examinations

Question

Which of the following salts shall cause more cooling when one mole of the salt is dissolved in the same amount of water? (Integral heat of solution at \(298 \mathrm{~K}\) is given for each solute.) (a) \(\mathrm{KNO}_{3} ; \Delta H=35.4 \mathrm{~kJ} / \mathrm{mol}\) (b) \(\mathrm{NaCl} ; \Delta H=5.35 \mathrm{~kJ} / \mathrm{mol}\) (c) \(\mathrm{KOH} ; \Delta H=-55.6 \mathrm{~kJ} / \mathrm{mol}\) (d) \(\mathrm{HBr} ; \Delta H=-83.3 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

Potassium nitrate (KNO3) with an integral heat of solution of 35.4 kJ/mol will cause more cooling than NaCl, KOH, or HBr when dissolved in water.

Step 1: Understand Endothermic and Exothermic Processes

When a salt is dissolved in water, the process can either absorb heat from the surroundings (endothermic, positive ΔH) or release heat to the surroundings (exothermic, negative ΔH). Cooling is associated with endothermic processes.

Step 2: Identify the Endothermic Reactions

Among the given salts, KNO3 and NaCl have positive values of ΔH, which means their dissolution is endothermic and will cause cooling.

Step 3: Compare the Magnitude of the Integral Heat of Solution

To determine which salt causes more cooling, compare the magnitude of the integral heat of solution (ΔH) for the endothermic reactions. The larger the positive value of ΔH, the more heat will be absorbed, and thus, the greater the cooling effect.

Step 4: Choose the Salt with the Highest Positive ΔH

KNO3 has an integral heat of solution of 35.4 kJ/mol, which is greater than that of NaCl, which is 5.35 kJ/mol. Thus, KNO3 will cause more cooling.

Key Concepts

Endothermic and Exothermic Processes

In physical chemistry, we encounter two fundamental types of reactions or processes: endothermic and exothermic. These terms describe whether a process absorbs heat from its surroundings (endothermic) or releases heat into its surroundings (exothermic).

During an endothermic process, the system gains heat as the surrounding temperature drops, which can be felt as cooling. In contrast, an exothermic process does the opposite; the system loses heat, and the surrounding temperature increases, which can be perceived as warming.

For example, when certain salts dissolve in water, the reaction requires energy to break the ionic bonds between the salt's cations and anions. This energy comes from the surrounding water, which cools down as a result, indicating an endothermic process. In other cases, when different salts dissolve, energy is released as the ions interact with water, making the solution warmer and indicating an exothermic process.

Heat of Dissolution

The heat of dissolution, or enthalpy of solution, is the amount of heat energy that is either absorbed or released when a substance dissolves in a solvent, such as water. This heat change is often expressed in kilojoules per mole (kJ/mol) and can be a positive or negative value, corresponding to endothermic or exothermic processes, respectively.

The heat of dissolution is crucial because it tells us about the nature of the interactions between the solute (the substance being dissolved) and the solvent. A high positive value suggests that a large amount of heat is absorbed to dissolve the substance, resulting in a significant temperature drop of the solution. Conversely, a high negative value indicates that a lot of heat is released, and the solution's temperature will increase.

Practical Application

Understanding the heat of dissolution helps in anticipating the temperature changes during various processes, which is essential for both laboratory and industrial applications where temperature control is vital.

Physical Chemistry Problems

In physical chemistry problems such as determining the cooling effect of dissolving different salts in water, it's crucial to consider the enthalpies of solution and apply the concepts of endothermic and exothermic processes. These problems require the application of thermodynamic principles to predict the observable outcomes of chemical processes.

When tackling such exercises, students must pay close attention to the given values of enthalpies and interpret whether processes are endothermic or exothermic. Correct interpretation informs the understanding of the system's energy changes and enables accurate predictions about the results.

Application in Exercises

In the given exercise, we distinguish between salts that absorb heat (endothermic) and those that release it (exothermic) upon dissolution in water. By understanding and comparing the enthalpy values, we can infer which substance will cause more cooling (or heating) in a solution—an invaluable skill for students in solving practical physical chemistry problems.