Question

Some water is placed in a coffee-cup calorimeter. When 1.0 \(\mathrm{g}\) of an ionic solid is added, the temperature of the solution increases from \(21.5^{\circ} \mathrm{C}\) to \(24.2^{\circ} \mathrm{C}\) as the solid dissolves. For the dissolving process, what are the signs for \(\Delta S_{\mathrm{sys}}, \Delta S_{\mathrm{surt}},\) and \(\Delta S_{\mathrm{univ}} ?\)

Short answer

In the dissolving process, the signs for the entropy changes are as follows: \( \Delta S_{sys} \) (system) is positive since entropy increases with increasing disorder. \( \Delta S_{surr} \) (surroundings) is positive since heat is released to the surroundings during the exothermic process, and temperature is always positive. Finally, \( \Delta S_{univ} \) (universe) is positive because it is the sum of the positive entropy changes for the system and surroundings.

Step-by-step solution

Determine the sign of ∆S_sys

To determine the sign of ∆S_sys, we must analyze the molecular states involved in the dissolving process. The solid ionic compound is in a highly ordered state. When it dissolves in the water, the ions disperse, and the overall system becomes less ordered. The change in entropy of the system (∆S_sys) will be positive, since entropy increases with increasing disorder.

Determine the sign of ∆S_surr

Since the dissolving process is exothermic, it releases heat to the surroundings. The sign of ∆S_surr depends on the sign of the heat (q) released and the temperature (T) at which the process occurs. Here, the heat is released to the surroundings, making q a negative value. The temperature is always positive. Therefore, ∆S_surr = -q/T, and the negative sign of q changes to a positive sign when multiplied by the constant negative sign. So, the change in entropy of the surroundings (∆S_surr) is positive.

Determine the sign of ∆S_univ

To find the sign of ∆S_univ, we sum the change in entropy for the system and the surroundings. Since both ∆S_sys and ∆S_surr are positive, their sum (∆S_univ) will also be positive. In conclusion, the signs for the entropy changes are as follows: ∆S_sys: Positive ∆S_surr: Positive ∆S_univ: Positive

Key concepts

Entropy

Entropy is a measure of disorder or randomness in a system. When we talk about a system becoming more disordered, we mean that the particles, like atoms or molecules, are moving and spread out in a less organized way.
During the dissolving process of an ionic solid in water, the molecular structure transforms. The ionic solid, initially in an ordered state as a lattice, shifts to a disordered state when its ions are dispersed in the solution.
This increase in disorder leads to a positive \( \Delta S_{\text{sys}} \) because entropy increases.

• A solid ionic compound is well-ordered and structured.
• When dissolved, it disperses into separate ions.
• This dispersion signifies a higher state of randomness.

This understanding of entropy helps explain phenomena where systems evolve towards greater disorder, following the second law of thermodynamics.

Exothermic Process

An exothermic process is one where energy is released in the form of heat during a reaction. In our context of calorimetry, when an ionic solid dissolves in water and the temperature increases, the process is exothermic.
This means heat is transferred from the system (the dissolving ionic solid) to the surroundings, like the water in the calorimeter.

• The system releases energy by decreasing its enthalpy (energy content).
• This released energy heats up the surroundings.
• The temperature rise confirms the exothermic nature of the process.

Consequently, the entropy change of the surroundings, \( \Delta S_{\text{surr}} \), is positive due to the heat flow into the environment, demonstrating how heat distributions contribute to entropy.

Thermal Equilibrium

Thermal equilibrium occurs when two objects interacting in a system reach the same temperature and no further heat transfer occurs. In calorimetry, reaching thermal equilibrium is key for accurate measurements.
Once the ionic solid has entirely dissolved in water, thermal equilibrium is reached when the solution stabilizes at the increased temperature.

• Heat flows naturally from hotter to cooler regions.
• Equilibrium is achieved when temperatures balance in the system.
• This state allows us to conclude the heat exchange process.

Understanding thermal equilibrium is essential in calorimetry experiments since it ensures accurate assessments of energy changes and supports the analysis of entropic changes within a system.