Question

The melting point for carbon diselenide \(\left(\mathrm{CSe}_{2}\right)\) is \(-46^{\circ} \mathrm{C}\) . At a temperature of \(-75^{\circ} \mathrm{C},\) predict the signs for \(\Delta S_{\mathrm{surr}}\) and \(\Delta S_{\mathrm{univ}}\) for the following process: \(\operatorname{CSe}_{2}(l) \rightarrow \operatorname{CSe}_{2}(s)\)

Short answer

For the process of CSe2 changing from liquid to solid at -75°C, the signs for the change in entropy are: \(\Delta S_{sys}\) is negative, \(\Delta S_{surr}\) is positive, and \(\Delta S_{univ}\) is positive.

Step-by-step solution

Determine the entropy change for the system (\(\Delta S_{sys}\))

Since we are given that CSe2 is changing from liquid to solid phase, this process is a freezing (or crystallization) process. In general, the entropy of a system decreases when a substance freezes. Therefore, for this process, \(\Delta S_{sys}\) will be negative.

Determine the temperature at which the phase change occurs

We are given that the phase change occurs at a temperature of -75°C. To understand the impacts on the surrounding entropy, it's useful to compare this to the melting point of the substance. The melting point for CSe2 is -46°C, which means that the temperature is lower than the melting point when the phase change occurs in this scenario.

Determine the sign of the entropy change for the surroundings (\(\Delta S_{surr}\))

To change from liquid to solid, heat must be released to the surroundings. This means that the heat flow is exothermic, which corresponds to a negative \(\Delta H\). Since the phase change is occurring below the melting point, the surroundings are colder, resulting in a greater impact of heat from the system. In this situation, the equation \(\Delta S_{surr} = -\frac{\Delta H}{T}\) will have a greater negative number in the numerator and a smaller absolute value (but still negative) in the denominator, resulting in a positive \(\Delta S_{surr}\).

Determine the sign of the entropy change for the universe (\(\Delta S_{univ}\))

The change in entropy for the universe is calculated as the sum of the entropy changes for the system and the surroundings: \(\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr}\). From Step 1, we found that \(\Delta S_{sys}\) is negative, and from Step 3, we found that \(\Delta S_{surr}\) is positive. In this case, since the process is occurring at a temperature below the melting point, the positive \(\Delta S_{surr}\) will have a greater magnitude than the negative \(\Delta S_{sys}\). Therefore, the overall \(\Delta S_{univ}\) will be positive. In conclusion, for the given process of CSe2 changing from liquid to solid at -75°C, the signs for the change in entropy are: - \(\Delta S_{sys}\): negative - \(\Delta S_{surr}\): positive - \(\Delta S_{univ}\): positive

Key concepts

Phase Change

When a substance undergoes a phase change, it transitions from one state of matter to another. This could mean changing from liquid to solid, solid to gas, or any other combination. In our example, carbon diselenide (CSe2) changes from a liquid to a solid. This particular change is known as freezing or crystallization. During a phase change like this, temperature remains constant, even though the heat energy is being absorbed or released by the substance.

• Melting refers to transitioning from solid to liquid.
• Freezing is going from liquid to solid.
• Boiling/evaporation means liquid to gas.
• Condensation changes gas to liquid.

These changes are important in understanding how energy and matter interact during different processes.

Entropy Change

In thermodynamics, entropy is a measure of disorder or randomness in a system. The second law of thermodynamics suggests that the total entropy of an isolated system can never decrease over time. When substances change phase, their entropy changes.
In our case, carbon diselenide changes from a more disordered liquid state to a more ordered solid state. Thus, the system's entropy (\(\Delta S_\text{sys}\)) decreases, and this is why \(\Delta S_\text{sys}\) is negative. However, when the surroundings absorb heat in an exothermic process, their entropy increases. Therefore, \(\Delta S_\text{surr}\) turns out to be positive.

• System entropy typically decreases when changing from liquid to solid.
• Surroundings gain entropy when heat is released to them.

Understanding these changes helps explain why certain processes occur spontaneously.

Thermodynamics

Thermodynamics is the study of energy, matter, and their interactions. It involves the laws that describe how heat and energy flow in different systems. The key to thermodynamics is understanding how energy changes during processes like phase changes.
There are four laws of thermodynamics guiding these interactions:

• The Zeroth Law establishes thermal equilibrium.
• The First Law introduces energy conservation.
• The Second Law discusses increasing entropy.
• The Third Law notes zero entropy at absolute zero.

For carbon diselenide, the process we evaluated requires examining the entropy changes in both the system and the universe, revealing how energy interactions during a phase change follow these laws.

Exothermic Process

An exothermic process involves the release of heat into the surroundings. This process contrasts with endothermic reactions, where heat is absorbed. In our case, when carbon diselenide freezes, it releases heat. This happens because liquids are generally at a higher energy level than solids, and converting from liquid to solid releases that energy.

• Exothermic processes decrease the energy content of the system.
• Heat flows from the warmer system to cooler surroundings.
• Temperature of the surroundings increases as a result.

It's important to note that exothermic processes often feel hot to the touch because of the heat being released, which fits with our example where carbon diselenide freezes and its entropy also shifts accordingly as discussed.