Which state in each of the following pairs has the higher entropy per mole of substance? (a) Ice at -40 °C or ice at 0 °C

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Understand that entropy is a measure of disorder or randomness in a system. Higher temperature generally increases entropy because particles have more energy and can move more freely.

Recognize that both substances in the pair are ice, meaning they are in the solid state. However, the temperatures are different: -40 °C and 0 °C.

Recall that as temperature increases, the kinetic energy of the molecules increases, leading to greater molecular motion and higher entropy.

Compare the two temperatures: -40 °C and 0 °C. Since 0 °C is higher, the ice at this temperature will have more molecular motion compared to ice at -40 °C.

Conclude that ice at 0 °C has higher entropy per mole than ice at -40 °C because the higher temperature allows for more molecular motion and disorder.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Entropy

Entropy is a measure of the disorder or randomness in a system. It quantifies the number of possible microstates that correspond to a given macrostate. Higher entropy indicates greater disorder and more available microstates, which typically occurs at higher temperatures or in more complex molecular arrangements.

Phase Changes

Phase changes refer to the transitions between solid, liquid, and gas states of matter. During these transitions, the arrangement and energy of molecules change significantly. For example, when ice melts to water, the molecular structure becomes less ordered, resulting in an increase in entropy.

Temperature and Entropy Relationship

The relationship between temperature and entropy is crucial in thermodynamics. As temperature increases, the kinetic energy of molecules also increases, leading to greater molecular motion and disorder. Therefore, a substance at a higher temperature generally has higher entropy than the same substance at a lower temperature, even if both are in the same phase.

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