(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 2 mol of gaseous reactants are converted to 3 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Entropy is a measure of randomness or disorder in a system. When a system becomes more random or disordered, its entropy increases.

The given reaction has 2 moles of gaseous reactants converting to 3 moles of gaseous products. This means the number of moles of gas particles increases during the reaction.

As we have an increase in the number of moles of gas particles, the system becomes more disordered (i.e., more random). This increased disorder in the system means that the entropy of the system (ΔS) increases. Consequently, the sign of ΔS is positive. So, the sign of ΔS for the given chemical reaction is positive. #b) Processes in which entropy of the system increases#

In Exercise 19.11, there are four processes. We need to analyze each of these processes to see if the entropy of the system increases for any of them: 1. Melting of 1 mole of ice at 0°C. 2. Freezing of 1 mole of water at 0°C. 3. Vaporization of 1 mole of boiling water at 100°C. 4. Sublimation of 1 mole of ice at -15°C under low pressure.

1. Melting of 1 mole of ice at 0°C: In this process, ice (a solid) is converted to water (a liquid). The molecules in a liquid are more disordered than in a solid, so the entropy of the system increases in this process. 2. Freezing of 1 mole of water at 0°C: In this process, water (a liquid) is converted to ice (a solid). The molecules in a solid are more ordered than in a liquid, so the entropy of the system decreases in this process. 3. Vaporization of 1 mole of boiling water at 100°C: In this process, water (a liquid) is converted to steam (a gas). The molecules in a gas are more disordered than in a liquid, so the entropy of the system increases in this process. 4. Sublimation of 1 mole of ice at -15°C under low pressure: In this process, ice (a solid) is directly converted to water vapor (a gas) without passing through the liquid state. The molecules in a gas are more disordered than in a solid, so the entropy of the system increases in this process.

Based on the analysis of the processes in Exercise 19.11, the entropy of the system increases for the following processes: 1. Melting of 1 mole of ice at 0°C 3. Vaporization of 1 mole of boiling water at 100°C 4. Sublimation of 1 mole of ice at -15°C under low pressure