Question

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which two moles of gaseous reactants are converted to three moles of gaseous products? (b) For which of the processes in Exercise \(19.9\) does the entropy of the system increase?

Short answer

For part (a), since the number of gaseous moles increases from 2 moles (reactants) to 3 moles (products), the overall randomness and dispersion of energy within the system have increased, resulting in a positive entropy change (∆S > 0). For part (b), as Exercise 19.9 was not provided, the key criteria to check for an entropy increase are an increase in the number of particles, increased energy dispersion, and increased randomness of the system.

Step-by-step solution

(Part A: Entropy change sign determination)

For the given chemical reaction where two moles of gaseous reactants are converted to three moles of gaseous products, let's analyze the entropy change. Entropy (∆S) typically increases with an increase in the number of particles in the system. In this particular case, the number of gaseous moles increases from 2 moles (reactants) to 3 moles (products). Since the number of particles has increased, the overall randomness and dispersion of energy within the system have increased. Consequently, the entropy change (∆S) should be positive. So, we can expect a positive ∆S for this reaction.

(Part B: Entropy increase in Exercise 19.9)

Exercise 19.9 is not provided. However, given a list of processes, we can determine whether the entropy would increase or not based on similar principles as discussed in Part A. Keep in mind that entropy increases when: 1. The number of particles in the system increases. 2. Energy dispersion is increased. 3. The randomness of the system increases (e.g., solid to liquid, liquid to gas). By analyzing the given processes in Exercise 19.9 based on these criteria, we can identify which processes will result in an increase in the entropy of the system.