16.2 Entropy

In the figure all of the possible distributions and microstates are shown for four different particles shared between two boxes. Determine the entropy change, ΔS, for the system when it is converted from distribution (b) to distribution (d).

Consider a system similar to the one in the figure, except that it contains six particles instead of four. What is the probability of having all the particles in only one of the two boxes in the case? Compare this with the similar probability for the system of four particles that we have derived to be equal to $\frac{1}{8} .$ What does this comparison tell us about even larger systems?

Consider the system shown in the figure. What is the change in entropy for the process where the energy is initially associated with particles A and B, and the energy is distributed between two particles in different boxes (one in A-B, the other in C-D)?

At room temperature, the entropy of the halogens increases from I₂ to Br₂ to Cl₂. Explain.

Indicate which substance in the given pairs has the higher entropy value. Explain your choices.

(a) C₂H₅OH(l) or C₃H₇OH(l)

(b) C₂H₅OH(l) or C₂H₅OH(g)

(c) 2H(g) or H(g)

Predict the sign of the entropy change for the following processes. Give a reason for your prediction.

(a) $\text{Na}^{+} \left(a q\right) + \text{Cl}^{−} \left(a q\right) \rightarrow \text{NaCl} \left(s\right)$

(b) $2 \text{Fe} \left(s\right) + \frac{3}{2} \text{O}_{2} \left(g\right) \rightarrow \text{Fe}_{2} \text{O}_{2} \left(s\right)$

(c) $2 \text{C}_{6} \text{H}_{14} \left(l\right) + 19 \text{O}_{2} \left(g\right) \rightarrow 14 \text{H}_{2} \text{O} \left(g\right) + 12 \text{CO}_{2} \left(g\right)$

Write the balanced chemical equation for the combustion of benzene, C₆H₆(l), to give carbon dioxide and water vapor. Would you expect ΔS to be positive or negative in this process?