Final answer:
When [S]in is less than [S]out, delta G is negative, indicating a spontaneous reaction in the forward direction, as the total entropy change of the universe is positive.
Step-by-step explanation:
If [S]in < [S]out, we are discussing the scenario related to entropy change in a chemical system. Entropy, S, indicates the degree of disorder or randomness in a system. According to the second law of thermodynamics, for a process to be spontaneous, the total entropy change of the universe, which is the sum of the entropy change of the system and the entropy change of the surroundings, must be positive (ΔSuniv > 0).
For the given scenario, where [S] refers to entropy, the notation [S]in < [S]out implies that the entropy within the system (in) is less than the entropy outside the system (out), indicating that the entropy of the universe is likely increasing (ΔSuniv > 0). This typically aligns with a spontaneous reaction in the forward direction, suggesting that the Gibbs free energy change (ΔG) for the process must be negative (ΔG < 0) under constant temperature and pressure, according to the equation ΔG = ΔH - TΔS.
Thus, when [S]in < [S]out, delta G is negative, which points to a spontaneous reaction in the forward direction. This conclusion is also supported by the fact that, if ΔG < 0, the reaction quotient (K) will be greater than 1, and if the reaction is an electrochemical cell, the cell's electromotive force (E) will be greater than zero.