Final answer:
A reaction that occurs with any size increase in enthalpy and any size decrease in entropy can never be spontaneous, as it goes against the second law of thermodynamics which states that entropy should increase or remain constant in a spontaneous process.
Step-by-step explanation:
The reaction that can never be spontaneous is (d) A reaction that occurs with any size increase in enthalpy and any size decrease in entropy. According to the second law of thermodynamics, for a process to be spontaneous, it must result in an increase or at least a constant entropy of the universe.
However, a process involving an increase in enthalpy and a decrease in entropy signifies that the process is moving towards greater order and lower energy dispersal which goes against the natural progression towards higher disorder (higher entropy).
An example supporting the statement that entropy never decreases in a spontaneous process is (b) The melting of an ice cube placed in a room which causes an increase in the entropy of the room. This is because the molecules in the ice cube gain energy and move from a more ordered state (solid) to a less ordered state (liquid), thus increasing entropy.
Contrastingly, a reaction that occurs with a large decrease in enthalpy and a small decrease in entropy, as in option (c), might still be spontaneous if the enthalpy change significantly overcompensates for the entropy change, especially at lower temperatures where the entropic contribution to free energy is less significant.