Final answer:
The residual entropy for 1 mole of CO at 0K is non-zero due to the existence of multiple nuclear spin states. The third law of thermodynamics posits zero entropy for a perfect crystal at absolute zero, but this can be an exception for certain molecules.
Step-by-step explanation:
The question is concerning the concept of residual entropy and specifically asks what the residual entropy is for 1 mole of carbon monoxide (CO) at 0K. Residual entropy refers to the entropy present in a perfectly organized crystal at 0K, which is not in accordance with the third law of thermodynamics. However, due to nuclear spin states, some molecules like CO can have residual entropy at 0K.
According to the third law of thermodynamics, the entropy of a perfect crystal at absolute zero is exactly zero. However, in reality, some crystals may not be perfect and can retain some degree of entropy. But CO is a linear molecule with distinguishable orientations, thus it can have different nuclear spin states even at 0K. This results in a non-zero residual entropy.
Considering that CO may have multiple accessible microstates even at 0K due to the aforementioned reasons, the answer is not (a) 0 J/K as a perfect crystal would have. While the precise value for CO is not provided here, the question is likely seeking a conceptual understanding rather than a concrete number, so it is important to acknowledge that some molecules like CO can have non-zero residual entropy at absolute zero.