Imagine that one carbon in buckminster-
fullerene (C60) is replaced by a silicon atom,yielding SiC59. This molecule can then orient in 60 different ways. What is the entropy of
one mole of SiC59 at T = 0 K?
1. 4.53 × 10−20 J/K
2. 27.3 kJ/K
3. 34.0 J/K
4. 5.65 × 10−23 J/K
To calculate the entropy of one mole of SiC59 at T = 0 K, we need to determine the number of different possible orientations and use Boltzmann's entropy formula.
In this case, the molecule SiC59 can orient in 60 different ways. Since there is only one carbon atom replaced by a silicon atom, the remaining 59 carbon atoms can be placed in any of the 60 positions. Thus, the number of different orientations is 60.
The formula for entropy is given by:
S = k * ln(W)
where S is the entropy, k is Boltzmann's constant, and W is the number of different possible orientations.
At T = 0 K, the temperature is absolute zero, and according to the statistical definition of entropy, the entropy of a system at absolute zero is zero. Therefore, the entropy of one mole of SiC59 at T = 0 K is zero.
Therefore, the correct answer to the question is not provided in the options provided.