When carbon monoxide forms a crystal, each molecule can be pictured as having two possible orientations, CO or OC, because the molecular dipole moment is quite small.Assuming two possible microstates for each CO molecule, calculate the value of S when one mole of CO forms a crystalline solid at 0 K.

Question

Quizplus · Accepted Answer

The entropy (S) can be calculated using the Boltzmann formula: S = k ln W, where k is the Boltzmann constant (1.38 x 10^-23 J/K) and W is the number of microstates. For one mole of CO molecules (6.022 x 10^23 molecules), with each molecule having two possible orientations, the total number of microstates W is 2^(6.022 x 10^23). The entropy is then S = (1.38 x 10^-23 J/K) ln(2^(6.022 x 10^23)) = (1.38 x 10^-23 J/K) * (6.022 x 10^23) ln(2) = R ln(2), where R is the gas constant (8.314 J/mol·K). Therefore, S = 8.314 J/mol·K * ln(2) ≈ 5.76 J/mol·K, assuming the system is at 0 K.

When Carbon Monoxide Forms a Crystal, Each Molecule Can Be