an oxygen (o₂) molecule is adsorbed onto a small patch of the surface of a catalyst. its known that the…

an oxygen (o₂) molecule is adsorbed onto a small patch of the surface of a catalyst. its known that the molecule is adsorbed on 1 of 576 possible sites for adsorption (see sketch at right). calculate the entropy of this system. round your answer to 3 significant digits, and be sure it has the correct unit symbol.

an oxygen (o₂) molecule is adsorbed onto a small patch of the surface of a catalyst. its known that the molecule is adsorbed on 1 of 576 possible sites for adsorption (see sketch at right). calculate the entropy of this system. round your answer to 3 significant digits, and be sure it has the correct unit symbol.

Answer

Explanation:

Step1: Recall the entropy formula

The entropy formula for a system with $W$ micro - states is $S = k\ln W$, where $k$ is the Boltzmann constant ($k=1.38\times 10^{- 23}\text{ J/K}$) and $W$ is the number of micro - states. Here, the number of possible adsorption sites $W = 576$.

Step2: Calculate the entropy

Substitute $W = 576$ into the entropy formula: [ \begin{align*} S&=k\ln W\ &=(1.38\times 10^{-23}\text{ J/K})\ln(576)\ &=(1.38\times 10^{-23}\text{ J/K})\times6.357\ &=8.77\times 10^{-23}\text{ J/K} \end{align*} ]

Answer:

$8.77\times 10^{-23}\text{ J/K}$