Question

A chlorine Cl and bromine Br atom are adsorbed on a small patch of surface (see sketch at right). This patch is known to contain 100 possible adsorption sites. The Cl and bromine Br atoms have enough energy to move from site to site, so they could be on any two of them. Suppose the Br atom desorbs from the surface and drifts away. Calculate the change in entropy. Round your answer to 2 significant digits, and be sure it has the correct unit symbol.

Answer 1

Explanation:

It is given that possible number of ways the Cl and Br can be absorbed initially are 100.

S, possible number of ways by which Br can be desorbed is as follows.

                  $100 \times 99$

Now, we will calculate the change in entropy as follows.

               $\Delta S = k_{B} ln (\frac{W}{W_{o}})$

where,   $k_{B}$ = Boltzmann constant = $1.38 \times 10^{-23}$

             $\Delta S$ = change in entropy

Therefore, we will calculate the change in entropy as follows.

             $\Delta S = k_{B} ln (\frac{W}{W_{o}})$

                         = $1.38 \times 10^{-23} J/K \times ln (\frac{100}{100 \times 99})$

                        = $1.38 \times 10^{-23} J/K \times -4.595$

                        = $-6.34 \times 10^{-23} J/K$

Thus, we can conclude that the change in entropy is $-6.34 \times 10^{-23} J/K$.