Question

The direct conversion of A to B is difficult. Hence it is carried out by following shown path $A \to C \to D \to B$
Given that $\Delta {S_{(A \to C)}} = 50eu$, $\Delta {S_{(C \to D)}} = 30eu$,$\Delta {S_{(D \to B)}} = - 20eu$ where eu is entropy unit
Then $\Delta {S_{(A \to B)}}$ is ________?

Answer 1

Hint: The above question is based on entropy of reaction. The concept of entropy provides us with deep insight into the direction of spontaneous change for many everyday phenomena.

Complete step by step answer:
Entropy is one of the fundamental concepts of science, with far-reaching consequences ranging from cosmology to chemistry. Entropy tells us about how the extent and direction of the spreading and sharing of energy can be related to thermodynamic properties of substances i.e. of reactants and products.
Entropy is a measure of the degree of spreading of thermal energy within a given system. This “spreading” can be spreading of the thermal energy from a compact space into a larger space or its sharing amongst previously inaccessible microstates of the given system.
Some examples of system and process and it's source of entropy increase of system are as follows:
- Two identical copper blocks , one at 20$^oC$ and the other at 40$^oC$ , are placed in contact with each other then the cooler block contains more unoccupied microstates, so heat flows from the warmer copper block until equal numbers of microstates are evenly populated in both blocks.
- Equal volumes of two different gases are allowed to mix with each other then the effect is the same as allowing each gas to expand to twice of each of their volume. The thermal energy of each gas is now spread over a larger volume.
Entropy is an extensive quantity which states that it is proportional to the quantity of matter in a system. Thus 100 g of copper has twice the entropy of 50 g copper at a constant temperature. This makes sense because the larger piece of copper contains double the number of energy levels which are able to contain more thermal energy.
Since, entropy is an extensive property. Also, the formula for change in entropy for a given reaction is the entropy of the product subtracted by the entropy of the reactant.
With reference to the above discussion, we may write that:
$\begin{align}
& \Delta {S_{(A \to B)}} = \Delta {S_{(A \to C)}} + \Delta {S_{(C \to D)}} + \Delta {S_{(D \to B)}} \\
& {\text{= 30 + 50 - 20 = 60 eu}} \\
\end{align} $


Note: Remember that entropy is a measure of a system’s thermal energy per unit temperature which is unavailable for doing work because work is obtained from ordered molecular motion. Therefore, the entropy is also a measure of the molecular disorder or randomness of a given system.