Question

The entropy change for the evaporation of one mole of n-hexane at \[{\mathbf{341}}.{\mathbf{7}}{\text{ }}{\mathbf{K}}\] is
\[[\Delta {H_{vap}} = 29\;KJ\;mo{l^{ - 1}}]\]:
A.$ + 84.87{\text{J}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$
B.$ - 84.78{\text{J}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$
C.$ - 87.84{\text{J}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$
D.$ - 84.47{\text{J}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}$

Answer 1

Hint: To answer this question, you should recall the concept of entropy. The entropy of a system is defined as a measure of randomness or disorder of a system. We shall substitute the appropriate values in the formula given below.

Formula used: \[\;\Delta G = \Delta H - T\Delta S\] where \[\Delta G\] is free energy, \[\Delta H\] is enthalpy, \[\Delta S\] is entropy and \[T\] is temperature.

Complete step by step solution:
The entropy of a system is used to describe the behaviour of a system in terms of thermodynamic properties such as temperature, pressure, entropy, and heat capacity.
The system is at equilibrium condition this means that the free energy associated with the system will be zero
\[ \Rightarrow \Delta G = 0\].
We will get the formula of entropy as:
\[ \Rightarrow \Delta {S_{vap}} = \dfrac{{{H_{vap}}}}{T}\].
Substituting these values in the given formula we have:
\[\Delta {S_{vap}} = + \dfrac{{29000{\text{Jmo}}{{\text{l}}^{ - 1}}}}{{341.7{\text{K}}}}\].
Solving this
\[\Delta {S_{vap}} = + 84.87{\text{J}}{{\text{K}}^{{\text{ - 1}}}}{\text{mo}}{{\text{l}}^{{\text{ - 1}}}}\].

Hence, the correct answer to this question is option A.

Note: Properties of Entropy
A.It is a thermodynamic state function which means that it depends on the state of the system and not the path that is followed.
B.It is represented by the symbol \[S\] but in the standard state, it is represented by \[S^\circ \].
C.It’s SI unit is \[{\text{J/Kmol}}\]
D.It’s CGS unit is \[{\text{cal/Kmol}}\].
As it is a measure of disorderness the greater disorder will be seen in an isolated system, hence entropy also increases. A system at higher temperatures has greater randomness than a system at a lower temperature. From these examples, it is clear that entropy increases with a decrease in regularity. Negentropy is a reverse of entropy. It means things become more in order. By ‘order’ it means in organisation, structure and function. One example of negentropy is a star system such as a solar system.