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For the reaction at \[{{\rm{0}}^{\rm{0}}}{\rm{C}}\] and normal pressure:
A. \[{\rm{\Delta H > T\Delta S}}\]
B. \[{\rm{\Delta H = T\Delta S}}\]
C. \[{\rm{\Delta H = \Delta G}}\]
D. \[{\rm{\Delta H}}\]

Last updated date: 23rd Jul 2024
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Hint: Equilibrium may be defined as the state of a process in which the properties like temperature, pressure, and concentration of the system do not show any change with the passage of time.

Complete Step by Step Solution:
Enthalpy change (\[{\rm{\Delta H}}\]) is defined as the total heat content of the system at constant pressure.
Entropy is the extent of disorder of randomness in a system. Entropy change (\[{\rm{\Delta S}}\]) of a substance measures the disorder or randomness in a system.
Gibb’s free energy of a system may be defined as the maximum amount of energy available to a system that can be converted into useful work. In simple words, Gibb’s free energy is the capacity of a system to do useful work. It is denoted by the symbol ‘G’.
Gibb’s free energy equation gives the relationship between change in enthalpy, change in entropy and temperature. The relationship is as given below.
\[{\rm{\Delta G = \Delta H}} - {\rm{T\Delta S}}\]
where, \[{\rm{\Delta G}}\]= change in Gibb’s free energy
\[{\rm{\Delta H = }}\]change in enthalpy
\[{\rm{\Delta S = }}\]change in entropy
\[{\rm{T = }}\]temperature in Kelvin
The given reaction is as:
From the above reaction, it can be said that a state of equilibrium between the condensation of vapours and the evaporation of water has been established. Equilibrium involves two reactions proceeding in opposite directions One of these reactions proceeds from the reactants towards the products and is called a forward reaction. The other reaction proceeds from the products towards the reactants and is called a reverse reaction. There is no further change in the concentrations of the reactants or products when the equilibrium is attained.
Temperature, \[{\rm{T = }}{{\rm{0}}^{\rm{0}}}{\rm{C}}\]
Convert the given temperatures from degree Celsius to Kelvin by using the relationship, \[{\rm{K}}{{\rm{ = }}^{\rm{0}}}{\rm{C}} + 273\]as shown below.
So, the temperature will become as:
\[{\rm{T = }}{{\rm{0}}^{\rm{0}}}{\rm{C = (0 + 273)K = 273K}}\]
At equilibrium, the change in Gibb’s free energy (\[{\rm{\Delta G}}\]) is taken to be zero.
Putting \[{\rm{\Delta G = 0}}\]in the Gibb’s free energy equation we get,
\[\begin{array}{l}{\rm{\Delta G = \Delta H}} - {\rm{T\Delta S}}\\ \Rightarrow {\rm{0 = \Delta H}} - {\rm{T\Delta S}}\\ \Rightarrow {\rm{\Delta H}} = {\rm{T\Delta S}}\end{array}\]
Hence, the correct choice is found to be \[{\rm{\Delta H = T\Delta S}}\]
Therefore, option B is correct.

Note: Gibb’s energy concept is more useful than the entropy concept to know the feasibility of a process because \[{\rm{\Delta G}}\]refers to the system only while \[{\rm{\Delta S}}\]refers to both system and surroundings. Actually, the two opposing reactions, the forward reaction and the reverse reaction are known to proceed simultaneously at equal rates.