Question

The entropy values (in J/Kmol) of hydrogen gas are 130.6, chlorine gas is 223.0 and hydrochloric gas is 186.7 at 298 K and 1 atm pressure. Then entropy changes for the reaction:
\[{{\rm{H}}_{\rm{2}}}\left( {\rm{g}} \right){\rm{ + C}}{{\rm{l}}_{\rm{2}}}\left( {\rm{g}} \right) \to {\rm{2HCl}}\left( {\rm{g}} \right)\] is:
A. +540.3
B. +727.3
C. -166.9
D. +19.8

Answer 1

Hint: Entropy is the measure of the extent of disorderness in a state of a thermodynamic system. It demonstrates the anomaly or absence of uniformness in the structure of a thermodynamic system.

Formula Used:
\[{\rm{\Delta }}{{\rm{S}}^{\rm{o}}}{\rm{ = }}\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{products}}} \right)} {\rm{ - }}\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{reactants}}} \right)} \]
 where \[{\rm{\Delta }}{{\rm{S}}^{\rm{o}}}\]= standard entropy
\[\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{products}}} \right)} \] = summation of entropies of products
\[\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{reactants}}} \right)} \] = summation of entropies of reactants

Complete Step by Step Solution:
Entropy change for a reaction can be calculated by subtracting the summation of entropies of reactants from the summation of entropies of products.
In this given reaction, temperature and pressure are 298 K and 1 atm respectively.
The entropy of one mole of a substance in the pure state at one atmospheric pressure and 298 K is called standard entropy and is denoted by \[{\rm{\Delta }}{{\rm{S}}^{\rm{o}}}\].
Given
\[{{\rm{S}}^{\rm{o}}}_{{\rm{(HCl)}}}\]=186.7 J/Kmol
\[{\rm{S}}_{\left( {{{\rm{H}}_{\rm{2}}}} \right)}^{\rm{o}}\]=130.6 J/Kmol
\[{\rm{S}}_{\left( {{\rm{C}}{{\rm{l}}_{\rm{2}}}} \right)}^{\rm{o}}\]=223 J/Kmol
Two moles of hydrochloric gas are produced.
For the given reaction,
\[\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{products}}} \right)} \]=2(186.7) J/Kmol=373.4 J/Kmol
One mole of hydrogen gas and chlorine gas is reacted.
\[\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{reactants}}} \right)} \]=(130.6+223) J/Kmol
=353.6 J/Kmol
Hence, the total entropy is given by
\[{\rm{\Delta }}{{\rm{S}}^{\rm{o}}}{\rm{ = }}\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{products}}} \right)} {\rm{ - }}\sum {{{\rm{S}}^{\rm{o}}}\left( {{\rm{reactants}}} \right)} \]
=(373.4-353.6) J/Kmol
=19.8 J/Kmol

So, option D is correct.

Additional Information: Entropy depicted by S is the degree of disorderness in a thermodynamic system. It simply indicates the abnormality or lack of an ordered structure in a thermodynamic system. It is an extensive property as the value of entropy or entropy change relies on the quantity of matter present in a thermodynamic system. Entropy is a state function as its value does not depend on the path by which the system has attained a specific state. It depends on only the initial and final state of the system.

Note: While attempting the question, the unit of entropy must be mentioned in each step of the calculation. The entropy of a reaction is given by the subtraction of the summation of entropies of reactants from the summation of entropies of products.