Entropy is the degree of randomness or disorder in any system. Solids are closely packed so they have lower entropy than liquids which in turn have lower entropy than gases. Gases have the highest degree of disorder or randomness. So when we look at a chemical reaction, the side with greater number of moles of gaseous compounds will have greater entropy.
a. [tex]C(s)+CO_{2}(g)-->2CO(g)[/tex]: In this reaction, the number of moles of gaseous products (2 mol) is greater than the number of moles of gaseous reactants (1 mol). Therefore, this reaction proceeds with an increase in entropy.
b.[tex]3Fe(s)+2O_{2}(g)-->Fe_{3}O_{4}(s)[/tex]: In this reaction, the number of moles of gaseous products ( no gases on product side) is less than the number of moles of gaseous reactants (2 mol). This proceeds with a decrease in entropy.
c.[tex]3O_{2}(g)+2KCl(s)-->2KClO_{3}(s)[/tex]: In this reaction, the number of moles of gaseous products ( no gases on product side) is less than the number of moles of gaseous reactants (3 mol). This proceeds with a decrease in entropy.
d.[tex]NH_{3}(g)+HCl(g)-->NH_{4}Cl(s)[/tex]:In this reaction, the number of moles of gaseous products ( no gases on product side) is less than the number of moles of gaseous reactants (2 mol). This proceeds with a decrease in entropy.
Therefore the correct answer is: a. [tex]C(s)+CO_{2}(g)-->2CO(g)[/tex]
