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Which quantity out of Delta(r)G or Delta...

Which quantity out of `Delta_(r)G` or `Delta_(r)G^(@)` will be zero at equilibrium?

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`Delta_(r)G= Delta_(r)G^(@) + RT ln K`. When reaction attains equilibrium `Delta_(r) G=0` so that`Delta_(r)G^(@)=- RT` ln K . Thus `Delta_(r)G^(@) =0` only when `K+1` . For all other values of `K, Delta_(r)G^(@) ` will be non-zero.
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(a) A sample of 1.0 mol of a monoatomic ideal gas is taken through a cyclic process of expansion and compression as shown in figure. What will be the value of DeltaH for the cycle as a whole? (b) Which quantity out of Delta_(r)G and Delta_(r)G^(Theta) will be zero at equilibrium?

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Standard Gibb's energy of reaction (Delta_(r )G^(@)) at a certain temperature can be computed Delta_(r )G^(@)=Delta_(r)H^(@)-T.Delta_(r )S^(@) and the change in the value of Delta_(r)H^(@) and Delta_(r)S^(@) for a reaction with temperature can be computed as follows : Delta_(r )H_(T_(2))^(@)-Delta_(r )H_(T_(1))^(@)=Delta_(r )C_(p)^(@)(T_(2)-T_(1)) Delta_(r )S_(T_(2))^(@)-Delta_(r )S_(T_(1))^(@)=Delta_(r )C_(p)^(@)ln.(T_(2)/T_(1)) " "Delta_(r )G^(@)=Delta_(r)H^(@)-T.Delta_(r)S^(@) and " by "Delta_(r )G^(@)=-"RT " ln K_(eq) . Consider the following reaction : CO(g)+2H_(2)(g)iffCH_(3)OH(g) Given : Delta_(f)H^(@)(CH_(3)OH,g)=-201 " kJ"//"mol", " "Delta_(f)H^(@)(CO,g)=-114" kJ"//"mol" S^(@)(CH_(3)OH,g)=240" J"//"K-mol, "S^(@)(H_(2),g)=29" JK"^(-1)" mol"^(-1) S^(@)(CO,g)=198 " J"//"mol-K, "C_(p,m)^(@)(H_(2))=28.8 " J"//"mol-K" C_(p,m)^(@)(CO)=29.4 " J"//"mol-K, "C_(p,m)^(@)(CH_(3)OH)=44 " J"//"mol-K" and " "ln ((320)/(300))=0.06 , all data at 300 K Delta_(r )G^(@) at 320 K is :

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