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Standard Gibb's energy of reaction (Delt...

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 )S^(@)` at 320 K is :

A

155.18 J/mol-K

B

150.02 J/mol-K

C

172 J/mol-K

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
D
`Delta_(r )S=-16+underset(300)overset(320)intDelta_(r )C_(p)(dT)/(T)`
`Delta_(r)S=-16 +(44-29.4-2xx28.8)ln.(320)/(300)`
`Delta_(r)S=-16 +(-43)ln.(320)/(300)=-18.78`
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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 )H^(@) at 300 K for the reaction is :