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The following reaction is performed at 2...

The following reaction is performed at 298 K
`2NO(g)+O_(2)(g)hArr 2NO_(2)(g)`.
The standard free energy of formation of NO (g) is 86.6 kJ / mol at 298 K. What is the standard free energy of formation of `NO_(2)(g)` at 298 K ? `(K_(p)=1.6xx10^(12))`.

A

1. R (298) ln `(1.6xx10^(12))-86600`

B

`86600+R(298)ln (1.6xx10^(12))`

C

`86600-(ln(1.6xx10^(12)))/(R(298))`

D

`0.5[2xx86,600-R(298)ln(1.6xx10^(12))]`.

Text Solution

Verified by Experts

The correct Answer is:
D
`2NO(g)+O_(2)(g)hArr 2NO_(2)(g)`
`Delta G^(@)=Delta G_(f)^(@)` (products) `- Delta G_(f)^(@)` (reactants)
`=2[Delta G_(f)(NO)_(2)]-[2Delta G_(f)^(@)(NO)+Delta G_(f)^(@)(O_(2))]`
`=2Delta G_(f)^(@)(NO_(2))-2xx86.6xx10^(3)-0 " "` …(i)
`Delta G^(@)=-RT lnK_(p)`
`=-R(298)ln(1.6xx10^(12))" "` ....(ii)
From eqns. (i) and (ii)
`2Delta G_(f)^(@)(NO_(2))-2xx86600`
`=-R(298)ln (1.6xx10^(12))`
`2Delta G_(f)^(@)(NO_(2))=2xx86600-R(298)ln (1.6xx10^(12))`
`therefore Delta G_(f)^(@)(NO_(2))=0.5[2xx86600-R(298)ln (1.6xx10^(12))]`
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