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Consider the reaction: 4NH(3)(g) +5O(2...

Consider the reaction:
`4NH_(3)(g) +5O_(2)(g) rarr 4NO(g) +6H_(2)O(l) DeltaG^(Theta) =- 1010.5 kJ`
Calculate `Delta_(f)G^(Theta) [NO(g)] if Delta_(f)G^(Theta) (NH_(3)) = -16.6 kJ mol^(-1)` and `Delta_(f)G^(Theta) [H_(2)O(l)] =- 237.2 kJ mol^(-1)`.

Text Solution

Verified by Experts

For the reaction `4NH_(3)(g) + 5O_(2)(g) to 4NO(g) + 6H_(2)O(l) DeltaG^(@) = -1010.5 kJ mol^(-1)`
`DeltaG^(@) = 4 Delta_(f)G^(@)[NO(g)] + 6Delta_(f)G^(@)[H_(2)O(l)]`
` - { 4Delta_(f)G^(@) [NH_(3)(g)] + 5Delta_(f)G^(@)[O_(2)(g)]}`
`therefore G^(@) = -1010.5 kJ mol^(-1)`
`Delta_(f)G^(@) [H_(2)O(l) ] = -237.2 kJ mol^(-1)`,
`Delta_(f)G^(@)[NH_(3)(g)] = -16.6 kJ mol^(-1)`
and `Delta_(f)G^(@)[O_(2)(g)] = 0` (convention)
`therefore -1010.5 = 4 Delta_(f)G^(@)[NO(g)]+ 6 xx (-237.2) - 4 xx (-16.6) - 5 xx 0`
`4Delta_(f)G^(@)[NO(g)] = -1010.5 + 1423.2 - 66.4 = 346.3 kJ mol^(-1)`
`Delta_(f)G^(@)[NO(g)] = 86.6 kJ mol^(-1)`.
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