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Calculate Delta(r)G^(Theta) for the foll...

Calculate `Delta_(r)G^(Theta)` for the following reactions using `Delta_(f)G^(Theta)` values and and predict which reactions are spontaneous.
a. `Ca(s) +CI_(2)(g) rarr CaCI_(2)(s)`
b. `H_(2)O(s) rarr Hg(l) +(1)/(2)O_(2)(g)`
c. `NH_(3)(g) +2O_(2)(g) rarr HNO_(3)(l) +H_(2)O(l)`
`Delta_(f)G^(Theta)` value `(kJ mol^(-1))` are:
`CaCI_(2)(s) =- 748.1, HgO(s) =- 58.84`
`NH_(3)(g) =- 16.45, HNO_(3)(l) = - 80.71`,
`H_(2)O(l) =- 237.13`

Text Solution

Verified by Experts

`Delta_(r)G^(@)` can be calculated from the relation :
`Delta_(r)G^(@) = Sigma Delta_(r)G^(@)("products") - SigmaDelta_(f)G^(@)("reactants")`
(a)`Ca(s) + CI_(2)(g) to CaCI_(2)(s)`
`Delta_(r)G^(@) = Delta_(f)G^(@)[CaCI_(2)(s)] - { Delta_(f)G^(@)[Ca(s)] + Delta_(f)G^(@)[CI_(2)(g)]}`
` = -748.1 - (0 + 0) = -748.1 kJ`.Reaction is spontaneous.
(b) `HgO(s) to Hg(l) + 1/2O_(2)(g)`
`Delta_(r)G^(@) = Delta_(f)G^(@)[Hg(l)] + 1/2Delta_(f)G^(@)[O_(2)(g)] - Delta_(f)G^(@)[HgO(s)]`
`= 0 + 0 - (-58.54) = 58.84 kJ`.Reaction is not spontaneous.
(c) `NH_(3)(g) + 2O_(2)(g) to HNO_(3)(l) + H_(2)O(l)`
`Delta_(r)G^(@) = Delta_(f)G^(@)[HNO_(3)(l)] + Delta_(f)G^(@)[H_(2)O(l)] - Delta_(f)G^(@)[NH_(3)(g)] + 2Delta_(f)G^(@)[O_(2)(g)]}`
` =-80.71 + (-237.13)- {-16.45 + 0}`
= - 80.71 - 237.13 + 16.45 = -301.39 kJ
Reaction is spontaneous.
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