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Show that the reaction CO(g) +(1//2)O(...

Show that the reaction
`CO(g) +(1//2)O_(2)(g) rarr CO_(2)(g)`
at `300K` is spontaneous and exothermic, when the standard entropy change is `-0.094 k J mol^(-1) K^(-1)`. The standard Gibbs free energies of formation for `CO_(2)`and `CO` are `-394.4`and `-137.2kJ mol^(-1)`, respectively.

Text Solution

Verified by Experts

`DeltaG^(@)` (for the reaction)
`=G_(f)&(@)("products") - G_(f)^(@) ("reactants ") = G_(f)^(@) (CO_2) - [G_(f)^(@)(CO) + 1/2G_(f)^(@) (O_2)]`
`= -394.4 -[-137.2 + 0] [ :' G_(f)^(@) (O_2) = 0] = 257.2 kJ`
Since, `DeltaG^(@)` for reaction is negative, so the reaction is spontaneous.
Also, `DeltaG^(@) = DeltaH^(@) - TDeltaS^@" or "-257.2 = DeltaH^(@) - (300 xx -0.094)`
`:. DeltaH^(@) = -285.4 kJ`
`DeltaH^(@)` is negative and thus reaction is exothermic.
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