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K(p) for the reaction MgCO(3((s))) to M...

`K_(p)` for the reaction `MgCO_(3_((s))) to MgO_((s)) + CO _(2_((g))) " is " 9 xx 10^(-10)`. Calculate `Delta G^(@)` for the reaction at `25^(@)C`.

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Verified by Experts

The correct Answer is:
`Delta G^(@) = 51.653 kJ mol^(-1)`
Given : `K_(p) = 9 xx 10^(-10)`
Temperature `= T = 273 + 25 =298 K `
`Delta G^(@) = ? `
`Delta G^(@) =- 2 .303 RT log_(10) K_(p)`
`=-2.303 x 8.314 xx 298 xx log_(10) 9 xx 10^(-10)`
`=- 2.303 xx 8. 314 xx 298 xx [bar(10).9542]`
`=- 2.303 xx 8.314 xx 298 xx [ - 9.0458]`
`= 51683 J mol^(-1)`
`=51. 683 kJ mol^(-1)`
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