The molar entropy content of `1 ` mole of oxygen `(O_(2))` gas at `300 K` and `1 atm` is `250 J mol e^(-1)K^(-1)`. Calculate `DeltaG` when 1 mole of oxygen is expanded reversibility and isothermally from `300K`, 1 atm to double its volume ( Take `R=8.314J mol e^(-1)K^(-1),log e=2.303)`

Options

A. 1.728 KJ `"mole"^(-1)K^(-1)`
B. 0
C. `-1.728 KJ "mole"^(-1)K^(-1)`
D. `0.75 KJ "mole"^(-1)K_(1)`

Answer

A

Explanation

`DeltaG=DeltaH - Delta(TS)`
`=DeltaH-TDeltaS " "`(isothermal)
`0=T DeltaS=-T(int (dq_("rev"))/(T))`
`-int dq_("rev")=- q_("rev")=W_("rev")`
as process is isothermal so `DeltaE=0=q_("rev")+ W_("rev")`
sp `" " DeltaG=- nRT "In" ((V_(f))/(V_(l))) =- RT "In" 2 k=- 8.314 xx300 xx0.693 xx 10^(-3) KJ mol^(-1) K^(-1)`
`=1.728 KJ mol^(-1) K^(-1)`