A reaction from unknown reactants `(R): R to P` is spontaneous at `37^(@)C` and goes to completion. If the molar entropy of the products (P) is measured to be 460 J/mol K, and 71.3 kJ of heat was given off in the process to the surroundings when I mol reacted, then the molar entropy of the reactants has to be

Options

A. at least-230 J/mol K
B. at the most 690 J/mol.K
C. at the most 230 J/mol K
D. at least 690 J/mol K

Explanation

Let us solve this at boundary condition of `Delta G ^(@) = 0`
`Delta S ^(@) = ( Delta H ^(@))/( T ) = ( - 71 . 3 xx 1000)/( 310) =- 230 JK ^(-1) implies - 230 JK ^(-1) = S _(m ) ^(@) (p) - S _(m) ^(@) (R) = 460 JK ^(-1) - S _(m) ^(@) (R)`
`implies S _(m) ^(@) (R) = 690 JK ^(-1). ` It is the maximum value of entropy which the reactant can have If ` S _(m) ^(@) gt 690 JK ^(-1) mol ^(-1) , Delta G ^(@) gt 0.`