TBR Chemistry, Chapter VIII, Passage IV, Question 28... Delta G stuff

[BBlocker]

The Delta H for a given reaction is 12.5 kJ/mole. The Delta S for the reaction is 25 j/mole K. At what temperature does the equilibrium constant equal 1.0?

A) 0C
B) 227C
C) 327C
D) 500C

Answer: B <---highlight to see

TBR Explanation: We use equation DeltaG = -RTlnKeq which shows us that Delta G = 0. Therefore, Delta G = DeltaH - TDeltaS; DeltaH = TDeltaS. Using this we solve for T. Simple enough, right?

My problem with this explanation: I thought the equation DeltaG = -RTlnKeq was used only for Delta G nod? Meaning Delta G calculated from starting 1M Products and Reactants, 1atm and 25 deg. C? In this case, using DeltaG nod = -RTlnKeq, we ONLY know that DeltaG nod = 0. This does not equate to DeltaG rxn = 0, right? Somehow TBR assumes this is the case. Since we now know that DeltaG nod = 0, we know DeltaGrxn = RTlnQ...... It's impossible to proceed from here to solve for Q....

Can anyone help clear up this confusion please?

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[Gauss44]

The Delta H for a given reaction is 12.5 kJ/mole. The Delta S for the reaction is 25 j/mole K. At what temperature does the equilibrium constant equal 1.0?

A) 0C
B) 227C
C) 327C
D) 500C

Answer: B <---highlight to see

TBR Explanation: We use equation DeltaG = -RTlnKeq which shows us that Delta G = 0. Therefore, Delta G = DeltaH - TDeltaS; DeltaH = TDeltaS. Using this we solve for T. Simple enough, right?

My problem with this explanation: I thought the equation DeltaG = -RTlnKeq was used only for Delta G nod? Meaning Delta G calculated from starting 1M Products and Reactants, 1atm and 25 deg. C? In this case, using DeltaG nod = -RTlnKeq, we ONLY know that DeltaG nod = 0. This does not equate to DeltaG rxn = 0, right? Somehow TBR assumes this is the case. Since we now know that DeltaG nod = 0, we know DeltaGrxn = RTlnQ...... It's impossible to proceed from here to solve for Q....

Can anyone help clear up this confusion please?

How I solved it:

Start with equation 3 from passage 4 (page 171): Delta G = Delta H - T*Delta S

rearrange to get, T + Delta G = Delta H / Delta S,

plug in zero for Delta G and you get, T = Delta H / Delta S,

plug in numbers, T = 12500/25,

solve for kelvins, T = 500 Kelvins

convert to C, T = 500 - 273 = 227 C

(Also note the relationship, Delta G = RTlnQ - RTlnK. When Delta G = 0, Q=K.)