Gibbs Free Energy of Formation: 1°C or 25°C? (And other exciting questions.)

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Using the equation ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction requires careful consideration of the temperature at which ΔG° is determined. It is crucial to use ΔG° calculated at the same temperature as the reaction, as different temperatures yield different equilibrium constants (Q). For example, if the reaction occurs at 50°C, the corresponding ΔG° should also be derived for that temperature, rather than using values from 1°C or 25°C. If ΔG° values at the desired temperature are unavailable, linear interpolation between known values can be a rough approximation, but more accurate results can be obtained using the van't Hoff or Gibbs-Helmholtz equations. Additionally, ΔG°' (with a prime) typically refers to standard conditions for biochemical reactions, which may differ from standard thermodynamic conditions. Understanding these distinctions is essential for accurate thermodynamic calculations.
Danny.Boy
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Hi there:

When using ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction, does it matter if I use ΔG° calculated at 1°C or 25°C? Also, why are there two choices and when are they each applicable? Finally, I have also seen ΔG°' written (note the prime). What does this mean and how does it differ from ΔG° conceptually and numerically?

I realize that these are very basic questions, so if you want to point me towards some elementary reading material I understand.

Thanks in advance,
Danny.Boy
 
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Danny.Boy said:
When using ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction, does it matter if I use ΔG° calculated at 1°C or 25°C?

Yes, it matters. If you use Delta G at 1 deg C, then you will also have to use a corresponding T and then equilibrium constant will be that for this temperature. The same way using Delta G at 25 deg Celsius yields Q for this very temperature.
The change of Q with temperature can be calculated with the van't Hoff equation:
http://en.wikipedia.org/wiki/Van_'t_Hoff_equation
 
Thanks for your reply DrDru, but I'm afraid I don't really follow. Perhaps a concrete example would help me understand. For example, consider this reaction at 50ºC (i.e., 323.15K):

[A]+→[C]+[D]

Using ΔG=ΔG°+RT ln Q, I get something like this:

ΔG=ΔG°+R×323.15×ln (([C][D])/([A]))

but what is the value of ΔG° that I should use? The value at 1ºC or 25ºC?
 
Danny.Boy said:
but what is the value of ΔG° that I should use? The value at 1ºC or 25ºC?
Neither of the two but the value at 50 deg. Celsius.
If you have both the values at 1 and at 50 degrees, you could linearly interpolate as a first approximation.
But, as I said, it would be more exact to calculate the value of Delta G0 at 50 degs from the van't Hoff or Gibbs-Helmholtz equation, see:
http://en.wikipedia.org/wiki/Gibbs-Helmholtz_equation

E.g. ##T_1=1^\circ##C, ##T_2=25^\circ##C and ##T_3=50^\circ##C,
then
##\Delta G^0(T_1)/T_1-\Delta G^0(T_2)/T_2=\Delta H ^0(1/T_1-1/T_2)##.
Solve this for ##\Delta H^0## and then solve
##\Delta G^0(T_1)/T_1-\Delta G^0(T_3)/T_3=\Delta H ^0(1/T_1-1/T_3)##
for ##\Delta G^0(T_3)##.
 
Aha! Makes sense. Thanks for explaining that.
 
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