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

In summary, when using the equation ΔG=ΔG°+RT ln Q to calculate the energy yield of a reaction, it matters at which temperature you use ΔG°. The value of ΔG° should correspond to the temperature at which the reaction is taking place. This is because the equilibrium constant, Q, changes with temperature. To calculate the value of ΔG° at a specific temperature, you can use the van't Hoff or Gibbs-Helmholtz equation.
  • #1
Danny.Boy
5
0
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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  • #2
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
 
  • #3
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?
 
  • #4
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)##.
 
  • #5
Aha! Makes sense. Thanks for explaining that.
 

1. What is Gibbs Free Energy of Formation?

Gibbs Free Energy of Formation is a thermodynamic concept that measures the amount of energy required or released when a substance is formed from its constituent elements at a given temperature and pressure. It is denoted by the symbol ΔGf and is typically measured in units of joules (J) or kilojoules per mole (kJ/mol).

2. Why is the temperature specified as 1°C or 25°C?

The temperature of 1°C or 25°C is commonly used because it is close to standard conditions for most chemical reactions (i.e. 1 atmosphere of pressure and a temperature of 25°C). This allows for easier comparison of Gibbs Free Energy values between different reactions.

3. How is Gibbs Free Energy of Formation calculated?

The Gibbs Free Energy of Formation is calculated using the equation ΔGf = ΣΔGf,products - ΣΔGf,reactants, where ΣΔGf,products and ΣΔGf,reactants represent the sum of the Gibbs Free Energy values of the products and reactants, respectively.

4. What does a negative value of ΔGf indicate?

A negative value of ΔGf indicates that the formation of the substance is thermodynamically favorable, meaning that the reaction will proceed spontaneously in the forward direction.

5. How is Gibbs Free Energy of Formation used in chemistry?

Gibbs Free Energy of Formation is an important concept in chemistry as it helps to determine the feasibility and direction of a chemical reaction. It is also used to calculate the equilibrium constant of a reaction, which is a measure of the extent to which a reaction will proceed towards products.

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