Exploring Free Energy Change: ΔG, ΔH, and ΔS

[MathewsMD]

If $ΔG_{sys} = ΔH_{sys} - TΔS_{sys}; ΔS_{sys} = \frac {-ΔH_{surr}}{T}$

Then, doesn't this expression just simplify to:

$ΔG_{sys} = ΔH_{sys} + ΔH_{surr}$ and isn't $ΔH_{sys} = -ΔH_{surr}$?

So then $ΔG = 0$...this does not seem correct...could anyone please clarify my mistake and the formal proof of free energy if it differs from the one I have shown?

Also, what is the explanation for why there is no free energy change during phase changes? I was merely told this without any explanation and one would be very helpful.

Finally, just a related question:

If you have 1 gram of ammonia and it dissolves in 50 grams of water to release 1000 J (just hypothetical). When calculating the temperature change of the water, using q = mcΔT, is m = 50g or 51g since the ammonia is now aqueous and inseparable from the water. Yet, it has slightly different properties now. I am unsure if it is treated just like a normal sample of water or not.

 

[Ygggdrasil]

ΔS_sys = -ΔH_surr/T only for reversible processes, and it is true that ΔG = 0 for any reversible process.

If the phase changes are occurring reversibly (e.g. melting at the melting point, boiling at the boiling point), then ΔG = 0 for the reason above.

For the last question, if you are really worried about an exact answer, you would also have to take into account that the heat capacity of the solution changes when you dissolve ammonia in it.

 

[Chestermiller]

ΔS_sys = -ΔH_surr/T only for reversible processes, and it is true that ΔG = 0 for any reversible process.

If the phase changes are occurring reversibly (e.g. melting at the melting point, boiling at the boiling point), then ΔG = 0 for the reason above.

For the last question, if you are really worried about an exact answer, you would also have to take into account that the heat capacity of the solution changes when you dissolve ammonia in it.

ΔG is not equal to zero for any arbitrary reversible process. For example, in the isothermal expansion of an ideal gas, ΔG=RTln(P₂/P₁).

 

[Ygggdrasil]

ΔG is not equal to zero for any arbitrary reversible process. For example, in the isothermal expansion of an ideal gas, ΔG=RTln(P₂/P₁).

You are right, I also should have specified any isobaric (constant pressure) reversible process. Chemists usually take the isobaric assumption for granted since most of our chemical reactions are performed at constant (atmospheric) pressure. Thanks for the correction.

 

[LudusRex]

I can provide some clarification and explanation for your questions.

Firstly, the expression $ΔG_{sys} = ΔH_{sys} - TΔS_{sys}$ is known as the Gibbs free energy equation, which relates the change in free energy of a system to its enthalpy change (ΔH) and entropy change (ΔS). This equation is valid for processes that occur at constant temperature and pressure. The expression you have shown, $ΔG_{sys} = ΔH_{sys} + ΔH_{surr}$, is not a correct simplification of the Gibbs free energy equation. This is because the enthalpy change of the system (ΔH_sys) and the surroundings (ΔH_surr) are not always equal in magnitude, and therefore cannot be simply added together.

To understand why there is no free energy change during phase changes, we need to look at the definition of free energy. Free energy (G) is a measure of the energy available to do work in a system. During a phase change, the energy is used to overcome intermolecular forces and change the arrangement of molecules, rather than doing any external work. Therefore, there is no change in free energy during a phase change. However, there is a change in enthalpy (ΔH) and entropy (ΔS) during a phase change.

In the case of your hypothetical scenario with ammonia dissolving in water, the total mass of the solution is still 50 grams (assuming no evaporation or other changes). Therefore, the mass of the water (50g) should be used in the calculation of temperature change, as the ammonia is now part of the solution and its properties have been incorporated into the overall properties of the solution. This is similar to how adding a solute to a solvent affects the properties of the solution as a whole, rather than treating them separately.

I hope this helps to clarify your questions about free energy change and its relation to enthalpy and entropy changes, as well as the absence of free energy change during phase changes. As scientists, it is important to carefully consider and understand the equations and principles we use in our research and experiments.