Question regarding hydrophobic forces

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Hydrophobic forces are primarily driven by entropy, as non-polar molecules aggregate to minimize the clathrate structures formed by water. Increasing temperature strengthens these hydrophobic forces, but this raises a question regarding the Gibbs free energy equation, dG = dH - TdS. At equilibrium, dG equals zero, suggesting that an increase in temperature leads to a decrease in entropy, which seems contradictory to the idea that hydrophobic forces increase. However, it is noted that raising the temperature shifts the equilibrium position, meaning that the relationship between enthalpy and entropy changes, and the system is no longer in equilibrium. Ultimately, for a process to be spontaneous, the Gibbs free energy must be negative, indicating that increased temperature and entropy can enhance hydrophobic interactions.
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I've been reading a bit, and I thought I understood it, but now I'm really confused:

I know that hydrophobic forces at room temperature are almost entirely entropy driven: because a system aims for maximal entropy, it pushes non-polar molecules into an aggregate in order to reduce the clathrate structures that water must form.

I also know that if you increase the temperature, then the hydrophobic forces get stronger.

Here's the problem: dG = dH - TdS;
At equilibrium, dG = 0 so dH = TdS.
In other words, if I increase the temperature, the entropy decreases. This would mean that a decrease in entropy leads to an increase in hydrophobic forces. Isn't this contradictory? I mean, a decrease in entropy would mean more order = more clathrate structures, so shouldn't this result in a decrease in hydrophobic forces? What's wrong with my reasoning?
 
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Hi,

I am not an expert on thermodynamics but does the enthalpy not increase as well with temperature - the values you get from a table is at 298 K so ...

By just raising the temperature your system is no longer in equilibrium this might be an approximation for certain temperature ranges - the enthalpy is a function of the heatcapacity and temperature changes. At equilibrium you can than see if the entropy of your system has increased.
 
For an event to be spontaneous G has to be negative so if entropy is increased the TdS term becomes larger, likewise with temperature, so G is more negative.

As stated above, changing T shifts the eqm position so dH (at the old T) is no longer = to TdS (at the new T).
 
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