spoiler AAMC FL 3 C/P question 41. need explanation on formulas

[I GET BUCKETS]

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the only formula I remember and understand for free energy is the following

so can someone please explain what is going on in these questions?

 

[Lawpy]

You should know the equation describing the relationship between Gibbs free energy and the equilibrium constant when solving equilibrium problems.

Gibbs free energy and equilibrium constants

The equation you listed is also important but it's used to determine if a given reaction is spontaneous based on the enthalpy and entropy seen. If a reaction is exothermic (so ΔH < 0) but has a positive entropy (ΔS > 0, for instance a solid reactant decomposes to create a gas product), ΔG will be negative and the reaction will be spontaneous in the forward direction, producing more products.

The ΔG = -RTln(K) connects between free energy for a reaction with the reaction's equilibrium constant, where K = [products]/[reactants]. A reaction with a large equilibrium constant (K > 1, so more products than reactants) will have a negative ΔG, which means the reaction is spontaneous in the forward direction, producing more products.

 

[I GET BUCKETS]

thanks for the explanation. Also, what about the equation in choice B what does free energy connect to?

 

[Lawpy]

thanks for the explanation. Also, what about the equation in choice B what does free energy connect to?

Nothing because the equations mistakenly replace the natural logarithm with an exponential function. If anything, the correct equation should be the following:

ΔG = -RTln(K) -->
-ΔG/RT = ln(K) -->
K = e^(-ΔG/RT)

Which is different from A or B. But the above equation form is similar to the Arrhenius equation k = Ae^(-Ea/RT) that describes the temperature dependence of rate constants for a chemical reaction (Arrhenius equation - Wikipedia)