[orgo814]

A question I have is "select the thermodynamic criterion for a spontaneous process in a closed constant pressure system immersed in a constant temperature bath"

For my choices d= delta
Choices= dU<0, dG<0, dA<0, dS>0


The answer is supposedly dG<0. I am confused because the fundamental equation (in terms of differentials for G is dG = VdP-SdT. So at constant T and P I expected dG = 0 not less.

The next question says the same problem and choices but with constant volume system immersed in constant T bath and the answer was dA<0. Same thing here- I expected from the fundamental equation for A that holding both V and T constant would mean A = O

[mjc123]

You are ignoring chemical change. dG = VdP - SdT + Σμ_idn_i

[orgo814]

Chemical change is equal to (dG/dN)T,P. How does this make it negative? Also how does this I explain the helmholtz energy for the second part of my question since we don't have chemical potential in that equation

[mjc123]

dn is negative for reactants, positive for products.
There may be some confusion here. Chemical potential is defined as μ₁ = (dG/dn₁)_{n2, n3...} i.e. adding matter to the system.
For chemical reaction in a closed system dG = μ₁dn₁ + μ₂dn₂ ...
where Σn_i is constant - or if not quite constant, depending on the reaction stoichiometry, no matter is being added or removed. The point is that "dn is negative for reactants, positive for products", so negative dG is possible.

[orgo814]

So we just assume we are working with reactants here..

What about the last part of my questions in regards to dA being negative at constant V and T

[orgo814]

Any input?