Question

What is a reaction with a negative `DeltaG` and occurs spontaneously?

Answer 1

What, an example? Because all reactions with `DeltaG < 0` are spontaneous by definition.

`"HCl"` reacting with `"Al"(s)` is quite spontaneous:

`2"Al"(s) + 6"HCl"(l) -> 2"AlCl"_3(aq) + 3"H"_2(g)`

As you form a gas and an aqueous solution from a solid and a concentrated aqueous solution, you increase the entropy of the system after the reaction (because gases move around much more than liquids and solids).

So, qualitatively, `color(green)(DeltaS_"rxn" > 0)`.

Furthermore, this reaction is known to release heat (you may or may not do it in lab someday), so `color(green)(DeltaH < 0)`, i.e. the reaction is exothermic.

Finally:

`DeltaG = DeltaH - TDeltaS`

So:

`DeltaG = (-) - T(+)`

But `color(green)(T > 0)` necessarily, by definition of it being in units of `"K"`. A negative minus any positive is another negative, so `bb(DeltaG < 0)` for this reaction at all temperatures.

Therefore, adding `HCl` to aluminum solid is spontaneous at at least room temperature.