reaction rate
Two completely separate questions hang over any reaction: will it happen, and how fast? Gibbs free energy answers the first; reaction rate answers the second. The rate is simply how quickly reactants are turning into products — measured as how much concentration changes per second. Some favorable reactions are over in a flash; others, equally favorable, crawl along for years. Rust forming, iron eventually fully oxidizing, is a downhill reaction that nonetheless takes a lifetime.
What sets the speed is the activation energy — the height of the energy hill the reactants must climb over before they can become products. Even a downhill reaction starts with an uphill stretch: bonds must stretch and partly break, electrons must rearrange, and only molecules with enough energy to crest that hill react. So a tall barrier means a slow reaction; a low barrier means a fast one. Two levers shift the rate dramatically: raising the temperature gives more molecules enough energy to clear the hill, and a catalyst carves a lower path over (or around) it. Concentration matters too — more crowded reactants collide more often.
Keeping rate and equilibrium separate is one of the most important habits in organic chemistry, and it has a name: kinetics (rate) versus thermodynamics (the final balance). The fastest-forming product is not always the most stable one. Under mild, quick conditions a reaction may give the product that forms fastest (kinetic control); given heat and time, it may settle into the most stable product (thermodynamic control). Many real outcomes — which alkene forms, which enolate, which addition product — turn on exactly this tug between speed and stability.
A roughly 10 degree C rise in temperature often doubles a reaction's rate, because more molecules now carry enough energy to clear the activation barrier.
Rate is set by the activation barrier, not by delta G; raise the temperature or add a catalyst to speed it up.
Fast and favorable are independent. Rate (kinetics) is about the height of the barrier; equilibrium (thermodynamics) is about the depth of the final valley. A reaction can be fast but unfavorable, or favorable but glacially slow — never assume one from the other.