A spontaneous reaction in Chemistry is that which is proceeding in a particular direction without the intervention of any external effect. As a spontaneous reaction proceeds (which can be relatively slow), free energy ΔG, which is the available energy for work, is released.
Gibbs free energy, ΔG, is released during a spontaneous process and hence the ΔG is negative because the reactants have more free energy than the products, hence, no energy input is needed for the reaction to proceed forward but rather an energy output. This is what makes a negative ΔG depict a spontaneous reaction.
There's less space, causing the air particles to collide with the walls of the container more frequently. Pressure is that energy caused by molecules striking a surface. Thus, compacting air molecules leads to higher pressure.