What are the primary factors that determine whether a volcano erupts explosively or relitivly quietly.

Chemical composition,temperature, viscosity
different chemicals in an erupting volcano's magma affects the temperature, which in turn affects the viscosity, which affects the eruption itself
for example, less silica content in the magma means lower temperature which means the lava cools down faster and hardens faster, which means the viscosity increases, which in turn results in  relatively quiet explosion.

Processes above and be sure to mention the movement of electrons and energy as the carbon atom moves from one reaction to another.