How does lowering the volume of a mixture speed up a chemical reaction?

Decreasing volume increases the probability factors for gas phase reactants to react and increases speed of reaction. (Postulates of KM Theory)  

Explanation:

There are 4 probablility reaction factors...

concentration

effective collisions

nature

temperature

Concentration => effective reactive concentrations means that the reactants are able to find one another. Decreasing volume increases the concentration of the reactants and the probability of reactants finding one another.

Effective Collisions => Reaction occurs when reactants are in specific orientations upon collision so that bonding of the elements can occur. Decreasing volume increases collision frequency which increases the probability of reactants interacting and bonding in the proper orientations.

Nature => Naturally reactive reactants must be in reaction environment. This is independent of volume of reaction chamber, but it is an obvious requirement for reactions to occur.

Temperature => Certainly increasing temperature increases the collision frequency and  probability of reaction. If temperature is increased at the same time as volume is decreased, the probability of reaction increases exponentially.