What property of matter determines the electrical conductivity of a substance?

"Valence" electrons or the free electrons

Explanation:

Electrical conductivity can be defined as the property of the substance to conduct electricity, heat etc through it. This conductivity is caused due to the migration of particles which are electrically charged within the atomic lattice of the substance.

The outermost electrons or the electrons in valence shell are the main cause behind the conductivity property exhibited by any substance. Higher the number of electrons in outer shell, higher the conductivity.

Since these electrons are in the outermost shell, they can move easily. Under an impact of applied heat, charge these electrons migrate through the atomic lattice and thus conducts electricity, heat as the case may be.