Firstly lets establish what argillite is and then we can see what information we can obtain to determine what the Mohs is. Argillite is a metamorphic rock (not sedimentary), and is an intermediate between shale and slate. Texturally, argillite does not possess true "slaty" cleavage.
So, as sediment compacts over the years, the action of burial increases the pressure and the temperature and the minerals that compose the rock must alter (metamorphose) to reach an equilibrium with its new environment. It does this by changing from a shale to an argillite (and if you increase the P-T setting even further, it'll change from an argillite to a slate). Because argillite is a rock, and is therefore compositionally heterogeneous in its mineral assemblage, it does not have a defined hardness on the Mohs scale. Minerals are designated hardness values, not rocks.
So, as sediment compacts over the years, the action of burial increases the pressure and the temperature and the minerals that compose the rock must alter (metamorphose) to reach an equilibrium with its new environment. It does this by changing from a shale to an argillite (and if you increase the P-T setting even further, it'll change from an argillite to a slate). Because argillite is a rock, and is therefore compositionally heterogeneous in its mineral assemblage, it does not have a defined hardness on the Mohs scale. Minerals are designated hardness values, not rocks.
