Final answer:
The characteristic of semi-permeable membranes that determines substance permeability is the size of its pores, which allows small molecules and solvents to pass while larger molecules are retained.
Step-by-step explanation:
The single characteristic of the semi-permeable membrane used in the lab that determines which substances can pass through is the size of its pores. Semi-permeable membranes allow only certain substances to pass through based on molecular size. For example, in dialysis tubing, small molecules and solvent can pass through the pores, whereas larger molecules like proteins and red blood cells are retained.
Membranes may also allow molecules to dissolve and diffuse across, depending on their chemical properties, which also plays a role in their semi-permeable nature.