Final answer:
Sodium is the mineral that most significantly influences the extracellular fluid osmolarity and the concentration of particular matter in the blood, as it is the primary determinant of the osmotic pressure gradient across cell membranes.
Step-by-step explanation:
The mineral that has the most influence on the concentration of particular matter in blood and the extracellular fluid osmolarity is sodium. Sodium is the major extracellular cation and is responsible for one-half of the osmotic pressure gradient between the interiors of cells and their surrounding environments. Sodium, along with chloride, helps to regulate the distribution and retention of body water, thus affecting bodily functions such as blood pressure and hydration levels. While other minerals like potassium, calcium, phosphorus, magnesium, and chloride play significant roles in the body, sodium's role in osmoregulation is crucial for maintaining the balance of fluids within and around cells.