The free energy for the oxidation of glucose to co2 and water is -686 kcal/mol, and the free energy for the reduction of nad+ to nadh is +53 kcal/mol. why are only two molecules of nadh formed during glycolysis when it appears that as many as a dozen could be formed?

Most of free energy available from oxidation of the glucose remains in pyruvate.

Explanation:

The overall reaction of the process glycolysis is:

Glucose + 2 NAD⁺ + 2 ADP + 2 Pi ⇒ 2 Pyruvate + 2 NADH + 2 H⁺ + 2ATP

Glucose is oxidized to give 2 molecules of pyruvate and 2 molecules of NADH and ATP (Energy currency).

Though the free energy of oxidation of glucose is high but only 2 NADH is formed because the most of the free energy that is being released from the oxidation of glucose remains in the pyruvate which is produced in the reaction and thus only 2 molecules are formed.

a polar bond is formed when electrons are shared unevenly between atoms