Is there any equation out there that links the change in enthalpy (H) to the change in cell potential/voltage (E)?

Yes, but the relationship involves the Gibbs Free Energy, which is G = H - TS, snd S is the entropy change. The change in G is approximatly the change in H in most cells.

See http://www.tannerm.com/relation.htm

To understand the relationship between the change in enthalpy (H) and the change in cell potential/voltage (E), it is important to consider the Gibbs free energy (G) in the context of electrochemical reactions.

The Gibbs free energy (G) is a thermodynamic property that measures the maximum amount of useful work that can be extracted from a system at constant temperature and pressure. It is related to enthalpy (H) and entropy (S) through the equation:

G = H - TS

Where:
- G is the Gibbs free energy
- H is the enthalpy
- T is the temperature in Kelvin
- S is the entropy change

For electrochemical reactions and cells, we can use the following equation:

ΔG = -nFE

Where:
- ΔG is the change in Gibbs free energy
- n is the number of moles of electrons transferred in the reaction
- F is the Faraday constant (approximately 96,485 C/mol)
- E is the cell potential or voltage

This equation relates the change in Gibbs free energy to the cell potential or voltage. However, it does not directly link to the change in enthalpy (H). Instead, it quantifies the maximum amount of work that can be obtained from the conversion of chemical energy to electrical energy within the cell.

Therefore, it is not straightforward to directly equate the change in enthalpy (H) with the change in cell potential/voltage (E). However, in most cases, the change in Gibbs free energy (ΔG) is approximately equal to the change in enthalpy (ΔH) for cells operating under standard conditions.