Thermodynamics heat, enthalpy, Gibbs We know the basic Thermodynamic equations are:
$$ dU=-PdV+ TdS + \mu dN$$
$$ dH=dU+d(PV)= TdS+ \mu dN + VdP$$
we typically assume constant Pressure for a reaction carried out in air and neglect the dP term
$$dG=dH-d(TS)=  \mu dN - SdT+ VdP$$
once again we neglect the dT and dP terms
but for heat of reaction we use the enthalpy not just the TdS term. When we have a battery though the electrical energy is the Gibbs free energy with the heat of reaction being TdS and other energy losses also contributing to the heat. When the reaction is not separated (not an electrochemical cell) then the Gibbs is part of the heat.
For a typical reaction where the chemicals are in contact why do they use the enthalpy to determine the heat of the reaction produced?
When a reaction occurs at constant pressure and no work other than expansion work  (such as electrochemical) is performed, then it can be shown, from the definition of the enthalpy and the first law of thermodynamics applied to a closed system, that the change in enthalpy is equal to the heat:
$$\begin{align}dH&amp;=dU+d(pV)\\&amp;=dw_{pV}+dw_{other}+dq+pdV+Vdp\\&amp;=-p_{ext}dV+dw_{other}+dq+pdV+Vdp\\&amp;=dq+dw_{other} \end{align}$$
The last equality follows when the pressure is constant and equal to the external pressure. When only pV work is done then clearly heat and enthalpy change are equal. Readily measured heats of reaction provide a very convenient way to determine values of the enthalpy state function which can be tabulated and employed in further thermodynamic computations.