What is the difference between \(\Delta H\) and \(\Delta E ?\)

ΔH, also known as the change in enthalpy, represents the heat absorbed or released during a chemical reaction at constant pressure. It is an extensive property and depends on the number of substances involved in the reaction. Enthalpy is the measure of the total energy of a thermodynamic system, including internal energy, pressure, and volume. When a reaction takes place at constant pressure, the difference in enthalpy of the products and reactants signifies the amount of heat absorbed or released by the reaction.

ΔE, also known as the change in internal energy, represents the difference in the total internal energy of the system before and after the reaction. Internal energy is a sum of the potential and kinetic energies of the molecules in the system. The change in internal energy of the system (ΔE) is determined by the heat added to or removed from the system, and the work done on or by the system.

Both ΔH and ΔE are thermodynamic quantities used to describe the energy changes in a system, but they represent different aspects of the system's energy. The primary difference between ΔH and ΔE is that ΔH is specifically concerned with the heat changes at constant pressure, whereas ΔE is concerned with the total change in internal energy. The relationship between ΔH and ΔE can be described by the equation: \[\Delta H = \Delta E + P\Delta V\] Where P is the constant external pressure, and ΔV is the change in volume of the system. When a reaction occurs at constant pressure, if there is no significant change in volume, ΔH and ΔE values are almost the same. However, if there is a noticeable change in volume during the reaction, then the ΔH and ΔE values can be significantly different due to the work done on or by the system. In conclusion, ΔH represents the change in enthalpy (heat content) of a system at constant pressure, while ΔE represents the change in the total internal energy of the system. The difference between the two scales depends on the particular process taking place and the conditions under which it occurs.