Question

What is the relation between $H$ and $U$?

Answer 1

We need to know that in chemistry thermodynamics is one of the important topics for monitoring the reaction. In thermodynamics, the word meaning is thermos means heat and dynamic means flow. In thermodynamics we study the flow of the heat in the chemical reaction. In this topic we focus on three main things. There are systems, surroundings and boundaries. We consider our reaction system and environment to be surrounding and in between the junction is the boundary.

Complete answer:
In thermodynamics, enthalpy is an important term. The enthalpy depends on the physical nature of the reactant. The unit and sign of the enthalpy is very important for chemical reactions. If the sign of enthalpy is negative, the reaction is exothermic. The sign of enthalpy is positive, the reaction is endothermic. If the chemical reaction is reversed, we will find out by using signs of enthalpy.
The enthalpy of the system depends on the internal energy, pressure and volume of the system.
The symbol of enthalpy is $H$.
The symbol of volume is $V$.
The symbol of pressure is $P$.
The symbol of internal energy is $U$.
The enthalpy formula is
$H = U + PV$
Here, we consider ${U_i}$ and ${U_f}$ are the initial and final internal energy of the system.
The initial and final volume of the system are ${V_i}$ and ${V_f}$.
The initial and final enthalpy of the system are ${H_i}$ and ${H_f}$.
The enthalpy for the initial stage of the system is given below,
${H_i} = {U_i} + P{V_i}$
The enthalpy for the final stage of the system is given below,
${H_f} = {U_f} + P{V_f}$
Subtracting the enthalpy equation of initial and final of the system.
${H_f} - {H_i} = ({U_f} + P{V_f}) - ({U_i} + P{V_i})$
${H_f} - {H_i} = ({U_f} - {U_i}) + (P{V_f} - P{V_i})$
${H_f} - {H_i} = ({U_f} - {U_i}) + P({V_f} - {V_i})$
$\Delta H = \Delta U + P\Delta V$
$\Delta H = {H_f} - {H_i}$
$\Delta V = {V_f} - {V_i}$
$\Delta U = {U_f} - {U_i}$
Here, $\Delta V$ is the change in the volume of the system in the chemical reaction.
The change in the internal energy of the system in the chemical reaction is $\Delta U$.
The change in the enthalpy of the system in the chemical reaction is $\Delta H$.
According to the above discussion, we conclude that the relation between $H$ and $U$ is$\Delta H = \Delta U + P\Delta V$.

Note:
As we know that the redox reaction is one of the types of the type of the type of chemical reaction. In this reaction reduction followed by oxidation in the reactants. The oxidation means the addition of oxygen or the removal of hydrogen or loss of electrons. The reduction means the addition of hydrogen or the removal of oxygen or the gain of electrons. The abbreviation of emf is electromotive force.