Question

The relationship between enthalpy and internal energy changes is
A. $\text{ }\\!\\!\Delta\\!\\!\text{ U = }\\!\\!\Delta\\!\\!\text{ H + P }\\!\\!\Delta\\!\\!\text{ V}$
B. $\text{ }\\!\\!\Delta\\!\\!\text{ H = }\\!\\!\Delta\\!\\!\text{ U + P }\\!\\!\Delta\\!\\!\text{ V}$
C. $\text{ }\\!\\!\Delta\\!\\!\text{ H = }\\!\\!\Delta\\!\\!\text{ U - P }\\!\\!\Delta\\!\\!\text{ V}$
D. $\text{P }\\!\\!\Delta\\!\\!\text{ V = }\\!\\!\Delta\\!\\!\text{ U + }\Delta \text{H}$

Answer 1

Hint: In thermodynamics enthalpy is used to refer to the total heat content of a system. Internal energy of a system is the energy contained within the system.

Complete step by step solution: Generally chemical reactions are carried out at constant pressure or atmospheric pressure. Let us consider one example to describe the relation between $\text{ }\\!\\!\Delta\\!\\!\text{ H}$ and $\text{ }\\!\\!\Delta\\!\\!\text{ U}$.
Suppose we are changing the state of any substance from solid to liquid at constant pressure then volume of that quantity will change.

The change is volume is represented by $\text{W=P (}{{\text{V}}_{\text{B}}}\text{-}{{\text{V}}_{\text{A}}}\text{)}$ where ${{\text{V}}_{\text{B}}}$ and ${{\text{V}}_{\text{A}}}$ are final volume and initial volume respectively and W represent total work done.
First law of thermodynamics states that $\text{ }\\!\\!\Delta\\!\\!\text{ E=Q-W}$, Q and W represents the energy of final state and initial state respectively.
Putting the value of W in the above equation we get H= E+PV, where E is same as U. E and U both are used to represents the eternal energy
Therefore, we can say that $\text{ }\\!\\!\Delta\\!\\!\text{ H}$ and $\text{ }\\!\\!\Delta\\!\\!\text{ U}$ are connected by the equation: $\text{ }\\!\\!\Delta\\!\\!\text{ H = }\\!\\!\Delta\\!\\!\text{ U + }\\!\\!\Delta\\!\\!\text{ ( PV )}$. Here we are taking constant pressure therefore, $\Delta \text{ ( PV)}$ changes into $\text{P }\\!\\!\Delta\\!\\!\text{ V}$. The above equation will become as: $\text{ }\\!\\!\Delta\\!\\!\text{ H = }\\!\\!\Delta\\!\\!\text{ U + P }\\!\\!\Delta\\!\\!\text{ V}$.

Therefore, option B is correct.
Additional Information:
At constant pressure when a substance changes enthalpy tells how much heat and work was added or removed from the substance.
In a chemical reaction when a substance becomes warmer or colder, it is a sign that heat is flowing to things around it or from things around it until its temperature is the same again.
The term internal energy is used to define the energy associated with the random, disordered motion of molecules.
Internal energy can be changed by changing the temperature or volume of the object without changing the amount of particles in the object.

Note: Students have the misconception that enthalpy and internal energy are the same. Internal energy is used to refer to the energy of molecular structure and molecular activity. On the other hand enthalpy is used to describe the internal energy and the product of pressure and volume of the system.