Last updated on January 16th, 2022 at 10:59 am

**Enthalpy of**_{ }a system may be defined as **the sum of the internal energy****(U)**** and the product of its pressure****(p)**** and volume****(v)****.**

It is denoted by the symbol H and is given by: **H = U + pV**

**Getting the Heat Transfer equation** (derivation)

Change in the internal energy of a system is:

Δ*U*= *q *+ *w *= *q –* *P*Δ*V* *where q *has a positive sign if the system gains heat and a negative sign if the system loses heat.

*Rearranging the equation to solve for q *gives the amount of heat transfer:

** q= ΔU+ PΔV** ……………. (1)

*Let*’s look at two ways in which a chemical reaction might be carried out.

**change in internal energy is equal to the heat absorbed or evolved at constant volume &** **constant temperature**

**change in internal energy is equal to the heat absorbed or evolved at constant volume &**

**constant temperature**

A) A reaction might be carried out in a closed container with a constant volume so that Δ*V *= 0.

In such a case, no *PV *work can be done so the energy change in the system is due entirely to heat transfer. We indicate this heat transfer at constant volume by the symbol *q*_{v}.

So from equation (1) above, we get ** q_{v} = ΔU [At constant volume; ΔV = 0]** ……………….(2)

**The change in internal energy is equal to the heat absorbed or evolved at constant volume and****constant temperature.**

**heat of reaction, **or **enthalpy change (**𝚫**H****)** | Enthalpy equation

**H**

B) Alternatively, a reaction might be carried out in an open flask or other apparatus that keeps the pressure constant and allows the volume of the system to change freely.

In such a case, ΔV is non-zero and the energy change in the system is due to both heat transfer and *PV *work.

We indicate the heat transfer at constant pressure by the symbol *q*_{p}:

** q_{p} = ΔU + PΔV [At constant pressure]** …………. (3)

Because reactions carried out at constant pressure in open containers are so common in chemistry, the heat change *q*_{p} for such a process at constant pressure is given a special symbol and is called the **heat of reaction, **or **enthalpy change (**𝚫**H****).**

**Δ H= ΔU + PΔV [At constant pressure] ……………… (4)**

*Definition: the heat change q _{p} at constant pressure is given a special symbol and is called the heat of reaction, or enthalpy change (𝚫H) *

*The enthalpy (H) of a system is the name given to the quantity U + PV.*

[ Also Read: Thermodynamics Notes (Chemistry)]

**Relationship between **Δ**H and **Δ**U**

**Relationship between**

The relationship* between *Δ

**H and**Δ

**U**can be presented by the following equations.

*Δ*H = ΔU +

*p*ΔV…………..(i)

*where*ΔU is the change in internal energy and ΔV is the change in volume of the system

This relationship* between *Δ

**H and**Δ

**U**can be presented by the following equation as well:

*q*

_{p}=

*q*

_{v}+ PΔV ……………… (ii)

**enthalpy change is a measure of heat** **change (evolved or absorbed) taking place** **during a process at constant pressure**

**enthalpy change is a measure of heat**

**change (evolved or absorbed) taking place**

**during a process at constant pressure**

Now, enthalpy is defined as

H = U + *p*V ……….(1)

Change in enthalpy, ΔH may be expressed as

ΔH = ΔU + Δ(*p*V)

ΔH = ΔU + *p*ΔV + VΔ*p*

If the process is carried out at constant pressure,

*i.e., *Δ*p *= 0, then

ΔH = ΔU + *p*ΔV …….. (2)

Now, ΔU = *q *+ *w*

If work done during the change is only expansion work,

*w *= −*p*ΔV so that

ΔU = *q *− *p*ΔV ……..(3)

ΔH = ΔU + *p*ΔV = *q *− *p*ΔV + *p*ΔV = q

∴ ΔH = *q _{p} *(at constant pressure)

where *q _{p} *indicates that heat change has taken place at constant pressure.

Thus, **enthalpy change is a measure of heat****change (evolved or absorbed) taking place****during a process at constant pressure.**

## Enthalpy – important points

- If
*q*is the amount of heat absorbed by the system then:**q****(at constant volume) =**Δ**U****q****(at constant pressure) =**Δ**H**

- Note that only the enthalpy
*change*during a reaction is important.

- As with internal energy, enthalpy is a state function whose value depends only on the current state of the system, not on the path taken to arrive at that state. Thus, we don’t need to know the exact value of the system’s enthalpy before and after a reaction. We need to know only the difference between final and initial states:

- Δ
*H*=*H*_{final}–*H*_{initial}=*H*_{products}–*H*_{reactants}

- Enthalpy is also called
**heat content.**Since H depends upon three state functions U, p,

[ Also Read: Thermodynamics Notes (Chemistry)]