# Enthalpy of A System

####
**Enthalpy of A System**

**❒**In a process carried at constant volume (say in a sealed tube), the heat content of a system is the same as internal energy (E), as no PV work is done.

**❒**But in a constant-pressure process, the system (a gas) also expends energy in doing PV work. Therefore, the total heat content of a system at constant pressure is equivalent to the internal energy E plus the PV energy. This is called the Enthalpy (Greek en = in; thalpos = heat) of the system and is represented by the symbol H.

**❒**

**Enthalpy (H):**is the total heat content of a system at constant pressure is equivalent to the internal energy E plus the PV energy.

**❒**Thus enthalpy is defined by the equation:

H =
E + PV ...(1)

###
**Enthalpy – A Function of State **

In the equation (1) above, E, P, V are all state functions. Thus H,
the value of which depends on

**the values of E, P, V must also be a function of state. Hence its value is independent of the path by****which the state of the system is changed.**####
**Change in Enthalpy**

If ΔH be the difference of enthalpy of a system in the final state
(H

_{2}) and that in the initial state
(H

_{1}),
ΔH =
H

_{2}– H_{1}...(2)
Substituting the values of H2 and H1, as from (1) and (2), we have:

ΔH =
(E

_{2}+ P_{2}V_{2}) – (E_{1}+ P_{1}V_{1})
= (E

_{2}– E_{1}) + (P_{2}V_{2}– P_{1}V_{1})
= ΔE
+ ΔPV

If P is constant while the gas is expanding, we can write:

ΔH =
ΔE + PΔV

ΔH =
ΔE + w (w = work) ...(3)

According to the First Law,

ΔE =
q – w ...(4)

where
q = heat transferred

From equations (3) and (4):

ΔH =
q when change in state occurs at constant pressure

This relationship is usually written as:

ΔH =
q

_{p}
where subscript p means constant pressure.

Thus ΔH can be measured by measuring the heat of a process
occurring at constant pressure.

####
**Units and Sign Conventions of Enthalpy**

**❒**Since

ΔH =
H

_{2}– H_{1}
ΔH is positive if H

_{2}> H_{1}and the process or reaction will be endothermic.
ΔH is negative if H

_{1}> H_{2}and the reaction will be exothermic.**❒**In case of a chemical reaction carried in the laboratory in an open vessel:

ΔH =
H products – H reactants = q

_{p}**❒**The heat of reaction at one atmosphere pressure is usually shown along with the equation. Thus,

**❒**The quantity of heat 68.32 kcal on the right hand represents – ΔH of the reaction.

**❒**The units of ΔH are kilocalories (kcal) or kilojoules (kJ).

####
**Relation Between ΔH and ΔE**

**❒**Calorific values of many gaseous fuels are determined in constant volume calorimeters. These values are, therefore, given by the expression:

q

_{v}= ΔE**❒**When any fuel is burnt in the open atmosphere, additional energy of expansion, positive or negative, against the atmosphere is also involved. The value of q thus actually realised, i.e., q

_{p}= ΔH, may be different from the equation:

ΔH =
ΔE + PΔV ...(1)

**❒**If gases are involved in a reaction, they account for most of the volume change as the volumes

of solids and liquids are negligibly small in comparison.

**❒**Suppose we have n

_{1}moles of gases before reaction, and n

_{2}moles of gases after it. Assuming

ideal gas behaviour, we have:

P V

_{2}= n_{2}RT
P V

_{1}= n_{1}RT
∴ P (V

_{2}– V_{1}) = (n_{2}– n_{1}) RT
PΔV
= Δn RT

Substituting in equation (1) we have,

**ΔH = ΔE + Δn RT**

####
**Solved Problem**

**For the reaction:**

**Calculate ΔH for the reaction.**

**Solution:**

*Reference:**Essentials of Physical Chemistry /Arun Bahl, B.S Bahl and G.D. Tuli / multicolour edition.*

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