Enthalpy - class-XII

Enthalpy : Chemical reactions are generally carried out at constant pressure (atmospheric pressure) and heat of reaction at constant pressure is called Enthalpy (H) as:
$H = U + PV$ (By definition).

 Net amount of energy given to athlete $= 1560 kJ$

Enthalpy: Chemical reactions are generally carried out at constant pressure (atmospheric pressure) so it has been found useful to define a new state function Enthalpy $(H)$ as :
$H = U + PV$ 

$C _{2}H _{4}(g)+H _{2}(g)\rightarrow C _{2}H _{6}(g)$

$\Delta n=1-2$

$=$ - 1

$C(s)+O _{2}(g)\rightarrow CO _{2}(g)$

$H$ is enthalpy.

Properties which depend on the amount of the substance (or substances)

present in the system are called extensive propterties. e.g. Mass,

volume, heat capacity, internal energy, entropy, Gibb's free energy (G),

surface area etc. These properties will change with change in the

amount of matter present in the system.
The absolute value of

internal energy cannot be determined because it is not possible to

determine the exact values for the constituent energies such as

translational, vibrational, rotational energies, etc. However, we can

determine the change in internal energy (U) of the system when it

undergoes a change from initial state (Ul) to final state (Uf).
Enthalpy

is not a matter. It doesn't have mass and it doesn't occupy space.

Therefore, we cannot measure its absolute value (like energy).
We can only measure the changes because the energy of the universe is constant.

The following reactions have the same heat of reaction at constant $P$ and constant volume as well.

$\Delta H = \Delta U + \Delta nRT$, where $\Delta n =$ Change in number of moles.

As we know,
$\Delta H = \Delta U + \Delta nRT$, where $\Delta n = n _P - n _R$ (n = number of moles)
$H _2(g) + I _2(g)\rightarrow 2HI(g)$      $\Delta n = 0$
$PCl _5(g)\rightarrow PCl _3(g) + Cl _2(g)$                     $\Delta n = 1$
$2H _2O _2(l)\rightarrow 2H _2O(l) + O _2(g)$                 $\Delta n = 1$
$C(s) + O _2(g)\rightarrow CO _2(g)$                  $\Delta n = 0$

Enthalpy is a system is defined as,

As we know,

As we know,
$\Delta H$ =$\Delta U+ \Delta n _g RT$
here, 
$H _2(g) + I _2(g)\longrightarrow 2HI(g)$ 
$\Delta n _g = 0$
so,
$\Delta H$ =$\Delta U$

The heat of reaction at constant pressure and heat of reaction at constant volume for the gaseous reaction 

We know that,
$\Delta H = \Delta E + \Delta nRT$
where,
$\Delta n =$ number of moles of gaseous products - number of moles of gaseous reactants
$= 2-3=-1$
So, $\Delta H = \Delta E - RT$

As we know,
$,\Delta H = \Delta U + \Delta nRT$
$\Delta n = n _{ P } - n _{ R }$
so
$\Delta U < \Delta H$ only if the number of mole of the reactants is less than that of the products.
$\Delta H > \Delta U$ only if the number of mole of the products is less than that of the reactants.

At constant pressure, the work done is pdv, the change in internal energy is du, and the heat added is dQ. All the listed equations are valid thermodynamic expressions for this condition.

As we know,
$,\Delta H = \Delta U + \Delta nRT$
$\Delta n = n _{ P } - n _{ R }$
$\therefore\Delta n = 2 \displaystyle - \frac { 5 }{ 2 } =\displaystyle -\frac{ 1 }{ 2 }$
$\therefore\Delta H = \Delta U \displaystyle - \frac { 1 }{ 2 }RT$
$\therefore\Delta U = \Delta H +\displaystyle \frac{ 1 }{ 2 }RT$
or $\therefore\Delta U > \Delta H$

The Hess's law states that the total enthalpy change during the complete course of a chemical reaction is the same whether the reaction is made in one step or in several steps. Hess's law is now understood as an expression of the principle of conservation of energy, also expressed in the first law of thermodynamics, and the fact that the enthalpy of a chemical process is independent of the path taken from the initial to the final state (i.e. enthalpy is a state function).

The given statement is false.
For a particular reaction $\displaystyle \Delta H = \Delta  E + P \Delta  V$
The change in enthalpy is equal to the sum of the change in the internal energy and the pressure volume work. This expression is applicable at constant pressure.

An isochoric process is a thermodynamic process during which the volume of the closed system undergoing such a process remains constant. 

The relationship between the enthalpy $H$, internal energy $E$, pressure $P$ and volume $V$ is $H=E+PV$
Hence, the expression for the enthalpy change becomes $\Delta H = \Delta U + \Delta (PV)$
Hence, the enthalpy change of a reaction will be equal to $\Delta U + \Delta (PV)$.

An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. In other words, in an isothermal process, the value ΔT = 0 and therefore the change in internal energy ΔU = 0 (only for an ideal gas) but Q ≠ 0, while in an adiabatic process, ΔT ≠ 0 but Q = 0.

$\Delta H=\Delta E+\Delta { n } _{ g }RT$ 

Enthalpy is abbreviated as $H$.
The abbreviations for other terms are:
Standard voltaic potential: $V$
Entropy: $S$ 
Gibbs free energy: $G$

Total enthalpy (H) is the product of the mass (m) of the system and the specific enthalpy (h) of the substance.

A mixture of 2 moles of carbon monoxide and one mole of oxygen in a closed vessel is ignited to get carbon dioxide. 

The vaporization occurs at constant pressure therefore the enthalpy change is equal to the work done by the heater:

The relationship between the enthalpy change and the change in the internal energy is
 $\Delta H=\Delta U+P\Delta V=\Delta U+\Delta n _gRT$
$\Delta U=\Delta H-\Delta n _gRT$
Substitute values in the above expression.
$\Delta U=\displaystyle 22.2-\frac{10}{18}\times 8.314\times 10^{-3}\times 373$
                       $=20.477 :kJ$
The change in internal energy is 20.477 kJ

Enthalpy is the measurement of energy in a thermodynamic system. It is equal to the internal energy of the system plus the product of pressure and volume. The thermal change that occurs in a chemical reaction is only due to the difference in the sum of internal energy of the products and the sum of the internal energy of reactants. At constant pressure, the heat of the reaction is exactly equal to the enthalpy change, of the reacting system.