In this article we will discuss about:- 1. Introduction of Chemistry of Combustion 2. Enthalpy of Formation 3. Enthalpy and Internal Energy of Reaction 4. Adiabatic Flame Temperature 5. Free Energy and Chemical Equilibrium 6. Equilibrium Constant for a Reaction.
Contents:
- Introduction of Chemistry of Combustion
- Enthalpy of Formation
- Enthalpy and Internal Energy of Reaction
- Adiabatic Flame Temperature
- Free Energy and Chemical Equilibrium
- Equilibrium Constant for a Reaction
1. Introduction of Chemistry of Combustion:
Thermodynamic relationships determine the equilibrium composition of product mixtures resulting from chemical reaction. The nature of the product species, their proportions, their temperature, and their pressure depend upon three major controlling factors. For one thing, the composition of the products of reaction is affected by material balance considerations.
ADVERTISEMENTS:
This requires that the total quantity of each chemical element in the product mixture be the same at that in reactants. We shall therefore consider the calculation of elemental composition of various mixtures and examine the laws of stoichiometry which apply in chemical reactions. Second, the resultant temperature and pressure of product mixtures depend upon the first law of thermodynamics.
Thus dictates that the total energy be conserved, just as the total ass is. Hence, this gives attention to calculation of flame temperatures of combustible mixtures. Third, equilibrium composition is determined by relationships that arise indirectly from the second law of thermodynamics.
The second law dictates that the composition of the products depends on temperature and pressure, whereas the first law dictates that the temperature and pressure of the product depend on their composition. Clearly, then, complex interactions are involved, and problems of calculation of product composition can be handled only by considering both laws simultaneously.
Although, the principles outlined here apply to any chemical reaction, particular attention will be given to an important class of chemical reactions, the combustion processes. Combustion may be defined as a rapid exo-thermic reaction between a fuel and an oxidizer in which chemical energy is liberated.
ADVERTISEMENTS:
2. Enthalpy of Formation
:
ADVERTISEMENTS:
To establish an enthalpy scale of elements and compounds, it is first necessary to choose an arbitrary datum for zero enthalpy. It was conventionally agreed to assign a zero value to the enthalpy of elements in their most stable forms at a standard state of 1 standard atmospheric pressure and 25°C (77°F). If an element has two or more stable forms, that form which is stable at 25°C is chosen as reference. With this standard reference state established, enthalpies of all species have a common base.
The enthalpy of formation of a compound is defined as the enthalpy change that accompanies the formation of 1 mole of the compound at the standard reference state from elements at the same state. The enthalpy of formation is given by the symbol h̅f0, where the subscript f refers to the formation of the compound from its elements, and superscript (0) indicates that all reactants and products are at the standard state. Thus, if elements Aa, Bb, and Cc at the same reference state, then the chemical equation can be written-
3. Enthalpy and Internal Energy of Reaction
:
ADVERTISEMENTS:
Chemical energy is part of the internal energy of a system and is attributed to the binding energy between the atoms of the substance. So far we have not considered chemical reactions and consequently chemical energy was excluded. Now, however, chemical energy constitutes the major part of the internal energy term in the first law.
In chemical reactions, one important concern is the amount of heat transfer due to the reaction.
Two cases will be considered-
ADVERTISEMENTS:
(1) When the reaction takes place at constant pressure,
(2) When it takes place at constant volume. Consider first, the constant-pressure process.
If no work other than reversible work is done, the first law of thermodynamics applied to a closed system is-
dQ = dH – VdP
4. Adiabatic Flame Temperature
:
Under adiabatic conditions, the temperature attained in a reaction is called the adiabatic reaction or flame temperature. In actual processes the combustion temperature is considerably less, owing to the inevitable heat interaction with the environment.
Also, some of the reactants may fail to react, or may decompose only partially. Dissociation of the products of combustion also results in a further reduction of the combustion temperature. The adiabatic reaction temperature is an upper limit of temperature and therefore is a useful parameter in the design of combustion chambers.
The adiabatic reaction (flame) temperature may be determined from the first law which reduces to-
∑HT = ∑Hp
The adiabatic reaction temperature can be computed, making use of (1) gas tables – % of excess air + Stoichiometric air – 100% excess air means gas tables to be used as 200%. (2) enthalpy of formation (3) enthalpy of combustion (4) specific heat equations.
5. Free Energy and Chemical Equilibrium
:
During the course of chemical reaction, many intermediate compositions are formed before equilibrium is reached and the final composition is attained. In a chemical reaction, the products can react in the reverse direction, forming reactants, just as the reactants form products in the forward direction. At equilibrium, the rates of the forward reaction and the reverse reaction are equal. Now the factors governing the final composition of a chemical system will be considered. The Gibbs function is the main criterion for equilibrium.
The reference state for the Gibbs face energy of formation is 25°C (77°F) and 1 standard atm. The stable form of each element at standard reference state is arbitrarily assigned a value of zero free energy of formation. The free energy change of any reaction is given by-
When a compound is formed from its elements, the result free-energy change at the standard state represents the standard free energy of formation G°f of the compound. A negative value of ΔG°f indicates that reactants at the standard state proceed spontaneously to products at the standard state. Conversely a positive value of ΔG° indicates the reaction does not take place spontaneously. Stand tables are available for the free energy of formation of several substances.
The free energy change of a chemical reaction under isothermal standard state conditions may be determined according to the equation-
The change of entropy ΔS° is determined from the absolute entropies of the reactants and products at the standard state according to the equation-
Absolute values of entropy of several pure substances at the standard state (1 atm. and 25°C) are also listed in the same tables. According to the third law of thermodynamics, the entropy of a pure substance in equilibrium approaches zero as the temperature reaches zero. Thus a datum point for entropy is established at zero absolute temperature. Note that elements as well as compounds have entropies greater than zero at 25°C and 1 atm pressure.
At other temperatures and pressures the absolute entropy of a perfect gas can be calculated from the Sackur- Tetrode equation which developed from statistical mechanics. When the entropy of a perfect gas is known at one pressure and temperature, its entropy at another set of temperature and pressure conditions can be calculated from-
6. Equilibrium Constant
for a Reaction:
This topic investigates the condition of equilibrium for a reaction given by the equation-
The subscript p is to emphasize that Kp is defined in terms of the partial pressure of reactants and products. Note that ΔG° and Kp are independent of the total pressure. They only depend on temperature and the nature of the reactants and products of the reaction. Recall also that in choosing the reference state, the will of pressure for the components was expressed in atmospheres.
Therefore, the value of Kp is based on this unit of pressure. In the preceding definition of Kp the partial pressures of the products are placed in the numerator and the partial pressures of the reactants are placed in the denominator. When the reaction is reversed, the value of the equilibrium constant becomes the reciprocal of that of the forward reaction. Values of Kp as a function of temperature are usually given in the form of an equation, table or graph.
The equilibrium constant may also be expressed in terms of mole fractions. Noting that the mole fraction of a component in a perfect gas mixture is equal to the ratio of the partial pressure of the component to the total pressure, equilibrium constant becomes-
that is, if the number of moles remain unchanged during the reaction. This means further that at constant temperature and pressure the volume of the gaseous components remains constant. Thus the equilibrium composition of a reacting system at a given temperature and pressure can be determined if the equilibrium constant is known.
The affinity Z can be expressed in terms of Kp as-
If ΔH° is positive (endothermic reaction), Kp increases with increasing temperature. Above equation is called Van’t Hoff equation. This equation may be used to determine the value of ΔH° as a function of temperature, provided that the variation of Kp with temperature is known.