Thermochemistry is the branch of physical chemistry which deals with the heat changes caused by chemical reactions. Thus, calorimetry can be used to measure the energy supplied or discarded as heat by a reaction and can identify q with a change in internal energy if the reaction occurs at constant volume or with a change in enthalpy if the reaction occurs at constant pressure. Conversely, if we know ΔU or ΔH for a reaction, we can predict the heat the reaction can produce.

A process that releases energy as heat into the surroundings is classified as exothermic and one that absorbs energy as heat from the surroundings is classified as endothermic. Because the release of heat at constant pressure signifies a decrease in the enthalpy of a system, it follows that an exothermic process is one for which ΔH<0. Conversely, because the absorption of heat results in an increase in enthalpy, an endothermic process has ΔH>0:

exothermic process: ΔH<0 and endothermic process has ΔH>0

Standard enthalpy changes:

The standard enthalpy change, ΔH0, the change in enthalpy for a process in which the initial and final substances are in their standard states:

The change in enthalpy that takes place when one mole of a compound is formed from its elements, all substances being in their standard states (298 K and 1 atm pressure).

The standard enthalpy change for a reaction or a physical process is the difference between the products in their standard states and the reactants in their standard states, all at the same specified temperature.

The standard enthalpy of vaporization, ΔvapH0, is the enthalpy change per mole of molecules when a pure liquid at 1 bar vaporizes to a gas at 1 bar, as in

H2O (l) → H2O(g) ΔvapH0 (373K) =+40.66kJmol-1

Standard enthalpies may be for any temperature but the conventional temperature for thermodynamic data is 298.15 K.

Enthalpies of physical change:

The standard enthalpy change accompanying a change in the physical state is called the standard enthalpy of transition and is denoted ΔtrsH0. The standard enthalpy of vaporization, ΔvapH0, is one example. Another is the standard enthalpy of fusion, ΔfusH0the standard enthalpy change accompanying the conversion of a solid to a liquid, as in

H2O (s) → H2O(l) ΔfusH0 (273K) =+60.1kJmol-1

Since enthalpy is a state function, so a change in enthalpy is independent of the path between the two states. This is of great importance in thermochemistry as it implies that the same value of ΔH0 will be obtained however the change is brought about between the same initial and final states. For example, the conversion of a solid to a vapour either as occurring by sublimation (the direct conversion from solid to vapour),

H2O (s) → H2O(g) ΔsubH0

or as occurring in two steps, first fusion (melting) and then vaporization of the resulting liquid:

H2O (s) → H2O(l) ΔfusH0

H2O (l) → H2O(g) ΔvapH0

Overall: H2O (s) → H2O(g) ΔfusH0 + ΔvapH0

Because the overall result of the indirect path is the same as that of the direct path, the overall enthalpy change is the same in each case, and we can conclude that (for processes occurring at the same temperature)
ΔsubH0 = ΔfusH0 + ΔvapH0

An immediate conclusion is that, because all enthalpies of fusion are positive, the enthalpy of sublimation of a substance is greater than its enthalpy of vaporization (at a given temperature).


Another consequence of H being a state function is that the standard enthalpy changes of a forward process and its reverse differ in its sign:

ΔH0 (A → B) = – ΔH0 (B → A)

For instance, because the enthalpy of vaporization of water is +44 kJ mol-1 at 298 K, its enthalpy of condensation at that temperature is -44 kJ mol-1.


The lattice enthalpy, ΔHL, is the change in standard molar enthalpy for this process. The lattice enthalpy is equal to the lattice internal energy at T=0; at normal temperatures, they differ by only a few kilojoules per mole, and the difference is normally neglected.

Experimental values of the lattice enthalpy are obtained by using a Born–Haber cycle. It is a closed path of transformations, that starts and ends at the same point, one step of which is the formation of the solid compound from a gas of widely separated ions. They are large when the ions are highly charged and small, for then they are close together and attract each other strongly.

Enthalpies of chemical change:

There are two ways of reporting the change in enthalpy that accompanies a chemical reaction. One is to write the thermochemical equation, a combination of a chemical equation and the corresponding change in standard enthalpy:

CH4 (g) g 2O2 (g) → CO2 (g) + 2H2O (g) ΔH0 = -890kJ

ΔH0 is the change in enthalpy when reactants in their standard states change to products in their standard states:
Pure, separate reactants in their standard states →pure, separate products in their standard states.

Alternatively, we write the chemical equation and then report the standard reaction enthalpy, ΔrH0 (or ‘standard enthalpy of reaction’). Thus, for the combustion of methane, we write

CH4 (g) g 2O2 (g) → CO2 (g) + 2H2O (g) ΔH0 = -890kJ

For a reaction of the form 2 A+B → 3 C+D the standard reaction enthalpy would be

ΔrH0 = { 3 H0m (C) + H0m (D)} – {2 H0m (A) + H0m (B)}

where H0m (J) is the standard molar enthalpy of species J at the temperature of interest.

In general,

ΔrH0 = ∑ Products vH0m – ∑ Reactants vH0m

where, in each case, the molar enthalpies of the species are multiplied by their (dimensionless and positive) stoichiometric coefficients, v.

Hess’s law:

Since ∆E and ∆H are functions of the state of the system, the heat evolved or absorbed in a given reaction must be independent of the manner in which the reaction is brought about. Thus it depends only on the initial state and final states of the system and not the manner or the steps in which the change takes place. This generalization is known as Hess’s Law and may be stated as:

The standard enthalpy of an overall reaction is the sum of the standard enthalpies of the individual reactions into which a reaction may be divided. The thermodynamic basis of the law is the path-independence of the value
of ΔrH0

The importance of Hess’s law is that information about a reaction of interest, which may be difficult to determine directly, can be assembled from information on other reactions.

Standard enthalpies of formation:

The standard enthalpy of formation, ΔfH0, of a substance is the standard reaction enthalpy for the formation of the compound from its elements in their reference states:

The reference state of an element is the most stable state of it at the specified temperature and 1 bar.

Standard enthalpy of formation is also defined as the change in enthalpy that takes place when one mole of a compound is formed from its elements, all substances being in their standard states (298 K and 1 atm pressure).

For example, at 298 K the reference state of nitrogen is a gas of N2 molecules that of mercury is liquid mercury, that of carbon is graphite, and that of tin is the white (metallic) form. There is one exception to this general prescription of reference states: the reference state of phosphorus is taken to be white phosphorus despite this allotrope not being the most stable form but simply the more reproducible form of the element. Standard enthalpies of formation are expressed in terms of enthalpies per mole of molecules or (for ionic substances) formula units of the compound.

The standard enthalpy of formation of ions in solution poses a special problem because it is impossible to prepare a solution of cations alone or of anions alone. This problem is solved by defining one ion, conventionally the hydrogen ion, to have zero standard enthalpies of formation at all temperatures:

ΔfH0 (H+, aq)= 0

The reaction enthalpy in terms of enthalpies of formation:

The value of ΔrH0 for the overall reaction is the sum of these ‘unforming’ and forming enthalpies. Because ‘unforming’ is the reverse of forming, the enthalpy of an ‘unforming’ step is the negative of the enthalpy of formation.


Hence, in the enthalpies of formation of substances, we have enough information to calculate the enthalpy of any reaction by using

ΔrH0 = ∑ Products fH0 – ∑ Reactants vΔfH0

The temperature dependence of reaction enthalpies:

Standard reaction enthalpies at different temperatures may be calculated from heat capacities and the reaction enthalpy at some other temperature.


It follows from equation (dH=CpdT) that, when a substance is heated from T1 to T2, its enthalpy changes from H(T1) to

H(T2) = H(T2) + T1T2 CpdT

(We have assumed that no phase transition takes place in the temperature range of interest.) Because this equation applies to each substance in the reaction, the standard reaction enthalpy changes from ΔrH0(T1) to

ΔrH0(T2) = ΔrH0(T2) + T1T2 ΔrC0pdT

where ΔrCp0 is the difference of the molar heat capacities of products and reactants under standard conditions weighted by the stoichiometric coefficients that appear in the chemical equation:

ΔrC0p,m = ∑ Products vC0p,m – ∑ Reactants vC0p,m

or, ΔrC0p,m = ∑ vjC0p,m (J)

Equation ΔrH0(T2) = ΔrH0(T2) + T1T2 ΔrC0pdT is known as Kirchhoff ’s law. It is normally a good approximation to assume that ΔrC0pis independent of the temperature, at least over reasonably limited ranges.


The experimental measurement of the enthalpy change is known as calorimetry. The heat given out or absorbed in a chemical reaction is measured in a suitable apparatus called a calorimeter.

Water Calorimeter:


This is a convenient apparatus for finding the heat changes accompanying chemical reactions taking place in solutions. The apparatus consists essentially of a water-bath with thermally insulated walls. A reaction chamber consisting of two limbs is suspended in the water-bath. Through the lid of the water-bath pass thermometer that records the temperature variations and a stirrer that stirs the water in the water-bath. A known quantity of water is taken in the water-bath and its temperature is noted down. The reacting substances are filled in the two limbs as shown. The reacting chamber is now turned upside down (position II) to allow the solutions to mix. They react and the heat produced during the reaction is taken up by water, raising its temperature. If the rise in temperature is t ºC, the heat absorbed by water ‘Q’ is given by

Q = W × 1 × t calories

But heat produced in the reaction is equal to that absorbed by water, hence heat of the reaction can be calculated.

Bomb Calorimeter:


This apparatus was invented by Berthelot. It is used to measure the heat of combustion of organic compounds. The apparatus consists of a sealed combustion chamber ( i.e., called bomb) that contains a weighed quantity of the substance in a dish along with oxygen under about a pressure of 20 atm. The bomb is lowered in water contained in an insulated copper vessel. This vessel is provided with a stirrer and a thermometer reading up to 1/100th of a degree. It is also surrounded by an outer jacket to ensure complete insulation from the atmosphere. The temperature of the water is noted before the substance is ignited by an electric current. After combustion, the rise in temperature of the system is noted on the thermometer and heat of combustion can be calculated from the heat gained by water and the calorimeter.


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