Enthalpies of Formation

Elements combine to form compounds, compounds on the other hand also combine with another compound to form a different compounds, these are just some of the reactions that occur in our environment and inside the laboratory.  All these reactions can either absorb or release heat, and therefore has the ∆H.

A particular important process used for tabulating thermochemical data is the formation of compound from its constituent elements.  The enthalpy change associated with this process is called enthalpy of formation (or heat of formation) and is symbolized as ∆H_f, where the subscript f indicates that the substance is formed from its elements.

The value of any enthalpy change is dependent on the conditions of  temperature , pressure, and state of the reactants and products.  That is why , in order to compare the enthalpies of different reactions, a standard  condition is set which is called the standard state.  The standard state of a substance is set at 1 atm pressure, and the temperature is at 25^oC (298 K). And therefore, the standard enthalpy of reaction is defined as the enthalpy change when all reactants and products are in their standard states, and is denoted as ∆H^o, where the superscript "^o" denotes standard-state condition.

The standard enthalpy of formation of a compound is the change in enthalpy for the reaction that forms 1 mol of the compound from its elements, with all substances in their standard states.  By convention, the standard enthalpy of formation of most stable form of any element is zero, because there is no formation reaction needed when the element is already in the standard state. The standard enthalpy of formation is symbolized as ∆H^o_f.  Example is the O₂, molecular oxygen is more stable form than any other form of oxygen O, O₃, and therefore the ∆H^o_f = 0.

Knowing the  standard enthalpy of formation can help us calculate the standard enthalpy of reaction, ∆H^o_rxn.  It can be calculated by the formula below:

∆H^o_rxn = ⅀m∆H^o_f(products) - ⅀n∆H^o_f(reactants)

where m and n is the coefficient in the balanced equation and the symbol ⅀, means the sum of the standard enthalpy of products or the reactants.

Click HERE for the List of Enthalpy of Formation of Some Substances

Let us have sample problems:

Sample Problem 1

The thermite reaction  involves aluminum and iron (III) oxide

2Al(s)  +  Fe₂O₃(s)  →  Al₂O₃(s)  +   2Fe(l)

This reaction is highly exothermic and the liquid iron formed is used to weld metals.  Calculate the heat released in kilojoules per mol of Al reacted with Fe₂O₃.  The ∆H^o_f of Fe(l) is 12.40 kJ/mol.

Solution:
Click the link above for the ethalpy of formation of the given substances.

                     ∆H^o_rxn = [∆H^o_f(Al₂O₃) + 2∆H^o_f(Fe)]  - [2∆H^o_f(Al) + ∆H^o_f(Fe₂O₃)]
                                 = [( -1669.9 kJ/mol) + 2(12.40 kJ/mol)]  -  [2(0) + (-822.2kJ/mo)]
                                 = [-1669.9 kJ/mol + 24.8 kJ/mol] - [-822.2 kJ/mol]
                                 = -1645.1 + 822.1 kJ/mol
                                 = -822.8 kJ/mol

Sample Problem 2

The standard enthalpy change for the reaction

CaCO₃(s)  →  CaO(s)  +  CO₂(g)

is 178.1 kJ/mol.  Calculate  the standard enthalpy of formation of CaCO3(s).  Use the value of enthalpy of substances from the link above.

Solution:

                

                ∆H^o_rxn  =  [∆H^o_f(CaO) +  ∆H^o_f(CO₂)] - [∆H^o_f(CaCO₃)]
       178.1 kJ/mol   =  [-635.5 kJ/mol + (-393.5 kJ/mol)] -  [∆H^o_f(CaCO₃)]
    [∆H^o_f(CaCO₃)]  = -1029 kJ/mol - 178.1 kJ/mol
                              =  -1207.1 kJ/mol

FOR ENTHALPY AND FIRST LAW OF THERMODYNAMICS TEST QUESTIONS CLICK HERE