Enthalpy and Enthalpy of Reaction

Chemical reactions can either absorb or release heat to the surroundings.  Enthalpy is a thermodynamics quantity that is account for the heat flow in chemical changes occurring at a constant pressure.  Enthalpy denoted by the symbol H, is equal to the internal energy plus the product of pressure and volume of the system:

H = E  +   PV

where E is the internal energy of the system, P is the pressure of the system , V is the volume of the system.  Enthalpy is a state function because internal energy,  pressure, and volume are all state function.  

For any chemical process, change in enthalpy can be calculated by 

∆H  =  ∆E  +  ∆(PV)

If the change occurs at constant pressure 

∆H  =  ∆E  +   P∆V

The change in enthalpy can be calculated by the change in internal energy plus the product of pressure and the change in volume.  Since work at expansion of gas is given by w = -P ∆V, so we can substitute -w for P ∆V and q +  w for ∆E.  Thus, 

∆H =  ∆E  +  P ∆V = q_p  +   w  -  w  =  q_p

the subscript  p on the heat, q, emphasizes change in constant pressure.  The change in enthalpy therefore
∆H = q_p at constant pressure.

When ∆H is positive (q_p is positive), the system has gained heat from the surroundings and the process is endothermic.  And when the ∆H is negative, the system has released heat to the surroundings, and the process is exothermic.

Example:
Indicate the sign of the enthalpy change, ∆H, in each of the following processes:
 a.  melting of ice cubes
 b. combustion of 1 g of butane

Solution:
To answer the problem we need to identify the system and find out if heat is released or absorbed by the system.  In a) ice is the system , the ice absorbs heat from the surroundings as it melts, so q_p or ∆H is positive and the process is endothermic. In b) the system is 1 g of butane and the oxygen required to combust it.  The combustion of butane in oxygen gives off heat, so q_p or ∆H is negative and therefore the process is exothermic.

Enthalpy of Reaction

Enthalpy of reaction, ∆H, is defined as the difference between the enthalpies of the products and the enthalpies of the reactants.

∆H = H(products) - H(reactants)

The enthalpy of reaction can be positive or negative depending on the process of the reaction.  For an endothermic reaction, in which the system absorbs heat from the surroundings, the ∆H is positive (∆H >0).  For an exothermic process in which the system releases heat to the surroundings, ∆H is negative (∆H <0).  

Thermochemical Equation

Thermochemical equation is a balanced equation that shows the enthalpy changes and   mass relationships.  It is important to specify a balanced equation when talking about enthalpy of reaction.  For example: 

H₂O(s)  →  H₂O(l)                          ∆H = 6.01 kJ/mol

The above equation shows the melting of ice and its change in enthalpy is 6.01 kJ/mol.  The per mol in the unit for ∆H means that this is the enthalpy change per mole of the reaction, that is 1 mole of ice is converted to 1 mole of liquid water.

Below are the guidelines that are helpful when using thermochemical equations:

1.  Enthalpy is an extensive property.  The magnitude of ∆H is directly proportional to the amount of the substance consumed in the process.   Let say for example the combustion of methane:

CH₄(g)  +  2O₂(g)  →   CO₂(g)   +   2H₂O(l)                  ∆H = -890 kJ/mol

One mole of methane releases 890 kJ of heat to the surroundings, doubling the amount will cause the increase of heat twice as much, 1780 kJ.

Let us have an example:
How much heat is released  when 4.50 g of methane gas is burned in a constant-pressure  system?

Solution: 
From the equation above, the combustion of 1 mole of methane, CH₄, released 890 kJ of heat to the surroundings.  The molar mass of methane = 16 g/mol.

Heat = 4.50 g CH₄ (1 mol CH₄/16.0 g CH₄)(-890 kJ/1 mol CH₄) = -250 kJ

2.  The enthalpy change of the reaction is equal in magnitude but opposite in sign to the ∆H  for the reverse reaction.  Example, the reverse of the combustion of methane:

CO₂(g)  +  2H₂O(l)  →  CH₄(g)  +   2O₂(g)                 ∆H = +890 kJ/mol

When the reaction is reversed, the roles of the reactants and products are also reversed.  As we can see reversing the reaction, the ∆H has the same magnitude but have an opposite sign, and this time positive.

3. The enthalpy change  for a reaction depends on the state of the reactants and products.  In writing thermochemical equation we should pay attention to the phase of the reactants and products, because it will guide you the proper value of ∆H of the reaction.   Lets say for example:

2H₂O(l)   →   2H₂O(g)                    ∆H = +88 kJ/mol

The equation above shows that 2 moles of liquid water needs 88 kJ of heat in order to convert  to 2 moles of water vapor.  While the equation below:

H₂O(s)  →  H₂O(l)                          ∆H = +6.01 kJ/mol

In the above equation shows that 1 mole of ice needs 6.01 kJ of heat in order to convert ice to liquid.  Given 2 moles of ice will only need 12.02 kJ of heat.  This shows that different phases of the same substance will have different change in enthalpy.



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