Entropy Changes in a Chemical Reaction

There is no easy method of measuring ∆S for a reaction, but we can use experimental measurements of variation of heat capacity for many substances at any temperature.   Absolute entropies are based on the reference point of zero entropy for perfect crystalline solid at 0 K.  Entropies are usually tabulated as molar quantities, in units of joules per mole-Kelvin (J/mol-K).

The molar entropy values of substances in their standard states are known as standard molar entropies and are denoted S^o.  The standard state for any substance is defined as the pure substance at 1 atm pressure.


Sample Molar Entropies of Some Selected Substances at 298 K

Substance                                     S^o, J/mol-K

Gases
H₂(g)                                                 130.7
N₂(g)                                                 191.6
O₂(g)                                                 205.2
H₂O(g)                                              188.8
NH₃(g)                                              192.5
CH₃OH(g)                                        237.6
C₆H₆(g)                                            269.2

Liquids
H₂O (l)                                              69.9
CH₃OH(l)                                        126.8
C₆H₆(l)                                            172.8

Solids
Li(s)                                                   29.1
Na(s)                                                  51.3
K(s)                                                    64.7
Fe(s)                                                   27.3
FeCl₃(s)                                            142.3
NaCl(s)                                              72.3
Al(s)                                                   28.3
Al₂O₃(s)                                            51.0

Based from the sample of molar entropies above, observations about S^o are the following:

1.  Unlike enthalpies of formation, the standard molar entropies of elements at the reference                      temperature at 298 K are not zero.

2.  The standard molar entropies of gases are greater than those of liquids and solids, consistent with         the interpretation of experimental observation.

3.  Standard molar entropies generally increase with increasing molar mass.

4.  Standard molar entropies generally increase with an increasing number of atoms in the formula of      the substance.

In summary, the number of significance of the vibrational degrees of freedom of molecules increase with the increasing mass and increasing number of atoms.

The entropy change in a chemical reaction can be calculated by the sum of the entropies of the products less the sum of the entropies of the reactants:

∆S  = ∑nS^o(products) -  ∑mS^o(reactants)

The coefficient n and m  are the coefficient in the balanced chemical equation.

Example 1

Calculate the ∆S^o for the synthesis of ammonia from N₂(g) and H₂(g)  at 298 K.

N₂(g)    +     3H₂(g)    →     2NH₃(g)

Solution:

Using the formula above, substitute the value of the molar entropies of the substances given in the table above:

∆S  =  ∑nS^o(products) -  ∑mS^o(reactants)

       =  2S^o(NH₃)   -  [S^o(N₂)  +   3S^o(H₂)
       =  (2 mol) (192.5 J/mol-K)   -   [(1 mol) (191.6 J/mol-K)  +  (3 mol)(130.7 J/mol-K)]
       =  - 198.4 J/K

Example 2

Using the standard entropies in the table presented above, calculate the standard entropy change, ∆S^o, for the following reaction  at 298 K.

Al₂O₃(s)  +  3H₂(g)   →    2Al(s)    +   3H₂O(g)

Solution:

∆S  =  ∑nS^o(products) -  ∑mS^o(reactants)

       =  [2S^o(Al)  +   3S^o (H₂O)]  -   [S^o(Al₂O₃)  +   3S^o (H₂)]
       = [(2 mol)(28.3 J/mol-K)  +  (3 mol)(188.8 J/mol-K)]  -  [(1 mol)(51.0 J/mol-K) +(3 mol)                                    (130.7 J/mol-K)]
       =  +180.39 J/K

FOR MOLAR ENTROPIES OF SOME SUBSTANCES JUST CLICK HERE