Putting It All Together

• Introduction
• Step One
• Step Two
• Step Three

At this point the unit, you have learned about enthalpy, entropy, and free energy. You should now be able to put these concepts all together, to determine whether or not a reaction will occur, with the help of only an enthalpy and entropy table. Let's consider this reaction:

P₄O₁₀ (s) + 6H₂O (l) --> 4H₃PO₄ (aq)
For this reaction, at 25°C, will it be spontaneous?

First, let's calculate the H for the reaction.

Remember the equation: H = H°_f (products) - H°_f (reactants)
Based on a table, you find that:

H°_f P₄O₁₀ (s) = -3110 kJ/mol
H°_f H₂O (l) = -286 kJ/mol
H°_f H₃PO₄ (aq) = -1288 kJ/mol
Since you have 6 moles of H₂O in the reaction, you must multiply the -286 kJ/mol by 6, resulting in -1716 kJ/mol.
You also have 4 moles of H₃PO₄, so -1288 kJ/mol becomes -5152 kJ/mol.

Now back to the equation:
H = (-5152 kJ/mol) - ((-1716 kJ/mol) + (-3110 kJ/mol))
H = (-5152 kJ/mol) - (-4826 kJ/mol) = -326 kJ/mol

Second, let's calculate S for the reaction.

Remember the equation: S = S° (products) - S° (reactants)
Based on a table, you find that:

S P₄O₁₀ (s) = 229 J/Kmol
S H₂O (l) = 70 J/K mol
S H₃PO₄ (aq) = 158 J/K mol
Since you have 6 moles of H₂O in the reaction, you must multiply the 70 J/K mol by 6, resulting in 420 J/K mol.
You also have 4 moles of H₃PO₄, so 158 J/K mol becomes 632 kJ/mol.

Now back to the equation:
S = (632 J/K mol) - ((420 J/K mol) + (229 J/K mol))
S = (632 J/K mol) - (649 J/K mol) = -17 J/K mol

Finally, let's calculate G.

Remember the equation: G = H - T S
Based on your calculations:

H = -326 kJ/mol
S = -17 J/ K mol
And you're told the reaction is at 25°C, but that must be converted to Kelvin.

25°C + 273 = 298 K
Also, your energy units for H and S do not match. H is in kJ, and S is in J. You must convert one (it doesn't matter which) to match the other. Let's convert S to kJ.

-17 J/K mol * 1 kJ/1000 J = -.017 kJ/K mol
Now we can plug the numbers into the equation to calculate free energy.

G = -326 kJ/mol - ((298 K)(-.017 kJ/K mol))
G = -326 kJ/mol - (5.066 kJ/mol)
G = -320.9 kJ/mol

Since G is negative, the reaction P₄O₁₀ (s) + 6H₂O (l) --> 4H₃PO₄ (aq) is spontaneous at 25°C.