## Section 7: Putting It All Together

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 = f (products) - f (reactants)
Based on a table, you find that:

f P4O10 (s) = -3110 kJ/mol
f H2O (l) = -286 kJ/mol
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

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.