1.3.2 Enthalpy, Entropy, and Spontaneous Changes

The two thermodynamic factors that determine whether or not a chemical reaction will actually occur: enthalpy (ΔH) and entropy (ΔS). A spontaneous reaction simply means that a reaction will occur; how fast it occurs is not an issue.

Let's summarize our general findings: ΔH- positive (endothermic) - reaction tends not to be spontaneous ΔH - negative (exothermic) - reaction tends to be spontaneous ΔS- positive - randomness increases - reaction tends to be spontaneous ΔS- negative - randomness decreases - reaction tends not to be spontaneous

What if we consider both enthalpy and entropy together? Is the reaction spontaneous? Negative Positive always! negative never! ??? positive

There are two situations where we cannot predict whether a reaction will occur or not - when both ΔH and ΔS are either positive or negative. Is there no way we can predict spontaneity in these cases? Of course there is!

3.3 Gibbs Free Energy Equation Both enthalpy and entropy changes are important in determining whether a reaction will occur or not. A relationship between these two factors can be expressed by Gibbs Free Energy

Gibbs Free Energy Equation ΔG = ΔH - TΔS Where ΔG = Gibbs Free Energy, in kJ ΔH = enthalpy change T = temperature, in Kelvin ΔS = entropy change (in kJ / K) ΔS must be expressed in kJ /K. When you calculated it before, the units were J / K. Divide by 1,000 to convert joules to kilojoules.

Gibb’s free energy IF: ΔG < 0 The reaction is spontaneous ΔG > 0 The reaction is not spontaneous ΔG = 0  The reaction is at equilibrium. Free energy change is the net driving force of a chemical reaction—whether spontaneous or not

Gibb’s Free Energy Generally, most exothermic reactions are spontaneous, even if entropy decreases exceptions are reactions occurring at high temperatures.

Example. Calculate ΔG for the following reaction at 25°C. Will the reaction occur (be spontaneous)? How do you know? NH3(g) + HCl(g) → NH4Cl(s) Also given for this reaction: ΔH = -176.0 kJ ΔS = -284.8 J/K

Another Method ΔG can also be calculated using a Table of Thermochemical Data and our familiar formula ΔG = ΣΔG° products - ΣΔG° reactants ΔG° for pure elements is equal to 0 kJ. Let's try the previous example again, this time using ΔG°f values from the Table of Thermochemical Data:

   NH3+ HCl→  NH4Cl ΔG: -16.5+ -95.3 -202.9    - 111.8 -202.9  ΔG=ΣΔG°f products - ΣΔG°f reactants   = - 202.9 - (-111.8) ΔG=-91.1 kJ answer

NOTE: The values given in the Table are for temperatures of 25°C (273 K); and only valid for that temperature. If the reaction occurs at another temperature, the formula ΔG = ΔH – TΔS should be used instead

Practice problems 1. Calculate ΔG at 25°C for the following reaction, by first calculating ΔH and ΔS. Once you've found ΔH and ΔS, solve for ΔG using the formula: ΔG = ΔH - T ΔS Will this reaction be spontaneous at this temperature? CH3CO2H (l) + 2 O2 (g) → 2 CO2 (g) + 2 H2O (g)

Problem #2 Again find ΔG at 25°C for the reaction CH3CO2H (l) + 2 O2 (g) → 2 CO2 (g) + 2 H2O (g) This time using the Table of Thermochemical Data and the formula: ΔG = ΣΔG° products - ΣΔG° reactants 

Problem #3 Fe2O3 (s) + 3 CO (g) → 2 Fe (s) + 3 CO2 (s) ΔG° = -31.3 kJ. Calculate the standard free energy of formation of the ferric oxide, Fe2O3, if ΔG°f of CO = -137 kJ/mol and ΔG°f of CO2 = -394 kJ/mol.