CHM 2046C Sample Module 13 Name: ___Answer_____

Part D: Derivation of Gibbs Free Energy Change & Discussion: 10 points

The quantity called the Gibbs free-energy change (∆G),

∆G = ∆H - T∆S, determines whether a chemical or physical process will occur spontaneously. Fill in the following:

∆G < 0 Process , a reaction is spontaneous

∆G = 0 Process , the reaction is at equilibrium

∆G > 0 Process, the reaction is non spontaneous

This quantity: ∆G = ∆H - T∆S is derived from the following equation:

∆S^o_universe = ∆S^o_system + ∆S^o_surroundings

Show this derivation with stepwise explanations/comments:

The second law of thermodynamics states that a reaction is spontaneous when the entropy of the universe increases. The change in the entropy of the entire universe when a reaction occurs is the sum of the entropy changes in the system and in the surroundings:

∆S^o_universe = ∆S^o_system + ∆S^o_surroundings

The entropy change for the surroundings occurs because heat leaves the system and enters the surrounding (or vice versa). Provided that the energy transfer is slow and it occurs at a constant temperature, the entropy change in the surroundings can be calculated by:

		q surr			qsys			∆H^osys
∆S^osurroundings	=	-------	=	–	-----	=	–	--------
		T			T			T

Upon substitution:

				∆H^osys
∆S^ouniverse	=	∆S^osystem	–	--------
				T

Multiplying through by –T :

–T∆S^o_universe = –T∆S^o_system + ∆H^o_sys

–T∆S^o_universe is defined as ∆G^o_sys

Therefore ∆G^o_sys = –T∆S^o_system + ∆H^o_sys

or simply

∆G^o = ∆H^o –T∆S^o

The free energy of the system must decrease if the entropy of the universe is to increase and the reaction is to be spontaneous.

Fill in the following Table to Predict Spontaneity:

∆H

∆S

∆G = ∆H - T∆S

Reaction Spontaneity-include temperatures

The table above is found as Table 16.2 in the McMurry text: