# Entropy and Free Energy

Entropy Entropy, S, is the quantitative measure of the degree of disorder in a system. Entropy is a measure of disorder or the amount of randomness in a system. All systems possess some degree of randomness because particles are always in constant motion. This graph shows how entropy gradually changes with temperature. At 0K, perfect crystals have 0 entropy. The largest jumps in entropy values occur at the melting and boiling points. The greatest change occurs at boiling point because a gas is significantly more disordered than a solid or liquid. There is a general tendency towards greater entropy nature tends to move from order to disorder in isolated systems. For example, gas molecules spread out over time to fill a space, increasing their entropy. Energy here is changing, from being concentrated to being more spread out: particles are becoming more disordered and so entropy increases. Gas molecules spread out Entropy increases Entropy increases when a solid dissolves: CuSO4.5H2O is a solid lattice. When it dissolves in water: CuSO4.5H2O Cu2+ (aq) + SO42- (aq) + 5H2O (l) The copper and sulphate ions are spreading out they are becoming more disordered so entropy increases. Entropy increases when there is an increase in the number of gas moles: Mg (s) + 2HCl (aq) MgCl2 (aq) + H2 (g) In a reaction where a gas evolved, entropy increases. The standard entropy, S of a substance is the entropy content of one mole of the substance under standard conditions. It has units J-1K-1mol-1. The entropy change of a reaction can be calculated using the standard entropies of the products and reactants: S = SS = SS (products) - SS (reactants) If a change makes a system more random, S is positive.S is positive. If a change makes a system more ordered, S is positive.S is negative. N2 (g) + 3H2 (g) 2NH3 (g) S N2 (g)

H2 (g) NH3 (g) +192 +131 +193 Use the data in the table to calculate S for this reaction. S for this reaction. S = SS = SS (products) - SS (reactants) S = SS = (2x193) [(192) + (3 x 131)] S = SS = -199 JK-1mol-1 We would expect the entropy value to be negative because more ordered system with fewer gaseous moles is produced. Gibbs Free Energy A spontaneous process proceeds on its own. Spontaneous processes lead to lower energy and increased stability. Exothermic reactions generally are spontaneous at room temperature. The enthalpy content decreases and excess energy is released to the surroundings. This increases stability. Some endothermic reactions can take place spontaneously at room temperature. The enthalpy content of the system increases: this must also increase stability. The reason that such a reaction can take place is entropy. A process is spontaneous if a chemical system becomes more stable and its overall energy decreases. The overall energy decrease results from contributions form entropy and enthalpy. The entropy contribution to the overall energy depends on temperature. Energy derived from entropy = TS is positive.S so as temperature increases, the energy derived from entropy becomes more significant. The free energy change S is positive.G is the balance between enthalpy, entropy and temperature for a process: S is positive.G = S is positive.H - T S is positive.S The feasibility of a reaction depends on the balance between enthalpy and entropy. Spontaneous processes happen

when S is positive.G is negative. Use the data in the table to: (a) determine the feasibility of the reaction at 25 temperature. (b) determine the minimum temperature for the reaction to take place (c) explain why the reaction becomes feasible at high temperatures. (a) S = SH = SS = SH f (products) - SS = SH (reactants) = [(-83) + (-393.5)] (-547.5) = +71 kJmol-1 S = SS = SS (products) - SS (reactants) S = SS = (44+214) (82) S = SS = +176 JK-1mol-1 f S is positive.G = S is positive.H - T S is positive.S S is positive.H = +71 kJmol-1 S is positive.S = +176 JK-1mol-1 = +0.176kJK-1mol-1 T= 25+273 = 298K S = SG = S = SH - T S = SS S = SG = 71 (298 x 0.176) S = SG = 18.552 kJmol-1 S = SG is positive therefore the reaction is not feasible. ZnCO3 (s) ZnO (s) + CO2 (g) ZnCO3 ZnO (s) (s) S = SHf -547.5 -83 393.5 S +82 +44 +214

kJmol-1 JK-1mol-1 CO2 (g) (b) S = SG = S = SH - T S = SS A reaction is first feasible when S = SG = 0: 0 = S = SH - T S = SS T S = SS = S = SH T = = = 403K (=130) (c) As temperature increases, TS = SS gets bigger. Eventually, when TS = SS = H, S = SG will be 0 and the reaction will then be feasible. Changing temperature and S is positive.G S is positive.H S is positive.S S is positive.G = S is positive.H - T S is positive.S Feasibility? -ve +ve Always -ve Always feasible In these circumstances, S is positive.G will always be negative so the reaction will always be feasible. S is positive.G = S is positive.H - T S is positive.S S is positive.H S is positive.S S is positive.G = S is positive.H - T S is positive.S Feasibility? -ve -ve -ve at low temperature Feasible at low temperature

S is positive.H S is positive.S S is positive.G = S is positive.H - T S is positive.S Feasibility? +ve -ve Always +ve Never feasible In these circumstances, S is positive.G will always be positive; two negatives give a positive, so S is positive.G will never be less than 0, hence the reaction will never be feasible. S is positive.H S is positive.S S is positive.G = S is positive.H - T S is positive.S Feasibility? +ve +ve -ve at high temperature Feasible at high temperature If S = SS is negative, T S = SS becomes a positive term in the equation. Provided that the T S = SS term is smaller than the value of S = SH, the reaction will be feasible because S = SG will be less than 0. For example, if S = SH is -110, and S = SS is -20, at a temperature of 5K, the TS = SS value will be -100. Putting this into the expression for S = SG : -110 (-100) = -10. The reaction is feasible at this low temperature. For the reaction to be feasible, S = SG must be negative. For this to be so, if S = SS is positive, the TS = SS term in the equation must be larger than the S = SH value. This will be true at high temperatures. Hence, reactions with positive S is positive.H and S is positive.S values are only feasible at high temperatures.

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