The direction of Chemical Change

Chapter 17 The direction of Chemical Change

Direction of spontaneous change • If a process is found to be spontaneous, the reverse process is non spontaneous. • Both spontaneous and non spontaneous processes are possible but only spontaneous process will occur naturally. Non spontaneous processes require the system to be acted upon in some way.

The distinction between spontaneous and non-spontaneous processes is formalized in the Second Law of Thermodynamics.

Entropy and disorder • Second Law of Thermodynamics: In any cyclic process the entropy will either increase or remain the same. • A more precise way to characterize entropy is to say that it is a measure of the "multiplicity" associated with the state of the objects. If a given state can be accomplished in many more ways, then it is more probable than one which can be accomplished in only a few ways.

For a glass of water the number of molecules is astronomical. The jumble of ice chips may look more disordered in comparison to the glass of water which looks uniform and homogeneous. But the ice chips place limits on the number of ways the molecules can be arranged. The water molecules in the glass of water can be arranged in many more ways; they have greater "multiplicity" and therefore greater entropy.

Class Practice • Calculate the change in entropy of a large tank of water when a total of 100J of energy is transferred to it reversibly as heat at 20⁰C.

Entropy of vaporization /fusion • The entropy of vaporization of a substance, ∆Svap , is the difference in molar entropies of the vapor and liquid phases of a substance at a stated temperature. • The entropy of fusion, ∆S fus is the difference in the molar entropies of the liquid and solid phases of a substance at a stated temperature.

The second law of thermodynamics states that the entropy of an isolated system tends to increase.

Class practice • Calculate the change in molar entropy when water vaporizes at its boiling point.

The third law of thermodynamics states that the entropy of a perfect crystal approaches 0 as the absolute temperature approaches 0.

Reaction entropy • The standard reaction entropy, ∆S ⁰f is the difference between the standard molar entropies of the products and the reactants. • ∆S ⁰f =∑nS⁰m (products) - ∑nS⁰m(reactants) • n is the various stochiometric coefficients. • The standard reaction entropy is usually positive(an increase in entropy) if there is a net production of gas in a reaction; it is usually negative( a decrease) if there is a net consumption of gas.

Class Practice • Calculate the standard reaction entropy for N₂(g) +3H₂(g)  2NH₃(g)

Entropy of the surrounding • Whenever we talk of entropy we must take into account the sum of the changes in the system, ∆S, and the surrounding ∆S surr • Total entropy change= entropy change of system + entropy change of surrounding • ∆Stot= ∆S + ∆S surr • Entropy change of surrounding=heat transferred to surroundings/temperature of surroundings • =enthalpy change of system/temp. of the surrounding • ∆Ssurr= - ∆H/T

A chemical reaction is spontaneous if it is accompanied by an increase in the total entropy of the system and the surroundings. Spontaneous exothermic reactions are common because they release heat that increases the entropy of the surroundings. • Endothermic reactions are spontaneous only if the reaction mixture undergoes a large increase in entropy.

Class Practice • Is the dissolution of ammonium nitrate to form a dilute aqueous solution spontaneous at 25⁰C ?

Free Energy • The total entropy change ∆Stot is the sum of the entropy changes in the system ,∆S and its surroundings , ∆S surr • ∆Stot= ∆S + ∆S surr ∆Ssurr= - ∆H/T • ∆Stot= ∆S - ∆H/T • ∆G = -T∆Stot= ∆H-T ∆S • ∆G is Gibbs free energy

The free energy change is a measure of the change in the total entropy of a system and its surroundings at constant pressure; spontaneous processes are accompanied by a decrease in free energy.

Free energy and equilibrium • If ∆G<0 process is spontaneous • If ∆G>0 the reverse of the process is spontaneous • If ∆G=0 process is at equilibrium • ∆G=0 at 0⁰C signifies the fact that water and ice are in equilibrium at that temperature.

Predicting the boiling point • ∆G = ∆H-T ∆S • We want the temperature at which ∆G=0 • ∆Hvap-Tb ∆Svap =0 • Tb =∆Hvap / ∆Svap • The melting point follows the same formula

Standard free energy • A thermodynamically stable compound is a compound with a negative free energy of formation. Such a compound has no tendency to decompose into its elements. • A thermodynamically unstable compound is a compound with a positive standard free energy of formation. Such a compound has a tendency to decompose into its elements.

The standard free energy of formation of a substance is the standard free energy of reaction per mole of compound when it is prepared from its elements in their most stable forms. The sign of ∆G⁰f tells us whether a compound is stable or unstable with respect to its elements.

Using free energies of formation • ∆G⁰f =∑n ∆G⁰f (products) - ∑n ∆G⁰f (reactants) • Standard free energies of formation are combined to calculate the standard free energy of the reaction.

Equilibrium constants • The reaction free energy is related to the composition of the reaction mixture by • ∆Gr= ∆G⁰r+ RTlnQ • At equilibrium ∆Gr = 0 and Q=K • 0 = ∆G⁰r+ RTlnK • Rearranging the equation • ∆G⁰r = -RTlnK • K<1 when ∆G⁰r >0 • K>1 when ∆G⁰r < 0

The equilibrium constant is related to the standard free energy of reaction by • ∆G⁰r = -RTlnK • K is expressed in terms of numerical values of the partial pressures of gases Kp and as the numerical values of the molar concentrations of solutes Kc.

Class Practice • Calculate Kp at 25⁰C for the equilibrium N2O4(g)↔2NO2(g)

Effect of temperature • The free energy increases with temperature for reactions with a negative ∆Sr⁰ and decreases with temperature for reactions with a positive ∆Sr⁰ .

Home work • Page 786 • 17.46,17.52, 17.71, 17.74

The direction of Chemical Change