Lecture 8 Stability and reactivity

We tend to say that substances are ‘stable’ or ‘unstable’, ‘reactive’ or ‘unreactive’ but these terms are relative and may depend on many factors. Thermodynamic and kinetic factors can also be important.

Stability and reactivity can be controlled by thermodynamic factors (depending only on the initial and final states and not on the reaction pathway) or kinetic ones (very dependent on the reaction pathway). Both factors depend on the conditions, and on the possibility of different routes to decomposition or reaction.

Enthalpy and Hess’ Law The enthalpy change (ΔH) in a reaction is equal to the heat input under conditions of constant temperature and pressure. Enthalpy is commonly used as a measure of the energies involved in chemical reactions. Endothermic reactions (positive ΔH) are ones requiring a heat input, and exothermic reactions (negative ΔH) give a heat output.

Hess’ Law states that ΔH does not depend on the reaction pathway( taken between initial and final states), and is a consequence of the First Law of Thermodynamics. ΔH can be expressed as the sum of the values for individual steps: ΔH = ΔH 1 + ΔH 2 +……..

Enthalpy change does depend on conditions of temperature, pressure and concentration of the initial and final states, and it is important to specify these. Standard states are defined as pure substances at standard pressure (1bar), and temperature(298K).

Schematic thermodynamic cycle illustrating the use of Hess’ Law

The standard enthalpy of formation of any compound refers to formation from its elements, all in standard states. By definition,it is zero for any element in its stable(standard ) state. enthalpy change ΔHΘ in any reaction to be calculated from

Entropy and free energy - Entropy (S) is a measure of molecular ‘disorder’, or more precisely ‘the number of microscopic arrangements of energy possible in a macroscopic sample’. - Entropy increases with rise in temperature and depends strongly on the state - Entropy changes (ΔS) are invariably positive for reactions that generate gas molecules.

The Second Law of Thermodynamics asserts that the total entropy always increases in a spontaneous process, and reaches a maximum value at equilibrium. Both internal and external changes are taken account of by defining the Gibbs free energy change (ΔG): for a reaction taking place at constant temperature (T, in kelvin)

Gibbs free energy change (ΔG)

From the Second Law it can be shown that ΔG is always negative for a feasible reaction at constant temperature and pressure and is zero at equilibrium. ΔS and ΔG for reactions do not depend on the reaction pathway. They depend even more strongly than ΔH on concentration and pressure.

Tabulated standard entropies may be used to estimate changes in a reaction from where SΘ values are not zero for elements

Equilibrium constants For a general reaction such as cC + dD aA +bB the equilibrium constant is K =[A] a [B] b /[C] c [D] d

where the terms [A], [B] as concentrations or partial pressures. (This assumes ideal thermodynamic behavior and is a much better approximation for gases than in solution.) A very large value ( ≫ 1) of K indicates a strong thermodynamic tendency to react, so that very little of the reactants (A and B) will remain at equilibrium. Conversely, a very small value ( ≪ 1) indicates very little tendency

to react: in this case the reverse reaction (C and D going to A and B) will be very favorable. For any reaction K may be related to the standard Gibbs free energy change (ΔG Θ ) according to (ΔG Θ ) = - R T lnK where R is the gas constant (=8.314 J K−1 mol−1) and T the absolute temperature (in K). Thus equilibrium constants can be estimated from tabulated values of and trends may often be interpreted in terms of changes in ΔHΘ and ΔSΘ.

Important notes - Equilibrium constants change with temperature in a way that depends on ΔHΘ for the reaction - In accordance with Le Chatelier’s principle, K increases with rise in temperature for an endothermic reaction, and decreases for an exothermic one.

Reaction rates - The rate of reaction generally depends on the concentration of reactants. Rate =k[A] n [B] m - where k is the rate constant and n and m are the orders of reaction with respect to reactants A and B. - Orders of reaction depend on the mechanism and are not necessarily equal to the stoichiometric coefficients a and b. The rate constant depends on the mechanism and especially on the energy barrier or activation energy associated with the reaction pathway.

- High activation energies (Ea) give low rate constants because only a small fraction of molecules have sufficient energy to react. - This proportion may be increased by raising the temperature, and rate constants approximately follow the Arrhenius equation.

Arrhenius equation K =Ae -Ea/RT - Large activation energies arise in reactions where covalent bonds must be broken before new ones are formed, or where atoms must move through solids. - Reactions involving free radicals, or ions in solution, often have small (sometimes zero) activation energies.

Catalyst -Reactions may be accelerated by the presence of a catalyst, which acts by providing an alternative pathway with lower activation energy. - A true catalyst by definition can be recovered unchanged after the reaction, and so does not alter the thermodynamics or the position of equilibrium