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Spontaneity, Entropy, and Gibbs Free Energy AP Chemistry Ms. Grobsky Where We Have Been and Where We are Going How do we describe the shape of a molecule? Molecules have predictable shapes and polarities based on minimizing repulsions and maximizing attractions Atoms more close together to lower energy and form bonds How is energy involved in a reaction? Energy is stored in bonds The heat content (enthalpy, H) of a system changes (ΔH) during a reaction Endothermic – ΔH is + (uphill) Exothermic – ΔH is – (downhill) Where We Have Been and Where We are Going How rapidly does a reaction progress? Kinetics Reaction rates, activation energy, catalysts, reaction mechanisms, temperature… The lower the activation energy (Ea), the faster a reaction proceeds How far towards completion does a reaction occur? Equilibrium Opposing reactions occur at equal rates K >> 1 means product favored at equilibrium Why do reactions proceed in the first place? Spontaneous Processes Spontaneous processes are those that can proceed without any outside intervention GIVEN SUFFICIENT ACTIVATION ENERGY The gas in vessel A will spontaneously effuse into vessel B But once the gas is in both vessels, it will NOT spontaneously reverse Spontaneous Processes Processes that are spontaneous in one direction are usually nonspontaneous in the reverse direction under same conditions Rusting of a nail Breaking of an egg Spontaneous Processes Processes that are spontaneous at one temperature may be nonspontaneous at other temperatures Above 0°C, it IS spontaneous for ice to melt Below 0°C, the reverse process is spontaneous (liquid water freezing) Reversible Processes In a reversible process, the system changes in such a way that the system and surroundings can be put back in their original state by exactly reversing the process Example Equilibrium processes are reversible and spontaneous in both directions Changes are infinitesimally SMALL in a reversible process Irreversible Processes Irreversible processes cannot be undone by exactly reversing the change to the system All spontaneous processes are irreversible What Contributes to Spontaneity? Change in Enthalpy (ΔH) Defined as heat/energy absorbed or given off at a constant pressure Change in Entropy (ΔS) Defined as a measure of randomness or disorder Cannot be directly measured Temperature of the Reaction (T) What is the temperature, or better said, the kinetic energy of the particles in the reaction? Enthalpy’s Contribution to Spontaneity Many (but not all) spontaneous processes proceed with a DECREASE in energy and are EXOTHERMIC (produces heat) at 25°C and 1 atm (STP) Not a direct correlation or a perfect explanation Endothermic (takes in heat) reactions that are non-spontaneous at room temperature often become spontaneous at higher temperatures Increase in energy often increases spontaneity Example The decomposition of limestone (calcium carbonate) occurs at 1100 K and 1 atm At 25°C and 1 atm , this reaction does not occur In summary, ΔH contribution is tied to the temperature of the reaction… What about Entropy? What is It? Entropy can be thought of as a measure of the molecular randomness or disorder of the system Change in entropy is denoted by ΔS First Law of Thermodynamics Energy in the universe is constant Energy cannot be created nor destroyed. It can only be transformed Second Law of Thermodynamics Randomness or disorder of the universe is increasing What are the Variables that Affect Entropy? Entropy on the Molecular Level What increases entropy? Adding particles Adding more particles increases the collisions and the randomness of motion Adding energy/increasing temperature Velocity of particle motions is increased Increasing volume Particles are allowed to roam in greater space; thus, more random motion How is Entropy Affected by Physical States? Entropy increases with the freedom of motion of molecules S (g) > S (l) > S (s) More energy means greater thermal disorder More freedom to move around in space means greater positional disorder What Happens to Entropy in Solutions? Dissolution of a solid Ions have more entropy BUT, some water molecules have less entropy as they are now grouped around the ions Usually, there is an overall increase in S The exception is very highly charged ions that make a lot of water molecules align around them Spontaneous Reactions and Entropy The driving force for a spontaneous process is an increase in entropy of the universe Third Law of Thermodynamics At absolute zero, a pure substance exists as a perfect crystal with no molecular movements No kinetic energy The entropy of a pure crystalline substance at absolute zero is 0 Summary of the Three Laws of Thermodynamics You can’t win, you can only break even You can only break even at T = 0 You can’t reach T = 0 Calculating Entropy For a chemical reaction, the change in entropy (ΔS) under standard conditions is calculated as: 0 ∆𝑆𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 0 𝑛𝑆𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − 0 𝑛𝑆𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 Standard entropies, ∆𝑆 0 , are analogous to standard enthalpies of formation, ∆𝐻𝑓0 Molar entropy values of substances are in their standard states 25°C and 1 atm Units for S are generally J/mol∙K Trends in Standard Entropies Standard entropies tend to increase with increasing molar mass Larger and more complex molecules have greater entropies Note for pure elements: 𝑆0 ≠ 0 ∆𝐻0 = 0 Predicting Relative S0 Values of a System Temperature changes S0 increases as the temperature rises Physical states and phase changes S0 increases as a more ordered phase changes to a less ordered phase Dissolution of a solid or liquid S0 of a dissolved solid or liquid is usually greater than the S0 of the pure solute However, the extent depends upon the nature of the solute and solvent Dissolution of a gas A gas becomes more ordered when it dissolves in a liquid or solid Atomic size or molecular complexity In similar substances, increases in mass relate directly to entropy Increases in complexity (i.e. bond flexibility) relate directly to entropy Example NO has less entropy when compared to NO2 and N2O4 The Relation between Entropy and Enthalpy Introducing Gibb’s Free Energy Introducing Gibb’s Free Energy Gibb’s Free Energy is defined as the energy available in a system that is available to do useful work Standard free energies of formation, ∆𝐺𝑓0 , are analogous to standard enthalpies of formation, ∆𝐻𝑓0 0 ∆𝐺𝑟𝑒𝑎𝑐𝑡𝑖𝑜𝑛 = 0 𝑛𝐺𝑝𝑟𝑜𝑑𝑢𝑐𝑡𝑠 − 0 𝑛𝐺𝑟𝑒𝑎𝑐𝑡𝑎𝑛𝑡𝑠 Gibb’s Free Energy & Spontaneity So far, we have used ∆S to predict the spontaneity of a process However, Gibb’s Free Energy is also related to spontaneity and is especially useful in dealing with the temperature dependence of spontaneity If ∆G is negative, the FORWARD reaction is spontaneous If ∆G is positive, the REVERSE reaction is spontaneous If ∆G is 0, the system is at equilibrium! Calculating ∆G ∆G can be calculated from ∆H and ∆S: 0 ∆𝐺 = ∆𝐻𝑠𝑦𝑠 − 𝑇∆𝑆𝑠𝑦𝑠 This relationship holds true as long as the temperature and pressure remain constant during the reaction There are two parts to the free energy equation: ∆H – the enthalpy term ∆S – the entropy term The temperature dependence of free energy comes from the entropy term The Effect of Temperature on ∆G and Spontaneity By knowing the sign (+ or -) of ∆S and ∆H, we can get the sign of ∆G and determine if a reaction is spontaneous High temperature favors the entropy term Low temperature favors the enthalpy term Calculating ∆G ∆G = 0 ∆Hsys − T∆Ssys The ∆Hrxn can be calculated from ∆Hf at STP The ∆Srxn is also calculated from the ∆S0 at STP The Gibb’s equation allows you to calculate ∆G and verify reaction spontaneity at other temperatures Gibb’s Free Energy and Equilibrium ∆G, ∆G˚, and Keq DG0 describes a reaction in standard state conditions 25°C, 1 atm DG must be used when the reaction is NOT in standard state conditions ∆G is related to ∆G˚ via the equation: ∆G = ∆G˚ + RT ln Q where Q = Reaction quotient R = Universal Gas Constant (8.314 J/K•mol) T = Kelvin temperature Qualitative Relationship Between the Change in Standard Free Energy and the Equilibrium Constant at a Given T ∆G = ∆G˚ + RT ln Q ∆G0 K ∆G0 = 0 K=1 ∆G0 < 0 K > 1 (Product favored) ∆G0 > 0 K < 1 (Reactant favored) • When ∆G0 = 0: ∆Gorxn = - RT ln K • The larger the value of K, the more negative the value of ∆Gorxn Relation between ΔG0 and K as Predicted by ΔG0 = - RT ln K ΔG0 = - RT ln K Gibb’s Free Energy and Equilibrium Position DG0 < 0 DG0 > 0