I. Entropy A. Entropy is a measure of the number of microstates of a system (the number of ways the system can be arranged). Microstates: Why Entropy Happens--Probability 1 2 3 Entropy is a state function that can be related to the number of microstates for a system (the number of ways the system can be arranged) and to the ratio of reversible heat to kelvin temperature. It may be interpreted as a measure of the dispersal or distribution of matter and/or energy in a system, and it is often described erroneously as representing the “disorder” of the system. Entropy is simply a measure how much the energy of atoms and molecules become more spread out in a process and can be defined in terms of statistical probabilities of a system or in terms of the other thermodynamic quantities. 4 B. The Entropy Scale. The Third law of Thermodynamics states that the entropy of a pure, perfectly ordered crystal substance at 0 K is 0. 1. 2. 3. 4. This gives us an absolute starting place from which to measure entropy. There are no negative values for entropy because nothing is more ordered than a pure, perfectly ordered crystalline substance at 0K. Further, elements in their standard state DO NOT have entropy values of 0!!!! The symbol for entropy is S where So indicates the entropy of a substance at standard temperature (25oC). 5 C. Relative entropies. The 2nd Law of Thermodynamics How does the reaction contribute to the randomness of the universe? This is summarized by the equation: ∆SUniverse = ∆SSystem + ∆SSurroundings 1. There are more ways to arrange the particles in a gas, than in a liquid, so Sgas >> Sliquid ≈ Saqueous 2. There are more available microstates for the particles in a liquid than a solid, so Sliquid > Ssolid 3. Aqueous substances have more entropy than liquid, so Saqueous > Sliquid 4. Elements of higher atomic mass have more entropy than elements of lower atomic mass. 5. The greater the complexity of the molecule, the greater the entropy. (This seems counterintuitive, but with more bonds and more atoms, there are more ways that the bonds can rotate and vibrate. Think of bonds more like springs rather than sticks.) 6 Molecular vibration - Wikipedia Substance and State (J/K mol) Iodine I2(s) I2(g) I2(aq) I(g) I-(aq) ICl(g) 116 261 137 181 106 248 Example: Which has more entropy? a. H2O(l) or H2O(g) b. H2(g) or H2O(g) c. NaCl(s) or NaCl(l) d. Cu(NO3)2 (aq) or Cu(NO3)2 (s) e. Cu(NO3)2 (aq) or CuNO3 (aq) f. N2(g) or N2(l) g. N2 (g) or N2H6 (g) h. F2 (g) or Cl2 (g) Tip: When predicting whether a reaction increases in entropy or decreases in entropy, you should first consider states of matter. If states of matter are the same on both sides, then you should consider how many particles are on each side of the equation (the side with more particles has more entropy). Example: Does entropy of the SYSTEM increase or decrease? A. Boiling water, H2O (l) à H2O (g) B. Dissolving a sugar cube in water, C12H22O11 (s) à C12H22O11 (aq) C. Stalactites being formed by: CO2 (g) + CaO (s) à CaCO3 (s) D. O2 (g) (1 atm, 25oC) à O2 (g) (0.1 atm, 25oC) 7 E. A bottle of wine being chilled: CH3CH2OH (l) (30oC) à CH3CH2OH (l) (20oC) F. Diluting tea that is too strong G. Making diamonds from graphite: C (gr) à C (diamond) H. Opening a can of Diet Coke I. Baking cookies J. 2 H2 (g) à 4 H (g) K. 2H2 (g) + O2 (g) à 2 H2O (g) L. 2 NH3 (g) à N2 (g) + 3 H2 (g) M. Ba(NO3)2 (aq) + CuSO4 (aq) à BaSO4 (s) + Cu(NO3)2 (aq) N. HCl (aq) + NaOH (aq) à NaCl (aq) + H2O (l) O. 2 HNO2 (aq) + CuCO3 (aq) à H2O (l) + CO2 (g) + Cu(NO2)2 (aq) D. Calculations of Entropy Changes: Entropy was originally defined as the change in energy in a process divided by the temperature at which it occurs. The standard entropy change in a chemical or physical process is the change in entropy that accompanies the conversion of reactants to products. For a chemical reaction: Example: Nitrogen dioxide is the red-brown gas that you can sometimes see in bottles of nitric acid and in polluted air. Predict the sign of the entropy change when nitrogen dioxide is formed from its elements in their standard state. Determine the standard entropy change, So, involved in the formation of nitrogen dioxide at 25oC. 8 E. Spontaneity - Two Factors: Enthalpy and Entropy CH4(g) + 2O2(g)→ CO2(g) + 2 H2O(l) Enthalpy: Entropy: ∆H = -802 kJ H2O(s)→ H2O(l) Enthalpy: Entropy: ∆H = 6.03 kJ NaOH(s)→ Na+(aq) + OH-(aq) Enthalpy: Entropy: ∆H = exo 4 Al(s) + 3O2(g)→ 2 Al2O3(s) Enthalpy: Entropy: ∆H = - 3351 Kj F. Calculations using Enthalpy and Entropy ∆SUniverse = ∆Ssystem + ∆SSurrounding ∆SSurroundings = -∆H/T ∆SUniverse = ∆Ssystem + -∆H/T H2O(l) → H2O(s) Is the above process spontaneous at: 1. -10 °C (263 K) 2. +10 °C (283 K) Solving for ∆SSurroundings = -∆H/T -10 °C (263 K) -(-6010 J mol-1 )/263 K = 22.9 J K-1mol-1 +10 °C (283 K) -(-6010 J mol-1 )/283 K = 21.2 J K-1mol -1 Solving for ∆SSystem = -22.0 J K-1 mol-1 ∆SUniverse = -10 °C : ∆Ssystem + ∆SSurrounding -22.0 J K-1 mol-1 + 22.9 J K-1mol-1 = 0.9 J K-1mol-1 +10 °C: -22.0 J K-1 mol-1 + 21.2 J K-1mol -1 = -0.8 J K-1mol-1 9