Lecture 2

# Lecture 2 - ENTROPY "Energy spontaneously...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ENTROPY "Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.” A rock falling A hot frying pan cooling down Iron rus>ng Air leaving a punctured >re Ice mel>ng in a warm room Dispersing Energy is internal energy, Which is molecular “mo>onal energy”: the transla>onal, vibra>onal, and rota>onal energy of molecules. MICROSTATE Molecules in a system translates (moves from one place to other); Rotates (at speciﬁc frequencies); Vibrates (at speciﬁc frequencies) At any instance the translational, rotational and vibrational states of the entire system is called a microstate. Total energy of the system is dispersed through the microstate. In another instance the microstate of the system is different. Energy is dispersed through a different microstate. For a given set of conditions, total energy in each microstate is identical to each other. A change in order is a change in the number of ways of arranging the particles and dispersing their energy of motion, and it is a key factor in determining the direction of a spontaneous process. Spontaneous expansion of a gas evacuated Transla4onal energy level increases; (2 x volume increase; 1 is the number of moles) The entropy increase due to expansion of a gas Total energy remains constant but more ways their energy can be distributed due to expansion of volume • A system with rela4vely few equivalent ways to arrange its components (or dispersion of energy) (smaller W) has rela4vely less disorder and low entropy (lower S). • A system with many equivalent ways to arrange its components (dispersion of energy) (larger W) has rela4vely more disorder and high entropy (higher S). The Concept of Entropy (S) more order less order solid liquid gas more order less order crystal + liquid ions in solu1on more order less order crystal + crystal gases + ions in solu1on Change of Entropy (S) Entropy is a state func4on; depends only on the ini4al and ﬁnal states of the system, not at the path it took ΔSsys = Sﬁnal  ­ Sini>al Conversion of dry ice to gaseous carbon dioxide ΔSsys = SCO2(g)  ­ SCO2(s) >0 Condensa4on of water vapor to liquid water ΔSsys = SH2O(l)  ­ SH2O(g) <0 1877 Ludwig Boltzmann S = k ln W where S is entropy, W is the number of ways of arranging the components of a system, and k is a constant (the Boltzmann constant),(k= R/NA (R = universal gas constant, NA = Avogadro’s number)). NA = 6.02214179×1023 mol ­1 R= 8.314472 JK ­1 mol ­1 R/NA = 1.38 X 10  ­23 J/K W IS A NUMBER; HAS NO UNIT S HAS THE UNIT OF J/K Quan>ta>ve Meaning of Entropy Change For 1 mol of atoms number of microstates is increased by 2NA Wf/Wi = 2NA Entropy Based on Heat Changes Gas is heated and work done on the system ENTROPY Change in the system can be described by ΔSsys= qrev/T T is the Temperature at which heat change occurs and q is heat absorbed by the system The process must be reversible (qrev) the second law of thermodynamics ΔSuniverse = ΔSsystem + ΔSsurroundings > 0 All real processes occur spontaneously in the direc4on of increased entropy of the universe (system + surroundings) If the entropy of the system decreases, increase of entropy of the surroundings must be large enough to compensate the system’s decrease. Standard Molar Entropy (S0) Absolute entropy of a substance can be determined A Perfect Crystal has a Zero Entropy at a Temperature of Absolute Zero Only ONE Microstate exist for a Perfect Crystal—One Way to Disperse Energy Visualizing the eﬀect of temperature on entropy The increase in entropy from solid to liquid to gas Entropy changes when salt is dissolved in water pure liquid pure solid MIX Dissolu>on of ethanol in water Entropy changes when a gas is dissolved in a liquid O2 gas O2 gas in H2O Entropy and vibra>onal mo>on Predic>ng Rela>ve So Values of a System 1. Temperature changes So increases as the temperature rises. 2. Physical states and phase changes So increases as a more ordered phase changes to a less ordered phase. 3. Dissolving a solid or liquid So of a dissolved solid or liquid is usually greater than the So of the pure solute. However, the extent depends upon the nature of the solute and solvent. 4. Dissolving a gas A gas becomes more ordered when it dissolves in a liquid or solid. 5. Atomic size or molecular complexity In similar substances, increases in mass relate directly to entropy. In allotropic substances, increases in complexity (e.g. bond ﬂexibility) relate directly to entropy. Sample Problem 1 PROBLEM: Predic>ng Rela>ve Entropy Values Choose the member with the higher entropy in each of the following pairs, and jus4fy your choice [assume constant temperature, except in part (e)]: (a) 1 mol of SO2(g) or 1 mol of SO3(g) (b) 1 mol of CO2(s) or 1 mol of CO2(g) (c) 3 mol of O2(g) or 2 mol of O3(g) (d) 1 mol of KBr(s) or 1 mol of KBr(aq) (e) Seawater at 2oC or at 23oC (f) 1 mol of CF4(g) or 1 mol of CCl4(g) Sample Problem 2 Explain if these processes are spontaneous or not: (a)  Water evaporates from a puddle in summer (b)  Methane burning in air (c)  An unstable isotope undergoing radioac4ve disintegra4on (d)  A lion chasing an antelope (e)  A son boiled ­egg becoming raw Sample Problem 3 Arrange each group in order of decreasing standard Molar Entropy (S0) (a) Mg, Ca, Ba (b) Hexane (C6H14), benzene (C6H6), cyclohexane (C6H12) (c) PF2Cl3 (g), PF5 (g), PF3 (g) (d)  Graphite, diamond, charcoal (e)  Ice, water (l), water (v) ...
View Full Document

## This note was uploaded on 02/18/2012 for the course CHEM 6C taught by Professor Hoeger during the Spring '08 term at UCSD.

Ask a homework question - tutors are online