CHEMICAL POTENTIAL – A QUANTITY IN SEARCH OF RECOGNITION Outline Che Chemic ical Po al Pote tential from th ntial from the e Be Beginn ginning ing 1. Chemical Potential as Basic Concept 2. Main Characteristics of the Chemical Potential Regina Rüffler Rüffler, Georg Job , Georg Job Regina 3. Quantifying the Chemical Potential 4. Influence of the Milieu 5. Outlook c/o. Institute of Physical Chemistry, University of Hamburg 41 st IUPAC World Chemistry Congress Torino, 9 August 2007 1. Chemical Potential as Basic Concept 1. Chemical Potential as Basic Concept Understanding the Chemical Potential Understanding the Chemical Potential A few properties, which can be understood without difficulty For and illustrated by everyday examples, • grabbing an apple, are sufficient to derive numerous useful statements • peeling a potato, about the physical and chemical behaviour of substances. • sewing on a button ..., is not necessary! the knowledge of the hand´s anatomy The chemical potential µ can be interpreted as measure for the general tendency of matter to change For (H ERACLITUS: „Everything flows“), f.e. • handling the chemical potential μ , • bread becomes dry, ∂ ⎛ G ⎞ = ⎜ • predicting chemical reactions, μ ⎟ ∂ • paper yellows, ⎝ n ⎠ p T , • calculating phase diagrams ..., • stone weathers etc. the thermodynamic apparatus is not necessary! Basis of phenomenological characterisation 1
1. Chemical Potential as Basic Concept 2. Main Characteristics of the Chemical Potential Wanted Phenomenological Characterisation An object or living being is characterised by its external properties ♦ The tendency of a substance and not by its internal structure . • to react with other substances, μ • to transform in another state, genotype • to redistribute in space, What is a prairie dog? could be expressed by the same quantity - namely the chemical potential μ . phenotype ♦ The magnitude of this tendency, that is the numerical value of µ • is determined solely by the nature of the substance For identifying a person often a few • and by its milieu (temperature, pressure, concentration, characteristic traits are sufficient: solvent, ...), - height: 5 feet 3 inches - weight: 129 lbs • but not by the nature of the other reactants. - light hair - blue eyes ♦ A reaction , transformation , redistribution proceeds only - 18 years old - dangerous desperado voluntarily if the tendency for the process in the initial state is more pronounced than in the final state. 2. Main Characteristics of the Chemical Potential 2. Main Characteristics of the Chemical Potential Weight as Model Correspondingly to the w eight w e have: The weight may serve as a simple model for The sum of the chemical potentials µ the direct metrization of a physical quantity. on each side of the reaction formula A´ + A´´ + ... → B´ + B´´ + ... Just the sum of the weights G on each side – – positive or negative ones – decides, positive or negative ones – determines, to in which direction a reaction tends. which side the seesaw leans. The candle burns, because 3 µ (O 2 ) + 2 µ ((CH 2 )) > 2 µ (CO 2 ) + 2 µ (H 2 O) Generally: Generally: The left side “wins”, if µ (A´) + µ (A´´) + ... > µ (B´) + µ (B´´) + ... The left side wins, if G (A´) + G (A´´) + ... > G (B´) + G (B´´) + ... Equilibrium is reached, if µ (A´) + µ (A´´) + ... = µ (B´) + µ (B´´) + ... Equilibrium is reached, if G (A´) + G (A´´) + ... = G (B´) + G (B´´) + ... 2
3. Quantifying the Chemical Potential 3. Quantifying the Chemical Potential Correspondingly to the w eight w e have: Reference Point of the Chemical Potential Each substance shows a tendency to change (to react , to The heights of mountains are not referred to the transform , to redistribute ...), in short a kind of „ drive “. A measure µ of geocentre but to the sea level, this „drive“ can be defined in a way analogously to that for the weight. temperatures in everyday life are not referred to absolute zero but to the freezing point of Each realisable reaction is water. comparable to a kind of scale which allows the comparison of chemical Similarly it is useful to choose for the values of the chemical potentials or their sums, respectively. potential a convenient point of reference , for example the pure ele- ments in their most stable modification at standard conditions (298 K But the measurement is often and 101 kPa). Their chemical potential is zero per definition. impossible due to inhibitions. In that For dissolved substances the concentration c in addition to p and T case, we must use indirect methods. must be specified (usual reference value: 1 kmol/m 3 = 1 mol/L). Because we are interested in a first basic knowledge of the Ions can be assigned a chemical potential as well. The most chemical potential, we consider the values at the moment as given. commonly appearing type of ion, H + , receives the µ value of zero. 3. Quantifying the Chemical Potential 3. Quantifying the Chemical Potential Examples for Values of Chemical Potentials Prediction of Possible Reactions Pure and dissolved substances at standard conditions (298 K, 101 kPa) If the chemical potentials of all substances in question are known, then Unit: Gibbs, short G (= J/mol) Substance Formel µ � / kG G their useful application is very simple. Iron Fe|s 0 µ = 0 valid for elements To decide whether a µ < 0 means that the Marble CaCO 3 |s -1128 process is possible or substance can be created Cane sugar C 12 H 22 O 11 |s -1544 not we only need to compare voluntarily from the elements. Water H 2 O|l -237 the sum of potentials in the initial and the final state of the reaction. Paraffin wax ≈ (CH 2 )|s +4 µ > 0 means that the substance tends to decom- Benzene C 6 H 6 |l +125 3 O 2 |g + 2 (CH 2 )|s → 2 CO 2 |g + 2 H 2 O|l pose in the elements. Acetylene C 2 H 2 |g +290 µ ⊖ /kG 3·0 + 2·(+4) > 2·(-394) + 2·(-237) Cane sugar C 12 H 22 O 11 |w -1552 additionally specified standard Ammonia NH 3 |w -27 +8 > -1262 concentration of c = 1 kmol/m 3 process possible! Ca 2+ |w Calcium(II) -553 3
3. Quantifying the Chemical Potential 3. Quantifying the Chemical Potential Dissolution of Marble Dissolution of Marble 1 1 Pocedure: Versuchsdurchführung: Hydrochloric acid is poured over two or Hydrochloric acid is poured over two or three pieces of marble. three pieces of marble. Observation: Foam develops that contains carbon dioxide. Explanation: Calcium carbonate is dissolved by hydrochloric acid, thereby forming gaseous carbon dioxide: CaCO 3 |s + 2 H + |w → Ca 2+ |w + H 2 O|l + CO 2 |g μ � /kG (-1129) + 2·0 > (-553) + (-237) + (-394) -1129 > -1184 reaction possible! 3. Quantifying the Chemical Potential 3. Quantifying the Chemical Potential Ammonia Fountain Ammonia Fountain 2 2 Procedure: Procedure: An inverted round-bottomed flask filled An inverted round-bottomed flask filled with ammonia gas is connected by a with ammonia gas is connected by a glass tube to a reservoir of water. glass tube to a reservoir of water. Observation: Water rushes up into the flask turning purple red as it enters and forming a fountain. Explanation: Ammonia gas is highly soluble in water according to NH 3 |g → NH 3 |w (702 liter ammonia dissolve in one liter water at 20°C!). μ ⊖ /kG -16 > -27 Just a few drops of water are enough to decrease the pressure in the flask so drastically that water is drawn upward into it in a strong jet . 4
3. Quantifying the Chemical Potential 3. Quantifying the Chemical Potential Carbide Lamp Carbide Lamp 3 3 Procedure: Procedure: Water is dripped cautiously onto some Water is dripped cautiously onto some lumps of calcium carbide. lumps of calcium carbide. Observation: The produced gaseous ethyne burns with a bright and sooty flame. Explanation: Calcium carbide reacts with water under formation of ethyne (acetylene) according to CaC 2 |s + 2 H 2 O|l → Ca(OH) 2 |w + C 2 H 2 |g μ ⊖ /kG (-68) + 2·(-237) > (-867) + (+209) -542 > -658 also substances with positive μ can be produced 4. Influence of the Milieu 4. Influence of the Milieu Temperature and Pressure Dependence Exam Example of Use: Melt ple of Use: Melting, Evap ing, Evaporatio oration Only in a zero approximation µ can be considered to be constant. At low temperatures (nearly) all gaseous substances are solid, because A more detailed approach considers the temperature and pressure µ (B|s) < µ (B|l) << µ (B|g) . dependence of µ . Often linear approaches are sufficient: = + ⋅ = + ⋅ μ μ α Δ T μ μ β Δ p Since liquid 0 0 solid 0 > α (B|s) > α (B|l) >> α (B|g) µ 0 : starting value of the chemical potential all potentials increase when the For the temperature ( α ) and pressure coefficients ( β ) of the chemical substances are heated we can expect potential of a substance B the following rules are valid: that the order will invert at higher 0 > α (B|s) > α (B|l) >> α (B|g) temperatures and all substances will melt and finally vaporize. 0 < β (B|s) < β (B|l) <<< β (B|g) If the values of µ und α are known the melting, boiling, and Already these qualtitative rules allow many useful conclusions. sublimation points can be calculated, but also decomposition temperatures etc. are available. 5
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