PHYSICAL CHEMISTRY Principles and Applications in Biological Sciences FOURTH EDITION TINOCO · SAUER · WANG · PUGLISI Periodic Table of t,fre Elements ,, 18 lA - 2A f Li Be 6Mt 9.ot218 24.30110 3B 4B SB 6B 7B 20 21 22 24 2,5 Ca Sc Ti 23 39.89113 40.078 4&.9559 3'1 38 39 11 12 Na Mg 22.- 19 K Rb Sr 8U671 87.62 · -5$ c 8A 13 14 15 16 J7 56 ~8B~ '28 26 27 v Cr Mn Fe 47.88 50.9415 51.9961 54.9381 55.847 40 41 42 43 44 ; Co >'I 58.9332 ' '' 45 y Zr Nb ·Mo Tc Ru~ Rh 88.9059 91.224 92.9064 95.94 (98) 101.67 102.906 57 72 73 74 75 76- •ta Hf Ta w Re· Os Ir 13'1.321 138.906 178.49 180.948 183.84 186.207 190.23 192.22 89 1M 105 Db Sg 107 Rf Bh lOs Hs · (261) (262) (263) (262) (265) ffl 88 Ra +Ac QZ3) 226.025 2%7.628 t Actinide series - 59 ~ Ni Cu Zn 58.693 63.546 65.39 46 47 106.42 107.868 48 78 Cd 112.411 ' 114.818 ·80 79 Au Hg 195.08 ' 196.967 I (269) 200.59 111 110 I (272) 81 Tl 112 I (272) I,;, ,_ J (287) 67 I ~ ' I (289) Sm Eu Gd 65 66 Pm Tb Dy Ho Er Tm Yb Lu 140.115 140.908 144.2.4 (145) 150.36 151.965 151.25 158.925 162.50 164.930 167.26 168.934 113.04 174.967 90 91 92 93 94 95 96 97 98 99 100 101 102 103 (260) Pa 232.038 231.036 63 64 68 69 70 Nd Th 62 2B Pr 60 61 (2~) lB 29 Pt 109 Mt 12 Ce 58 *Lanthanide series 106 11 Pd , Ag 77 Ba Fr 10 u Np Pu A.Jn Cm Bk Cf Es Fm Md No 238.1129 237.048 (244) (243) (247) (247) (251) (252) (251) (258) (259) 71 Lr Atomic masses are relative to carbon-1 For certain radioactive elements, the numbers listed (in parentheses) are the mass numbers of the most stable isotopes The scheme for numbering of groups is explained on page 50 The metals are rand the nonmetals are • · Metalloids are indicated by •· The noble gases are • Elements 110, 111, and 112 have not yet been named I Miscellaneous Conversions and Abbreviations To coavert from: To: calories calories calories electron volts electron volts electron volts electron volts ergs ergs ergs molecule- ergs molecule- joules joules joules joules mol- joules mol- kilowatt-hours kilowatt-hours kcal mol- kcal mol- kcal mol- kilojoules moi- kilojoules mol:- kilojoules mol- ergs joules kilowatt-hours kcalmol- ergs joules kilojoules mol- calories joules joules mol- kcalmol- calories ergs kilowatt-hours ergs molecule-1 kcal mol- calories joUles electron volts ergs molecule- joules mol- electron volts ergs molecule- kcal mol- Multiply by: 4.184 X 4.184 1.162 X 23.058 1.602 X 1.602 X 96.474 2.390 X 10-7 6.022 X 1.439 X 0.2390 107 2.778 X 1.661 X 2.390 X 8.606 X 3.600 X 0.04337 6.949 X 4.184 X 0.01036 1.661 X 0.2390 107 10- 10-12 10- 19 10- 1016 1013 10-7 10- 17 10- 1(}'i 106 10- 14 103 10- 14 Length angstrom = 10- 10 m 10-8 em inch = 2.54 em foot = 30.48 em mile = 5280 ft = 1609 m O.lnm Mass pound = 453.6 g kg = 2.205 pounds Energy erg = g em2 s- joule = kg m s- Force newton = kg m s- = lOS dyn dyne = gems- = 10- N Pressure atmosphere = 760 mrnHg (Torr.) 1.013 x 106 dyn em-2 1.013 X lOS newton m- 1.033 > O consistent with Eqs (3.7) and (3.8) b We have already calculated that q rev ~S = RT ln2 (system) = R ln +0 Molecular Interpretation of Entropy An amount qrev of heat is transferred into the system from the surroundings One way for this transfer to occur reversibly is to choose the surrounding temperature higher than T by only an infinitesimal amount In other words, the surrounding temperature is also T For the surroundings, the heat input is -qrev and AS (surroundmgs) = -qrev -y = -R ln Note that for this reversible process, AS (system)+ AS (surroundings)= is consistent with Eq (3.7) Molecular Interpretation of Entropy The microscopic or molecular interpretation of entropy is that it is a measure of disorder The more disorder, the higher is the entropy Therefore, the second law tells us that the universe is continually becoming more disordered This does not mean that a small part of the universe (the system) cannot become more ordered Every time we freeze an ice tray full of water in the freezer, we are increasing the order inside the ice tray However, the disorder caused by the heat released outside the freezer compartment more than balances the order created in the ice The total disorder in the universe has increased; the total entropy of the universe has increased Many biological processes involve decreases of entropy for the organism itself but they are always coupled to other processes that increase the entropy, so that the sum is always positive Photosynthesis in green plants results in the conversion of simple substances like C02 and H 20 into an enormously complex organism There is a very large decrease in entropy associated with the growth of a plant, but it comes at the expense of an enormous increase in entropy in the Sun to produce the light that is essential for photosynthesis to occur It is a pessimistic but accurate view that anything we will always add to the disorder of the universe Feynman (1963) defines disorder as the number of ways the insides can be arranged so that from the outside the system looks the same For example, mol of ice is more ordered than mol of water at the same temperature, because the water molecules in the liquid may have many different arrangements but still have the properties of liquid water The water molecules in the solid ice can have only the periodic arrangement corresponding to the crystal structure of ice to have the properties of ice The molar entropies of water at 0°C, atm are the following: Entropy mol- H 20(s) H 20(1) H 20(g) 41.0 J K- 63.2JK- 188.3 J K- These values are consistent with the fact that the water molecules in ice are highly ordered, whereas in water vapor the molecules are free to move about in a relatively large space The liquid state is intermediate, but it is more like the solid than the gas in terms of disorder For monatomic elements, the en- 77 78 Chapter The Second Law: The Entropy of the Universe Increases tropy can be qualitatively related to the hardness of an element; hard solids are more ordered and have lower entropies than soft solids This is illustrated for carbon at 25°C, atm: Entropy mol- Characteristic Carbon (diamond) Carbon (graphite) Hard Soft All entropies increase as the temperature is raised, because increasing molecular motion increases disorder and thus increases the entropy Knowing that entropy is a measure of disorder allows us to understand and predict entropy changes in reactions In the gas phase, if the number of product molecules is less than the number of reactant molecules, entropy decreases If the number increases, entropy increases Two examples at 25°C and atm are shown below The superscript in 6.5° specifies that the values are for reactions in which all reactants and products are in their standard states, which we will define later Reaction 2H2(g) + 2(g) ~ 2H20(g) -88.9 PC1 (,~) ~ PCIJ(g} + Cl2(g) 181.9 If the number of molecules is unchanged by the reaction, a small change in entropy-either positive or negative-is expected For reactions in solution, it is more difficult to predict the entropy change because of the large effect of the solvent Two solute molecules may react to form one product molecule, but unless we know what is happening to the solvent-whether it is being ordered or disordered-we cannot predict the change in entropy However, we can rationalize and interpret the measured results A few examples of reactions carried out at 25°C, atm are as follows: Reaction ~ f /w COl- (aq) + H+ (aq)~HC03- (aq) NH 4+(aq) + Col- (aq)~NH3(aq) + HC03- (aq) OH- (aq) + H+(aq) ~H20( f) NH/ (aq) + HC03- (aq) ~C02 (aq) + H 20(!) + NH3(aq) NH3(aq) + H+(aq) ~NH4+ (aq) HC204- (aq) + OH-(aq) ~Cpl-(aq) + H 20(l) 9." ~~(aq)~CH4 (CC14 ) ~1 rJ_J/$f -::;::' +148.1 +146.0 +80.7 +94.2 +2.1 -23.1 +75 Fm the Illest four 'eactions, neut