Thermodynamics IV - Free Energy and Chemical Equilibria Chemical Potential (Partial Molar Gibbs Free Energy)

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1 Thermodynamics IV - Free Energy and Chemical Equilibria Chemical Potential (Partial Molar Gibbs Free Energy) increase in the Gibbs free energy of the system when 1 mole of i is added to a large amount of the system at constant T and P G = n1 1 + n2 2 B A B A dg = idn 1 - idn 1 = ( i - i) dn1 ( - ) < 0 - dg < 0 - spontaneous. B i B i A i ( - ) > 0 - dg > 0 - non-spontaneous B i A i ( - ) = 0 - dg = 0 - at equilibrium A i spontaneous processes proceed from a state of high chemical potential to one of lower chemical potential For the reaction: aa + bb cc + dd G = (d + c - (a + b ) D C) A B 1

2 Reactions of Gases - Dependence of on P At constant T, for an ideal gas: If P 1 is taken as standard state, then this becomes: In a mixture of ideal gases, partial pressures are used: 2

3 Equilibrium Constant CHEM Review Test III We derived the following equations for ideal gases: G = -RTlnK G = G + RTlnQ where for the reaction: aa + bb cc + dd The pressures used to calculate Q are the partial pressures of each species, measured in atm and divided by 1 atm. Thus they are unitless values and Q is unitless. Similarly K is unitless. G - all species present at standard state G - any other set of conditions specified K, relates to G which relates to standard state concentrations, and not to G (at equilibrium) which is 0. Q>1- unfavourable contribution to G. Q<1- favourable contribution to G. Another form of this equation is: Q > K - G > 0 - non-spontaneous Q < K - G < 0 - spontaneous 3

4 Non-ideal Systems Activity A = A + RTlnaA Activity effective pressure or effective concentration corrects the measured concentration for any nonideal behaviour standard state must be specified, when at standard state, a=1 unitless quantity For the reaction: aa + bb cc + dd K is calculated using the activities of all the species 4

5 Standard States Ideal Gases partial pressure of 1 atm - = RTlnP A A A Real Gases the extrapolated state where P A is 1 atm, but the properties are extrapolated from low pressures where the behaviour is ideal A rangefrom 0 to 1 low P - all gases ideal- A 1 as P 0 atmospheric P ~ 1- can be treated as ideal A - = RTln P = RTln + RTlnP P, <1 A A A A A A A Solids/Liquids pure substance at 1 atm pressure a = 1 A 5

6 Solutions a A = AconcentrationA A, depends on the activity of the other components concentration of A, can be: mole fraction, molarity or molality Solvent Standard State the pure component uses mole fraction as X A 1, A 1, and a A XA Very dilute solutions asolvent 1 Dilute or ideal solutions asolvent X Real solutions asolvent X Solute Standard State solvent solvent extrapolated state where c is 1 M or 1 m but the properties are extrapolated from very dilute solution 6

7 Molarity -1 mol L or M, symbol is c a A = A ca ca 0, A 1 and a A 1 Dilute or ideal solutions Real solutions a A = c a = A A AcA Molality -1 mol kg, symbol is m a = m m 0, 1 and a 1 A A A A A A Dilute or ideal solutions Real solutions 7 a A = ma a = m A A A m more accurate than c - mass can be more accurately measured than volume is not dependant on temperature Biochemists for H is =1 when the [H ] = 10 M or ph 7.0 a of the other species in solution are set equal to the sum of all the concentrations of all the species of that molecule at ph 7.0 don t need ionization constants and concentrations of the individual species 0 G ' specifies reactions run at ph 7 with all other reactants and products at 1 M concentration

8 Activity Coefficients of Ions often set to 1 to simplify calculations good for small, uncharged species, and singlycharged ions at low c not good for multiply- charged species and higher c activity coefficients for cations and anions cannot be measured separately - only a mean activity coefficient for an ion-counterion pair for a 1:1 electrolyte ± = ( + ) ½ - 2 a for a 1:2 electrolyte ± = ( + ) - for a 1:3 electrolyte ± = ( + ) 3 ¼ - for calculation of individual activity coefficients in very dilute solution - the Debye-Hückel equation log = 0.509Z 2 I ½ i i 8

9 Calculation of Equilibrium Concentrations assume that all of the relevant equilibrium constants are known, and that the solution is ideal so all activity coefficients are 1 problem is algebraic, you must have as many equations as there are unknown species equations include: mass balance, charge balance, and equilibrium expressions assumptions and simplifications can be made based on past experience and knowledge of the system 9

10 Effect of T on K exothermic reaction - increasing T shifts reaction to reagent side endothermic reaction - increasing T shifts reaction to product side van t Hoff equation holds over small ranges of T (~50 K) where H is constant van t Hoff plot: plot of lnk vs 1/T, slope = - H /R and a y-int= S /R Effect of P on K for ideal gases, K is independent of pressure this does not mean that the partial pressures of all the species involved does not change with pressure Effect of a Catalyst on K K is not effected by a catalyst Thermodynamics of Metabolism Reading Assignment: Tinoco pp

11 G and Electrochemistry CHEM Review Test III direct measurement of the G G = -nf inert electrodes, presence of electrolyte bubbling of gases, salt bridge, cell notation Standard Reduction Potentials potentials can only be measured for a cell zero point reference half-cell is: + - H (aq, a=1) + e ½H 2 (g, P=1 atm) =0.000 V tabulated standard potentials cell = cathode - anode standard potentials are not multiplied by stoichiometric coefficients Concentration Dependence of The Nernst Equation: = - RT/nF lnq or at 25 C: = /n logq When G = 0, =0 and = RT/nF lnk Biological Redox Reactions Reading Assignment: Tinoco pp

12 Thermodynamics V - Free Energy and Physical Equilibria One Component Systems - Phase Equilibria one component, two phases for the two phases is equal at constant T and P a plot of vs T is linear, with a slope of lines intersect at the T f and Tb G increases with increasing P greatest change is observed for the vapour phase T f and T b shift to higher T with an increase in P shift in T f assumes that the V l > V s - not true for water Classius-Clapeyron Equation variation of vapour pressure with T plot of lnp vs 1/T, slope= assumes that does not vary with T for melting points: 12

13 Phase Diagrams plot P vs T for all three phases of a pure substance can determine vapour pressure at any T and bp, mp at any P normal bp is T where P = 1atm on L/V line normal mp is the T where P = 1 atm on the S/L line triple point, critical point Partial Molar Volumes for an ideal solution, the molar volumes of the pure substances add to the volume of the solution for a real solution they don t and partial molar quantities must be used depends on intermolecular forces between like and unlike molecules 13

14 Two or More Component Systems - Solutions relates the potential of a component of a solution to the potential of the same species in the pure state at the same temperature through the ratio of the vapour pressure of the component in the solution to the vapour pressure of the component in the pure state adding a solute to a solvent decreases the chemical potential of the solvent Raoult s Law applies to solvent in many solutions and both components of an ideal solution Positive deviation intermolecular forces between unlike molecules are less than those between like molecules vapour pressure > an ideal solution Negative deviation intermolecular forces between unlike molecules are stronger than those between like molecules vapour pressure < an ideal solution 14

15 Henry s Law vapour pressure of a volatile solute follows Henry s law P 2 = kx2 k = Henry s law constant (atm or torr) also be written P 2 = k m 2 - m = molality, k (atm -1 mol kg of solvent) holds only for dilute solutions solubility increased if solute reacts with solvent or is complexes with something else in solution Ideal Solutions intermolecular forces between the molecules are equal whether the molecules are alike or not H mix = 0 and V mix = 0 the solvent and solute obey Raoult s law over the entire range of X Real Solutions ideal dilute solutions no interaction between solute and solvent solvent obey s Raoult s law solute obey s Henry s law the activity coefficients are assumed to be 1 real solutions activity coefficients 1, deviate from both Raoult s and Henry s laws 15

16 Colligative Properties CHEM Review Test III changes are due to changes in chemical potential of solvent in solution versus pure solvent depend only on the number of solute molecules and not on the kind of solute used to determine molecular weight of the solute applies to ideally dilute solutions with non-volatile, non-electrolyte solutes Vapour Pressure Lowering P 1* - P 1 = P = X2P* 1 this is not an effect of changes in intermolecular forces - occurs even in ideal solutions an entropy effect solute molecular weight (M ) can be found using: 2 method is limited vapour pressures cannot be measured as accurately as other parameters sensitive to temperature for high molecular weights: change in vapour pressure is too small to measure; may be more change due to impurities than to the solute under study 16

17 Boiling Point Elevation at T b, vapour pressure = P ext, dissolution decreases solvent vapour pressure and increases T b equilibrium between solution and solvent vapour dissolution decreases the of the solvent by RTlnX 1 plot of vs T: line is lower than pure solvent - higher T for the intersection with vapour phase Freezing Point Depression equilibrium between solution and solid solvent plot of vs T - lower T for the intersection between the liquid and solid phases phase diagram: solid/liquid and liquid/vapour lines are lowered, no change in the solid/vapour line 17

18 Solubility equilibrium between solution and solid solute works best for slightly soluble solutes can use any convenient concentration units Osmotic Pressure solution is separated from the pure solvent by a semipermeable membrane - solvent will move from higher to lower osmotic pressure is the pressure that must be applied to a solution to keep it in equilibrium with the pure solvent at the same temperature = crt determining molecular weight of the solute = RT most useful for determining molecular weights larger changes and more accurate measurements pressure is due to any solutes which cannot pass through the membrane - can be selected to be permeable to everything but the solute of interest 18

Lecture 6. NONELECTROLYTE SOLUTONS

Lecture 6. NONELECTROLYTE SOLUTONS NONELECTROLYTE SOLUTIONS SOLUTIONS single phase homogeneous mixture of two or more components NONELECTROLYTES do not contain ionic species. CONCENTRATION UNITS percent