Electrochemistry & Solutions 1. Solutions and Mixtures Department of Chemistry Electrochemistry & Solutions 1. Solutions and Mixtures Year 1 – Module 3 8 Lectures Dr Adam Lee afl2@york.ac.uk

Aims To: Understand physical chemistry of solutions and their thermodynamic properties  predict/control physical behaviour  improve chemical reactions Link electrochemical properties to chemical thermodynamics  rationalise reactivity.

Synopsis Phase rule Clapeyron & Clausius-Clapeyron Equations Chemical potential Phase diagrams Raoults law (Henry’s law) Lever rule Distillation and Azeotropes Osmosis Structure of liquids Interactions in ionic solutions Ion-ion interactions Debye-Huckel theory Electrodes Electrochemical cells Electrode potentials Nernst Equation Electrode types Recommended Reading R.G. Compton and G.H.W. Sanders, Electrode Potentials Oxford Chemistry Primers No 41. P. W. Atkins, The Elements of Physical Chemistry, OUP, 3rd Edition, Chapters 5, 6 & 9. P. W. Atkins, Physical Chemistry, OUP, 7th Edition, Chapters 7, 8 & 10 OR 8th Edition, Chapters 4, 5, 6 & 7.

Phase Diagrams

Vacuum Pump

No. of degrees of freedom No. of components No. of phases

Gibbs Free Energy Josiah Willard Gibbs 1839 -1903 Josiah Willard Gibbs Gibbs Free Energy American mathematical physicist developed theory of chemical thermodynamics. First US engineering PhD…later Professor at Yale.

1799 - 1864 Benoit Paul Emile Clapeyron Parisian engineer and mathematician. Derived differential equation for determining heat of melting of a solid

Modified eqn. for Liquid/Gas and Solid/Gas Lines: Clausius - Clapeyron Eqn. Maths dx/x = dlnx dp/p = dlnp = ò dx x n 1 + 2 T dT dp V H D Clapeyron Equation Rudolf Julius Emmanuel Clausius 1822 -1888

Clausius-Clapeyron Equation

99

GA = GoA + nART ln pA, GB = GoB + nBRT ln pB Consider ideal gas at constant temperature: dG = Vdp – SdT = Vdp Since pV = nRT, If initial state 1 = STP (1 atm) In general for a mixture AB: GA = GoA + nART ln pA, GB = GoB + nBRT ln pB since GA = nAA A = Ao + RT ln pA

p = pA + pB

nA nB nA+ nB Ginitial = nAA + nBB = nA[ + RTlnp] + nB[B + RTlnp] yA yA yB yB Ginitial = nAA + nBB = nA[ + RTlnp] + nB[B + RTlnp] Gfinal = nA[ + RTlnyAp] + nB[B + RTlnyBp] G = Gfinal - Ginitial = RT[nAlnyAp – nAlnp + nBlnyBp - + nBlnp] nA nB nA+ nB A B Initial Final ya yb Gmixing ya yb

yA yA yB yB yA yA yB yB Gmixing Smixing ya ya 1 yb 1 yb

 Chemical Potential (in English!) G  ln(pressure) Molecules acquire more spare energy Gibbs Free Energy Greater “chemical potential”  G  ln(pressure) Pressure Low Pressure High Pressure Constant Temperature Effect of environment on this free energy Energy free for molecules to “do stuff”at STP Gmolar = G molar + RT lnp

Why do we use Chemical Potential? Gibbs Free Energy (G) is total energy in entire system available to “do stuff” - includes all molecules, of all substances, in all phases G = nAA + nBB For single component e.g. pure H2O For mixtures e.g. H2O/C2H5OH No real need to use  Free energy from 2 sources G = nH2OH2O Free energy only comes from H2O G = nH2OH2O+nEtOHEtOH  tells us how much from H2O versus C2H5OH

Why do we different molecules have different Chemical Potentials? Involatile Volatile Ethanol can soak up much more energy in extra vibrational modes and chemical bonds - will respond differently to pressure/temperature increases Chemical Potential : 1. A measure of "escaping tendency" of components in a solution 2. A measure of the reactivity of a component in a solution Free Energy (G) &  Gas-phase molecule Liquid-phase Solid-state Pressure

Raoult's law Volatility eqns. of straight lines passing thru origin Total pressure above boiling liquid

lnxA xA runs between 0 (none present) to 1 (pure solution) Mixing (diluting a substance) always lowers xA  this means mixing ALWAYS gives a negative lnxA lnxA Mixing always lowers  Pure B Pure A Dilution xA 1

Volatile Involatile

Volatile Involatile

Case 2: -ve deviation A more attracted by B (e.g. CHCl3 + acetone) mixH = < 0 b.pt. > ideal A B Case 3: +ve deviation A less attracted by B (e.g. EtOH + water) mixH = > 0 b.pt. < ideal

Summary: Raoult’s Law for Solvents Proportionality constant pA = xA . pAΘ Total pressure Volatile high vapour pressure Liquid p o A 1 x · Partial pressure of A Involatile low vapour pressure p pBΘ 1 x o B Partial pressure of B pB = xB . pBΘ A B

= tendancy of system to increase S High p0ө(A) Low p0ө(A) High order: low S Less order: higher S A A A A Strong desire to  S Less need to  S Boiling of A favoured A happier in liquid p0ө = vapour pressure = tendancy of system to increase S

Proportionality constant Amount in solution

Dissolution is EXOTHERMIC For dissolution of oxygen in water, O2(g) O2(aq), enthalpy change under standard conditions is -11.7 kJ/mole.

Consider O2 dissolution in water: pH2O pO2 Solvent: H2O Solute: O2 H2O O2 Henry's law accurate for gases dissolving in liquids when concentrations and partial pressures are low. As conc. and partial pressures increase, deviations from Henry's law become noticeable Consider O2 dissolution in water: Important in Green Chemistry for selective oxidation Cinnamic Acid Cinnamaldehyde Cinnamyl Alcohol Similar to behavior of gases - deviate from the ideal gas law at high P and low T. Solutions obeying Henry's law are therefore often called ideal dilute solutions. Aspects of Allylic Alcohol Oxidation Adam F. Lee et al, Green Chemistry 2000, 6, 279

 A yA xA

Liquid-Gas Distribution Volatile Involatile B A LIQUID GAS Lever Rule Tie-line LIQUID GAS A B A-B Composition Liquid-Gas Distribution

Example Problem The following temperature/composition data were obtained for a mixture of octane (O) and toluene (T) at 760 Torr, where x is the mol fraction in the liquid and y the mol fraction in the vapour at equilibrium The boiling points are 110.6 C for toluene and 125.6 C for octane. Plot the temperature/composition diagram of the mixture. What is the composition of vapour in equilibrium with the liquid of composition: 1. x(T) = 0.25 2. x(O) = 0.25 Boiling/ Condensation Temperature Liquid Vapour x(T) = 1, T = 110.6 C x(O) = 1, x(T) = 0, T = 125.6 C P.W. Atkins, Elements of Phys.Chem. page 141

y1 boiling  x1 x2 cool y2

Case 2: -ve deviation A more attracted by B (e.g. CHCl3 + acetone) mixH = < 0 b.pt. > ideal A B Case 3: +ve deviation A less attracted by B (e.g. EtOH + water) mixH = > 0 b.pt. < ideal

azeotropic composition

A B Residue Distlllate B A

Topics Covered (lectures 2-4)  Chemical Potential - A(l) = A(l) + RTlnxA - A(g) = A(g) + RTlnpA  Mol fractions - A = nA / nA+nB  Raoult’s Law - pA = poA xA pB = poB xB - ideal solutions - +ve/-ve deviations  Vapour-pressure diagrams - Tie-lines - Lever Rule

Solutions Equations Phase Rule F = c - p + 2 c = components degrees of freedom p = no. of phases Clapeyron Equation H = enthalpy of phase change V = volume change associated with phase change Clausius-Clapeyron Equation or Mol fractions xA = nA / nA+nB ni = mols of i yA = pA / pA + pB pi = partial pressure of i Raoults Law pA = poA xA and pB = poB xB Lever Rule (for tie-line joining phases via point a) nl =no. moles in liquid phase nv =no. moles in liquid phase

A(solution) < A(solvent) Contains solute (e.g. NaCl, glucose) WHY?!!! Solvent A A(l) = A(l) + RTlnxA