Solubility, mixtures, non-ideality OUTLINE

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1 Solubility, mixtures, non-ideality Equilibrium? OUTLINE Class exercise next class bring laptop, or use class tablet Enthalpy, Entropy The Gibbs Function ΔG and K Mixtures Chemical Potential 1

Enthalpy 1. "Bond Heat" Can combine reaction ΔH f to calculate ΔH f of the new reaction. Example: 1.

504 kcal/mol add the 2 to get C (graphite) C (diamond) What do we add to what? ΔH f = (94.051-94.

897 kj/mol Enthalpy "phase change heat" Heat of Fusion Δh fus heat absorbed to melt, (-Δh fus = released) Heat of

2 Enthalpy 1. "Bond Heat" Can combine reaction ΔH f to calculate ΔH f of the new reaction. Example: 1. C (graphite) + O 2 (g) CO 2 ΔH f = kcal/mol 2. CO 2 C (diamond) + O 2 (g) ΔH f = kcal/mol add the 2 to get C (graphite) C (diamond) What do we add to what? ΔH f = ( ) kcal/mol ΔH f = kcal/mol = kj/mol Enthalpy "phase change heat" Heat of Fusion Δh fus heat absorbed to melt, (-Δh fus = released) Heat of Vaporization Δh vap heat absorbed to vaporize (-Δh vap = released) + heat - heat Snowflake photos by Wilson Bentley circa Other "kinetic energy heat" If no phase changes and chemical reactions, Δheat ~ ΔT: ΔH = C p ΔT 2

Entropy - S Entropy = system disorder (chaos) Naturals systems prefer minimum energy, maximum entropy Q r = TΔS, at constant P ΔS = C p /ΔT (where C p = heat capacity) The standard state for any

3 Entropy - S Entropy = system disorder (chaos) Naturals systems prefer minimum energy, maximum entropy Q r = TΔS, at constant P ΔS = C p /ΔT (where C p = heat capacity) The standard state for any compound S is determined relative to S of H + (hydrogen) = 0 at STP. Like ΔH, ΔS reaction : ΔS reaction = ΣΔS f (products)- ΣΔS f (reactants) "Free Energy", or the Gibbs Function G Total system energy available for chemical work is known as Gibbs Free Energy, ΔG ΔG reaction = 0 at chemical equilibrium Like other variables of state, ΔG is additive: ΔG reaction = ΣΔG f (products) - ΣΔG f (reactants) Since ΔG = ΔG + RT lnq (where Q is the reaction coefficient, not heat) AT EQUILIBRIUM -How are Q and K related? -What is ΔG? Makes: ΔG = -RT lnk 3

"Free Energy", or the Gibbs Function G In closed systems Specifically: G = f ( H, T*S ) ΔG = ΔH - TΔS So, reactions drive to ΔG = 0 so they drive to minimum (heat) energy (ΔH), and minimum (-ΔS) or

4 "Free Energy", or the Gibbs Function G In closed systems Specifically: G = f ( H, T*S ) ΔG = ΔH - TΔS So, reactions drive to ΔG = 0 so they drive to minimum (heat) energy (ΔH), and minimum (-ΔS) or maximum entropy "Free Energy", or the Gibbs Function G To adjust to none-stp: ΔG = VΔP - SΔT Consider a P-T phase diagram like -> Now change P and T (dp, dt): dδg = ΔVdP ΔSdT = 0 Rearranging, we arrive at the famous Clapeyron Equation (slope in P-T plot): dt = ΔV and because DS = DH/T, dt = TΔV dp ΔS dp ΔH 4

5 Using G and K: Find K eq for malachite precipitation from water? 2Cu 2+ (aq) + CO 2-3 (aq) + 2 OH - (aq) Cu 2 (OH) 2 CO 3 (s) "copper 2+ "carbonate "hydroxyl "malachite" cation" anion" anion" 2 steps: 1) ΔG reaction = ΣΔG f (products) - ΣΔG f (reactants) 2) ΔG o = -RT lnk Step 1 ΔG reaction = ΣΔG f (products) - ΣΔG f (reactants) Make sure your units match (R has units too)! 2Cu 2+ (aq) + CO 2-3 (aq) + 2 OH - (aq) Cu 2 (OH) 2 CO 3 (s) So how do we calculate ΔG reaction? ΔG reaction = ( ) kcal/mol ΔG reaction =-46.02kcal/mol = -46,020 cal/mol Step 2 From ΔG o = -RT lnk, we get ΔG o /(RT) = -lnk -46,020/( ) = -lnk K = e 46,020/( ) K= 5.45 x or about

6 Partial Molar Quantities In a multi-component system => partial molar value e.g. V, P, H, or S as f (molar change (dn) in 1 component) V a ph = dv/dn a (constant T, P): volume of comp a in phase ph depends on the change in volume due to a change in amount of comp a. Assumes that all volumes from different comps add up to 1 phase: V ph = S V a /n a i Partial Molar Volume useful for understanding properties of mixtures: partial molar volume helps evaluate volume change Ex. 1: compare volumes: 1 mole of calcite, CaCO 3, versus 1 mole of dolomite, CaMg[CO 3 ] 2 Ex. 2: volume change in a magma: 1 mole of pure forsterite Mg 2 SiO 4 versus 1 mole of Fo 80 = (Mg 0.8 Fe 0.2 ) 2 SiO 4 i/file:forsterite-olivine-4jg54a.jpg 6

7 Partial Molar Gibbs Free Energy = chemical potential Chemical Potential, μ: - Change in G with compositional change Add up all the μ s and proportions for all components gives ΔG: Σμ i Δn i = ΔG at constant T, P for one component a and at n other = constant, this becomes μ a Δn a = ΔG or μ a = ΔG/Δn a Chemical Potential contd Helpful in: 1. describing open systems: If moles of >=1 component not fixed due to exchange with surroundings (know μ and moles, still get ΔG) 2. studying mixtures and solutions: μ helps determine G of solution relative to pure components In a closed system at equilibrium, ΔG = Σμ i Δn i = 0 7

Chemical Potential contd again μ i applies even when the system lacks

gas phase mixtures c. liquid mixtures d.

the exchange of one component between multiple phases of a closed system.

Δn Rb cpx = 0 μ Rb plag Δn Rb plag = -μ Rb cpx Δn Rb cpx Rb exchanges

8 Chemical Potential contd again μ i applies even when the system lacks "pure" phases: Ex.: a. solid solutions or substitutions in minerals b. gas phase mixtures c. liquid mixtures d. solutes in water Chemical Potential contd again again again μ i look at the exchange of one component between multiple phases of a closed system. Ex. 1: Rb in plagioclase and clinopyroxene μ Rb plag Δn Rb plag + μ Rb cpx Δn Rb cpx = 0 μ Rb plag Δn Rb plag = -μ Rb cpx Δn Rb cpx Rb exchanges between plag <-> cpx: Δn Rb plag = -Δn Rb cpx So: μ Rb plag = μ Rb cpx What s exchange of element between phases known as? 8

9 Chemical Potential contd again again Examples continued: Ex. 2: small amounts of Ar in the atmosphere and oceans... μ atm Ar Δn atm Ar + μ ocean Ar Δn ocean Ar = 0 (at equilibrium) Since Ar transfers air <-> ocean: Δn Ar atm = -Δn Ar ocean (increase in 1 = decrease in other) So: μ Ar ocean / μ Ar atm = 1, from which we can derive Henry s Law (K = P Ar atm / conc Ar ocean ) Chemical Potential contd again 4 For multiple components of a single phase e.g., Rb, Sr, Ba and K in plagioclase Case of ideal mixture the components behave in fractional proportions to how they would in pure substances: no energy effect of interaction of ideal components For systems of i ideal components... μ i = μ i * + RT lnx i μ i * : chemical potential at pure i (X i = 1) and X i is the mole fraction of component i (e.g., X i = n i /n tot ) 9

10 Non-ideality in mixtures What if materials in mixtures do not behave ideally? Gasses Ideal gasses: ideality means no interactions!= real world So add up partial pressures to get total pressure: P i = X i P Total Chemical potential for an ideal gas is then: μ i = μ i * + RT lnp i Non-Ideality contd But most gasses are not ideal Non-ideal: they have an effective pressure, known as the Fugacity, F (often written as f ) Typically F i < P i Fugacity and pressure are related by fugacity coefficient γ i F i = γ i P i Typically, γ i gets lower as P total increases (note: γ i = 1 in an ideal gas; Many gasses behave close to ideally at low P) 10

11 Non-Ideality in Chemical Mixtures In geology mostly F(ugacity) instead of P if high pressure, e.g.: plutonic bodies in the mantle or crust metamorphism of crustal rocks high pressure geothermal fluids In Earth and lab experiments overburden-based lithostatic pressure is important, measured as F Bottom line: F is a measure of effective P and the divergence between F & P is a function of pressure Non-Ideality in ionic aqueous solutions Solute activities (apparent concentrations) in aqueous solutions differ from ideal concentrations due to solute-solute and solutesolvent interaction So similar to gasses, for solutions: μ i = μ i * + RT lnx i Activity, a i : effective concentration of a solute Related to molarity or molality by activity coefficient, γ i : a i = γ i m i What is the difference between molarity and molality? 11

12 Non-Ideality in the class room What do we really mean by activity, or apparent concentration? Activity = Effective Concentration CASE 1 ideal Yah, yah, yah!!!! This example should help to illustrate the point Instructor CASE 2 Non-ideal Blah, blah, blah! Students 4 students (all alert) activity = concentration (ideal case) γ=1 Zzzzzzzzzzz Instructor Students 4 students (1 alert, 3 sleeping) activity (1) concentration (4) (non ideal case) γ=1/4 =

The Second Law of Thermodynamics (Chapter 4)

The Second Law of Thermodynamics (Chapter 4) First Law: Energy of universe is constant: ΔE system = - ΔE surroundings Second Law: New variable, S, entropy. Changes in S, ΔS, tell us which processes made