Enthalpy vsT:Kirchhoff’sLawxablab.ucsd.edu/15/u3.pdf · Crystallization/freezing...
Transcript of Enthalpy vsT:Kirchhoff’sLawxablab.ucsd.edu/15/u3.pdf · Crystallization/freezing...
Enthalpy vs T: Kirchhoff’s Law Can we start from ΔH at T1 and calculate
ΔH at another temperature T2? By defini<on : The heat capacity itself depends on
temperature, but near 270-‐370K in most bio logical cases we can assume Cp=const
H (T2 ) ≈ H (T1)+CPΔT
PP T
HC ⎟⎠
⎞⎜⎝
⎛∂
∂≡
dTCTHTH P
T
T∫+=2
1
)()( 12
Gustav Robert Kirchhoff, 1824-‐1887, a German physicist
Kirschhoff’s Law: Example • Enthalpy of forma<on of aspirin
molecule is 736 kJ/mol at 298K and its heat capacity is 225 J/(mol K). Find ΔH and H at 36.6 C
• Solu<on:
736+0.225 (36.6-‐25.0)~739 kJ/mol
TCTHTH PΔ+≈ )()( 12
Enthalpy and Internal Energy • For liquids and solids because the thermal expansion is small. • Even if gas is produced in a reac<on, the extra ‘work’ is only: H – U = PV = RT = 2.5 kJ/mol = 0.6 kcal/mol that is much smaller than a typical process or transi<on in liquids or solids (e.g. burning or dissolu<on, or par<<on) • Enthalpy characterizes the internal energy changes (corrected
by the pressure effects) in any of the P-‐Pharm-‐related transi<ons
ΔH ≈ ΔU
Summary Constant Volume Constant Pressure
Defines Heat at constant volume Heat at constant pressure
Energy Internal Energy, U Enthalpy, H=U+PV Contribu<ons Total poten3al and kine3c
energy Total energy shi7ed by PV
Heat Capacity
Ideal Gas Cv= ½RNDOF (excited at T)
Increments
Ground State Only ΔU with respect to a described ground state (0) makes sense. CV does not depend on U0
Same for ΔU and CP
Cp =Cv +P∂V∂T
Cv =∂U∂T
Cp =Cv + RΔU ≈ CVΔT ΔH ≈ CPΔT
Specific Heat Capacity (per mass)
• Enthalpy: H = U+PV • P=const: ΔH=q • Calorimetry: ΔH= smΔT
s : specific heat capacity, swater = 4.186 j/(g °C) Or 1 cal/(g °C) in calories
Cau<on about the sign of heat q: exothermic reac<on means NEGATIVE heat.
ΔH between two states with the same element composi<on at constant
pressure
• State 1, H1 (P) • State 2, H2 (P)
ΔH shows which state has lower internal energy (corrected by PΔV) ΔH defines if the heat is produced or absorbed during the transi<on
ΔH = H2 – H1=q
Reac<ons and Transi<ons Forward Reverse State 1 State 2 Comments Examples
Transitions of pure substances Condensation Evaporation (vap) Gas X(g) Liquid X(l)
Crystallization/freezing Melting/Fusion(fus) Liquid X(l) Solid X(s) Depends on crystal Deposition Sublimation Gas X(g) Solid X(s) Iodine, dry ice
Solid phase transition (trs) - CrystalFormA X(sA) CrystalFormB X(sB) Insulin crystal forms Isomerization - Isomer A Isomer B Thalidomide stereo-
isomerization Transitions in mixtures
Mixture separation Mixing (mix) Separated pure liquids or gases Mixture Emulsion preparation
Precipitation/Crystallization Dissolution X(aq) X(s) Depends on crystal form/ composition
Making/dissolving drug powders; kidney toxicity
“Boiling” Gas dissolution X(aq) X(g) In mixtures: T=f(Concentrations)
Inhalers, Dissolution of N2, O2 or CO2 in blood
Solute partition between immiscible liquid phases - Solute in phase A
(e.g. water) Solute in phase B
(e.g. octanol) Passive membrane permeation, logP
Binding (b) Dissociation (d) P + L PL (complex) Binding of drugs to protein targets or carriers
Reduction/Electron gain (eg) Oxidation X + e– X– Protonation Deprotonation A– or B AH or BH+ Drug (de)ionization
Chemical reactions Generic chemical reaction (r) - Reactants Products Metabolic transformations
Formation (f) Atomization (at)* Elements (standard states) X (s,l,g,aq) May be imaginary Universal currency,
tabulated - Combustion Oxides Substance + O2
A practical method for ΔHf° determination
Activation (‡) Deactivation X in ground state X activated
Chemical energy of a drug • Enthalpy gets lower as covalent bonds are formed
• Burning (reac<on with O2) is an overall increase of the number of bonds and/or the ‘strengths’ of bonds. Some bonds are formed, some broken but to total balance is more bonds or stronger bonds.
• The reference states for the ΔHf values are not isolated single atomic elements (see the next slide)
Nitroglycerin: drug or dynamite?
• used to treat angina and heart failure since 1879
• Mechanism: converts into Nitric Oxide (�NO), a potent vasodilator, wound healing
• NO-‐synthase ac<vated by garlic, morphine, L-‐arginine increases NO
• 4 C3H5(ONO2)3(liq) è12 CO2 + 10 H2O + 6N2 + O2 +4�1.5 MJ of heat
• Density = 1.6 g/mL (MM 227.09) , 4 moles -‐> 570 mL; Products: 710 L
Ascanio SobreroFirst synthesized NG
Alfred NobelFellow student of Sobrero Warning: Nitroglycerin patch explosions during defibrilla<on may be
due to voltage breakdown involving the metal mesh in some patches.
Enthalpy of forma<on • Imaginary reac<on: forma<on of a substance, in a given state (s/l/g/
aq), from its elemental components, in their standard states. (aq means aqueous solu<on )
• The reac<on can occur at different T and P condi<ons • ΔHf° is the molar enthalpy of forma3on • The standard state of a substance, mixture, or solu<on is an arbitrarily
chosen reference point; open its state at STP: P = 1 bar, T = 273 K).
• The standard states of elements are: – Liquid: Hg and Br2 – Gas: He, Ne, Ar, Kr, Xe, Rn (inert gases) an H2, O2, N2, F2, Cl2 – Most stable solid allotrope: other elements (e.g. graphite for C)
• ΔHf° for an element in its standard state is 0. • ΔHf° values for many substances are tabulated. • E.g. hsp://webbook.nist.gov/chemistry/ • Solid allotrope (allo-‐ other, trope – form)
Some ΔHf° values at 250C [kJ/mol]
Mercury, bromine liquid Hg, Br2 0
Inert gases gas He, Ne, Ar, Kr, Xe, Rn 0
Hydrogen, oxygen, nitrogen, fluorine, chlorine gas H2, O2, N2, F2, Cl2 0
Carbon Solid (graphite) C 0 Carbon Solid (diamond) C 1.8 Ammonia aqueous NH3 -‐80.8 Ammonia gaseous NH3 -‐46.1 Sodium carbonate solid Na2CO3 -‐1131 Sodium chloride (table salt) aqueous NaCl -‐407 Sodium chloride (table salt) solid NaCl -‐411.12
Sodium chloride (table salt) liquid NaCl -‐385.92
Sodium chloride (table salt) gaseous NaCl -‐181.42 Sodium hydroxide aqueous NaOH -‐469.6 Sodium hydroxide solid NaOH -‐426.7 Sodium nitrate aqueous NaNO3 -‐446.2 Sodium nitrate solid NaNO3 -‐424.8 Sulphur dioxide gaseous SO2 -‐297 Sulphuric acid liquid H2SO4 -‐814 Silica solid SiO2 -‐911 Nitrogen dioxide gaseous NO2 +33 Nitrogen monoxide gaseous NO +90 Water liquid H2O -‐286 Water gaseous H2O -‐241.8 Carbon Dioxide gaseous CO2 -‐393.5
Trading Bond Energies to Reduce H Bond Energy (kJ/mol). The forma<on energy is Nega<ve. 297 H-‐I 347 C-‐C 163 N-‐N 364 H-‐Br 611 C=C 418 N=N 368 H-‐S 837 C:::C 946(315)N:::N 389 H-‐N 305 C-‐N 222 N-‐O 414 H-‐C 615 C=N 590 N=O 431 H-‐Cl 891 C:::N 436 H-‐H 360 C-‐O 464 H-‐O 736 C=O 565 H-‐F 339 C-‐Cl 151 I-‐I 142 O-‐O 159 F-‐F 498(249) O=O 193 Br-‐Br 243 Cl-‐Cl You need posi<ve energy to break a bond
Forward and Reverse Processes
• Standard enthalpy changes of forward and reverse processes must differ only in sign
• Example: vaporiza<on and condensa<on (T=373K):
00ABBA HH →→ Δ−=Δ
ΔHwater→vapor0 = 40.68kJ /mol
ΔHvapor→water0 = −40.68kJ /mol
Thermodynamic Cycle • Choose mul<pliers by stoichiometry and orient transi<ons
• Go clockwise and ΣΔHXY=0
• Flip a sign of ΔH if arrow is in the opposite direc<on.
B
C D
A
€
ΔHA→B0 + ΔHB→C
0 − ΔHD→C0 − ΔHA→D
0 = 0
Example: 4 states and 3 known transi<ons
ΔH ?
Cycle: drug binding example
DrugConf_A + Protein → DrugConf_B + Protein
[DrugConf_A•Protein] → [DrugConf_B•Protein]
ΔH1 -‐ΔH2 -‐ ΔH3 + ΔH4=0
ΔH1
ΔH2
ΔH3 ΔH4
Hess’ Law • From heats of forma<on to the heat of reac<on
• Direct consequence of the fact that H is a state func<on
• Watch stoichiometry coefficients (νi). Example:
2H2 + O2 => 2H2O νΗ2 =2 νΟ2 =1 νΗ2Ο =2
€
ΔHreaction0 = ν p∑ ΔH f ( products)
0 − νr∑ ΔH f (react )0
Elements
Products Reactants
Germain Hess (1802-‐1850) Swiss-‐born Russian chemist and doctor
Use: H(T)=CpΔT to calculate ΔH at higher temperature
Thermochemical Characteriza<on of Reac<ons and Transi<ons
Ini<al State ⇒ Final State • ΔH = H(final state) – H(ini<al state) • ΔH ≡ heat of reac<on or transi<on
– ΔH < 0 means “⇒” is exothermic (produces heat) – ΔH > 0 means “⇒” is endothermic (absorbs heat)
Covalent Bond forma<on is exothermic • Coun<ng bonds: Example: burning
2 H2 (2 bonds) + O2 (1 bond) => 2H2O (4 bonds) Balance: + 1 bond ΔH is nega<ve Number of covalent bonds increases : exothermic
Reac<on examples: enthalpy
ΔH – + –TΔS
–
+ Bonds form or get stronger, heat
Bonds break, or get weaker, cold
• Burning (covalent bonds formed)
• Freezing (non covalent) • Condensa<on • Acid-‐base
neutraliza<on
• Mel<ng • Evapora<on (always)
Example: dissolu<on • Drug(solid) + H2O ⇔ Drug(aq) • Molar heat of reac<on at infinite dilu<on:
1 mole of drug dissolved at infinite amount of H2O (drug already present in solu<on may affect dissolu<on enthalpy)
• No covalent bonds change during dissolu<on (except pH-‐dependent protona<on/deprotona<on)
• The interac<on balance is delicate, includes drug-‐drug water-‐water and drug-‐water bond strengths.
• If the reac<on involves strong non-‐covalent bond breakage, it may be endothermic
• If crystal interac<ons are weak but drug-‐water interac<ons are strong – dissolu<on is exothermic
• Q: does nega<ve value mean dissolu<on?
Drug Dissolu<on: Micro-‐crystal size affects kine<cs/rates but not equilibrium (ie whether dissolves)
HCl NO2-‐NH4-‐ NH3 KOH CsOH NaCl KClO3 CH3COOH NaOH
Molar heat of dissolu<on at 298 K Substance ΔH dissolution
(kJ/mol) HCl (gas) -74.84 no gas interactions, strong water int Ammonia (gas) -30.50 Acetic Acid (liquid) -1.51 NaCl 3.88 Ammonium Nitrate 25.69 Potassium Chlorate 41.38 Lidocaine HCl 43.5 strong crystal int, weaker water int Procaine HCl 30.5
Balance of ΔH contribu<ons in dissolu<on 1. Breaking solute asrac<ons for liq or solids (endothermic) 2. Breaking water-‐water asrac<ons (endothermic) 3. Forming water-‐solute interac<ons (exothermic)
Ice Packs • Ammonium nitrate and ammonium chloride dissolve in water endothermically
• When broken: mixing (+NH4 )(-‐NO3) with water • Exchanging strong ionic bonds for weaker polar bonds (less bonds -‐> posi<ve ΔH -‐> cold)
• For ammonium nitrate ΔH dissolu<on = +25.69 kJ/mol
Heat Pads • Crystalliza<on: Sodium-‐acetate : weaker bonds in water to stronger ionic bonds
• heat of crystalliza<on of sodium acetate tri-‐hydrate is -‐35.9 to -‐39.3 kJ/mol
• Dissolu<on: magnesium sulfate : weaker bonds to stronger bonds
• anhydrous MgSO4 is about -‐54.37 kJ/mol
• includes forma<on of a hydrate Epsomite (very exothermic) + its dissolu<on in water (slightly endothermic)
Understanding ΔH : evapora<on • Evapora<on: liq→gas • ΔH = 44kJ/mol @ 300K • ΔU = 44-‐RT = 41.5kJ/mol • 3.7 non-‐covalent bonds (hydrogen bonds) per molecule in water, zero in gas
• Number of bonds decreases: system gets colder: evapora<on is endothermic.
Example: protein/ligand binding • P for protein (target), L for ligand (drug) • Assume simple 1:1 stoichiometry: P + L ⇔ PL • Molar heat of reac<on: 1 mole of P + 1 mole of L form 1 mole of PL
• The reac<on is open (but not always) exothermic • Asn: The reac<on is (typically) reversible:
– not all reactants (P & L) are converted to products (PL) – heat is propor<onal to the amount of product that is formed – used in determina<on of binding affini<es by ITC
Generic Name MW ΔH (kcal/
mol) Nelfinavir 567.8 3.1 Indinavir 613.8 1.8
Saquinavir 670.8 1.2 Tipranavir 602.7 -0.7 Lopinavir 628.8 -3.8
Atazanavir 704.9 -4.2 Ritonavir 720.9 -4.3
Amprenavir 505.6 -6.9 Darunavir 547.7 -12.7
Enthalpy of binding of several an<-‐HIV drugs to their target protein,
HIV protease
Molar heat of drug binding to blood plasma proteins
Drug Protein ΔH binding (kcal/mol)
Propranolol α-acid glycoprotein -11.1 Warfarin human serum albumin -2.44
Will this drug bind?
• Energy and enthalpy of the drug in a pocket is lower by 2 kcal/mole than of the same drug in water.
• The drug looks like this: