PloEng ln K vs 1/T Example of van't Hoff Plot Review
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Transcript of PloEng ln K vs 1/T Example of van't Hoff Plot Review
1/28/15
1
Rela+onship between Gibbs free energy of reac+on and the equilibrium concentra+ons is defined by constant K
RTGKo
reactionΔ−=ln
Review: concentra+ons and energies
Where G0 comes from chem. poten+als (molar free energies) at standard 1M concentra+ons, while K is calculated at equilibrium concentra+ons.
Concentra+ons instead of Heats
• ΔG0 contains Enthalpic (ΔH) and Entropic (-‐TΔS) contribu+ons. How do we measure them?
• Example: Levosalbutamol vs Salbutamol (racemic)
• Chiral transition: ln(CR/CL) = -(GR-GL)/(RT)
RTGKo
reactionΔ−=ln
“As a bronchodilator, it is used to treat asthma and Chronic obstruc+ve pulmonary disease (COPD). In general, levosalbutamol has similar pharmacokine+c and pharmacodynamic proper+es to salbutamol; however, its manufacturer, Sepracor, has implied (although not directly claimed) that the presence of only the R-‐enan+omer produces fewer side effects.” Wikipedia
Enthalpy and Entropy from Equilibrium at several temperatures: van’t Hoff Equa+on
RS
RTHK
or
or Δ
+Δ
−=ln
RS
RTHK
RS
RTHK
or
or
or
or
Δ+
Δ−=
Δ+
Δ−=
22
11
ln
ln
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Δ=⎟⎟
⎠
⎞⎜⎜⎝
⎛
122
1 11lnTTR
HKK o
r
Equilibrium constant at two different temperatures:
Subtrac+ng:
Subs+tu+ng ΔG for ΔH-‐TΔS:
Jacobus Henricus van’t Hoff (1852-‐1911), a Dutch chemist
Alterna+ve to Calorimetry. Idea: • Equilibrium concentra+ons depend on T • Higher T will favor the reac+on direc+on with gain of entropy. • Recipe: Measure K ( T )
Plo]ng ln K vs 1/T
)10ln(3.2,3.23.2
log =Δ
+Δ
−=RS
RTHK
or
or
RHor /Δ−
RS
RTHK
or
or Δ
+Δ
−=ln
Van’t Hoff Equation with log10
The slope is The intercept is RSor /Δ
Example of van’t Hoff Plot
1/T(K)0.0020 0.0022 0.0024 0.0026 0.0028 0.0030 0.0032
log
K
8
10
12
14
16
18Nd(OH)3(cr) + 3H+ = Nd3+ + 3H2O(l)
Review • The chemical poten+al of component J: – Gas – Liquid mixture – ΔG and entropy of mixing.
• The chemical equilibrium – K via concentra+ons and reac+on stoichiometry
– From K, to ΔGo
– From K at T1 and T2, to ΔHo and ΔSo, Van’t Hoff lnK = −
ΔrGo
RT
⎟⎟⎠
⎞⎜⎜⎝
⎛−
Δ−=⎟⎟
⎠
⎞⎜⎜⎝
⎛
212
1 11lnTTR
HKK o
0
ln0
ccRT ic
ii += µµ
]][[][..,
1 BABAKgeaK
n
iii
•==∏
=
ν
)ln(0
0
PPRT iP
igi += µµ
ai below may also be molar frac+on xi or concentra+on ci depending on the standard state and ideality
RS
RTHK
or
or Δ
+Δ
−=ln
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Gas-‐Solu+on Equilibrium for Each Solu+on Ingredient
• i may be water or drug
• xi -‐ Solute (or solvent) molar frac+on
• * -‐ pure (saturated) ingredient
µi,liq = µi,vap ; µi,liq* = µi,vap
*
µi,liq* + RT ln xi = µi,vap
* + RT ln pipi*
!
"#
$
%&
RT ln xi = RT lnpipi*
!
"#
$
%&
xliqi = pgi / pi
*g pure
Raoult’s Law
• Solvent (eg water) pressure vs molar frac+on of non-‐vola;le solute
• Vapor pressure of a solu+on is decreased as the solute concentra+on is increased
• P*water = 0.23 bar at 20oC (100C?)
P = xw P*w= (1- xsolute) P*
w
P*w-P=ΔP = xsolute P*
w
French physicist François-‐Marie Raoult
• Water pressure will be lower as you add salt • Salty water will boil at higher temperature
xliqi = pgi / pi
*g purei is water
Henry’s Law (gas in solvent) • Gas dissolves in liquid propor+onally to
its pressure. Example: Oxygen in blood
• Here K is an empirical constant, slope of the tangent to the experimental curve.
• Pi = xi P0 -‐ Dalton’s law
Pi,gas = xi,sol⋅KxH
Henry’s Law
Raoul’s Law for xsolvent→1 Henry’s Law for xsolute→0 Mixtures that obey
and are called ideal-dilute solutions.
xliqi = pgi / pi
*g pure i is gas component (eg oxygen)
Air Pressure vs O2 in Blood • oxygen (O2) : KH=769.2 L·∙atm/mol • carbon dioxide (CO2) : KH=29.4 L·∙atm/mol • hydrogen (H2) : KH=1282.1 L·∙atm/mol
8,848 m (M.Everest) 4,421 m (M.Whitney)
Temp (C) P(kPa) P(mmHg) 0 0.6 4.5 3 0.8 6.0 5 0.9 6.8 8 1.1 8.3 10 1.2 9.0 12 1.4 10.5 14 1.6 12.0 16 1.8 13.5 18 2.1 15.8 19 2.2 16.5 20 2.3 17.5 21 2.5 18.7 22 2.6 19.8 23 2.8 21.1 24 3.0 22.4 25 3.2 23.8 26 3.4 25.2 27 3.6 26.7 28 3.8 28.4 29 4.0 30.0 30 4.2 31.5 32 4.8 36.0 35 5.6 42.0 40 7.4 55.5 50 12.3 92.3 60 19.9 149.3 70 31.2 234.1 80 47.3 354.9 90 70.1 525.9 100 101.3 760.0
Water pressure vs T
Ph = P0 • e -‐M g h/RT
Classifica3on of Membranes
Permeable impermeable semi-‐permeable Cellular plasma membrane is semi-‐permeable
Osmosis • The biological membrane is not permeable for electrolytes
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Osmosis • Differen+ally permeable membrane • Osmo3c pressure is the hydrosta+c pressure produced by a solu+on in a space divided by a differen+ally permeable membrane due to a differen+al in the concentra+ons of water (or other solute).
Osmo+c Pressure
• Colliga+ve property. Osmo+c pressure depends on the number of solute molecules, not on their iden+ty
• Water flows to the area where there are more non-‐water molecules
• Osmo+c pressure looks like the gas law formula, where n is the total number of moles of the solute par+cles
• For V = 1L , Δn/V becomes ΔM • Posm = Phigher-‐Plower PosmV = ΔnsoluteRT
Posm = ΔMsoluteRT
Higher pressure : lower pressure
P1V = n1,soluteRTminusP2V = n2,soluteRT
Deriving van’t Hoff’s equa+on for Osmo+c Pressure
• Decrease in Free energy in the “polluted” chamber is compensated by extra work PosmV. V=1L = 10-‐3 m3
at T=36oC • M is molarity (molar concentra+on), not mass! • The total M can be calculated via van’t Hoff’s
factors, i, i.e. M →i!M
GP =GP0+VΔP
PosmV = −nwRT ln xw= −nwRT ln(1− xstuff ) ≈ nwRTxstuff
Posm = (nstuff /V )RT = ΔMRTPosm[bar]= ΔMRT ≈ 25.7ΔM[bar]
Van’t Hoff factor, i• The number of moles of par+cles per mole of solute is the van't Hoff factor, i.
• How many moles of ALL DERIVATIVE FORMS are in solu3on upon adding 1 mole of solid solute?
• E.g. NaCl results in Na+ and Cl-‐, x1=0, x2=1 i=2• Example with par+al dissolu+on:
– 50% undissociated, 30% in 2 par+cles, 20% in 3 par+cles: i = 0.5 + 2*0.3 + 3*0.2 = 1.7; P=25.7*i*M [bar]
€
i = x1 + 2x2 + 3x3 + ..
Posm=ΔM RT i
Examples • The observed lower van’t Hoff factors illustrate the differences between ac+vi+es and concentra+ons. Ions are not fully independent on each other.
Tonicity
Isotonic, Hypotonic , Hypertonic environments (plant cells)
Normal Turgid Plasmolysis
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Cell Lysis
• Cells are full of stuff, water flows into them un+l the number of molecules inside and outside equates.
• Water moves in and out via aquaporins • When solu+on around the red blood cells is diluted, water flows into the cell and it explodes. This is how cellular components and proteins are extracted
Cell shrinkage
• Too many molecules OUTSIDE the cell cause them to shrink and dye
• Salt, sugar are an+bacterial agents par+ally because they suck all the water from the cells and the cells get crushed.
Molality
• Molarity M ≡ n / liter of solu;on • Mole frac+on x ≡ n / Σni • Molality m ≡ n / kg of solvent
1 molal solu+on: 1 mole of solute per 1kg of solvent
x = nsolute/nwater = Msolute /55.5 One liter of water contains 55.5 Moles of water molecules.
Osmolarity and Osmolality • The number of moles of substance mul+plied by the van’t Hoff factor per liter of solu+on is called osmolarity
• a mole of glucose in solu+on is one osmole, whereas a mole of NaCl in solu+on is two osmoles
• (m)osmolarity – (m = milli) . 1 osmol of solute = when dissolved in 1 liter of solu;on will exert an osmo+c pressure equal to that of 1 mole of an ideal unionized substance
• …molality -‐ … per 1kg of solvent
Tonicity of intravenous fluids • Osmolality: total solute concentra+on in a fluid
compartment. • Tonicity: the combined ability of solutes to
produce a osmo+c driving force that causes water to move from one compartment to another. – Solutes that are capable of moving water are
called “effec+ve osmoles”. – These are solutes that are unable to cross from
the ex t race l lu la r to the in t race l lu la r compartment: sodium, glucose, mannitol, sorbitol.
– The control of tonicity will determine the normal state of cellular hydra+on and cell size. This is of par+cular concern in the case of brain cells.
• Pharmaceu+cal labeling regula+ons may require a statement on tonicity.
Non-‐polar molecules cross membranes: oxygen, carbon dioxide, ethanol Water, urea use some assistance
Fas+ng glucose: 4.4 to 6.1 mmol/L (79.2 to 110 mg/dL) Urea: ~ 3 to 7 mmol/L
Examples
• Osmolali+es of some intravenous fluids
• High tonicity of enteral feeding of premature infants has been implicated in necro+sing enterocoli+s (NEC)
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What Osmolarity is Normal? • Osmolarity of plasma is 285-‐295 mosmoles/L • I.V.: any fluid > 550 mOsm/L should not be infused rapidly • The higher the tonicity, the lower should be the rate of infusion.
• Calculated osmolarity in mM units = 2[Na+] + (2[K]) +[Glucose]+[Urea]+ ([Ethanol]) ( all in mmol/L) (glucose MM=180g/mol: 3.5 – 6.5 mmol/L)
• Alterna+ve formula with [Conc] in mg/dL (corrected by MM): 2[Na+] + [Glucose]/18 + [BUN]/2.8 + [Ethanol]/3.7 – BUN means Blood Urea Nitrogen: 6 to 20 mg of urea per 100 ml of blood (6–20 mg/dL, 2 to 7 mmol/L)
– Na+ ~11g/mol; glucose MM=180g/mol
How to measure osmolari+es?
• Osmolari+es of iv or oral medica+ons can be measured by freezing point depression
• Why?
• Osmometer that measures freezing point depression
• Osmometer that measures vapor pressure depression
Boiling and Freezing Points
• Adding solute makes the liquid state more desirable because of the entropy increases and the chemical poten+al becomes lower.
€
Δµwater = RT ln(1− xsolutes) ≈ −RTxsolutesΔSwater _ in _ solution = Rxsolutes
€
µw = µwpure + RT ln xw
Boiling point eleva+on of a solu+on
• A solu+on exhibits a higher boiling temperature than that of pure solvent
ΔTboiling = Kbx
Pure solvent: xw = 1, boiling temperature T*
0=Δ−Δ ∗ STH vapvap
Solute added: xw < 1, boiling temperature T
€
Δ vapH −T(Δ vapS + Rxsolute ) = 0
€
ΔT⋅ Δ vapS = ΔT⋅ Δ vapH /T = TRxsolute
ΔT = T −T∗ ≈ xsoluteRT∗2
Δ vapH
'
( ) )
*
+ , ,
Pure solvent: xw = 1, freezing temperature T*
Solute added: xw < 1, freezing temperature T
Freezing point depression of a solu+on
• A solu+on exhibits a lower freezing temperature than that of pure solvent
ΔTfreezing = Kf x
€
ΔT = T −T∗ ≈ xsoluteRT∗2
Δ fusH
&
' ( (
)
* + + €
Δ fusH −T∗Δ fusS = 0
€
Δ fusH −T(Δ fusS + Rxsolute )
Review • Chemical poten+al of the same molecule in
different phases or compartments (osmosis) must be equal
• Chemical poten+al of water is lower (be|er) in solu+on If xsolutes is small:
• Osmo+c pressure: Posm=MRT, where M is molarity corrected by dissocia+on, i, M=iM0
• Osmosis: semi permeable membranes. • Osmolarity and Tonicity: coun+ng solutes
that can not cross the membrane and taking dissocia+on into account ( i, van’t Hoff’s factor).
• Boiling point eleva+on • Freezing point depression (Kf does not
depend on solutes!). Kf = 1.858 K kg/mol • Water pressure reduc+on: Raoult’s law • Gas dissolu+on in water: Henry’s law • The effects are entropic and to the first
approxima+on do not depend on the nature of solutes (colliga+ve proper+es)
€
µw _ in _ solution = µw _ pure + RT ln(xw )Δµw = RT ln(1− xsolutes) ≈ −RTxsolutesΔSw ≈ Rxsolutes
Posm =ΔnsolV
RT = iMRT
ΔTboiling = KbxsolutesΔTfreezing = K f xsolutesPw_ vap_ solution = Pw_ vap_ purexwaterPsolute_ in_ gas = KHenry
solutexsolute_ in_water
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Osmo+c Pumps for Drug Delivery
• Acutrim® Delivered the appe+te suppressant phenylpropanolamine for 16h
• Other products under development are a controlled release form for vitamin C and a drug combina+on for trea+ng symptoms of the common cold
Semi-‐permeable
OROS (Osmo+c [Controlled] Release Oral [Delivery] System) is a controlled release oral drug delivery system in the form of a tablet. The tablet has a rigid water-‐permeable jacket with one or more laser drilled small holes. As the tablet passes through the body, the osmo+c pressure of water entering the tablet pushes the ac+ve drug through the opening in the tablet.
Delivery by Osmo+c Pressure
Some Problems: § P ~ 25 atm • ΔM § Subject to dose dumping if membrane breaks § [e.g. someone chews it]
§ Slightly more expensive to formulate than coa+ng tablets
§ Possible hole plugging
Drugs delivered by OROS: Adalat OROS (nifedipine) Alpress LP (prazosin) Cardura XL (doxazosin) Concerta (methylphenidate) Covera-‐HS (verapamil) Ditropan XL/Lyrinel XL (oxybutynin) DynaCirc CR (isradipine) Glucotrol XL (glipizide) Invega (paliperidone) Jurnista / Exalgo (hydromorphone) Procardia XL (nifedipine) Volmax (salbutamol)
Reminders: concentra+ons • Molality is rarely used • Molarity: symbol “M” means moles/liter not moles.
• Physiological concentra+ons are low. • millimolar (mM) = 10-‐3 M • micromolar (µM) = 10-‐6 M • nanomolar (nM) = 10-‐9 M • picomolar (pM) = 10-‐12 M
• Molar frac+on (dimensionless) x ≈ M/55.5 • The water number is 5 (55.5 M)
– 18g : 1mole ; 1000g (L) n=55.5
A simple model of a pa+ent
• Two Compartment Model – Intracellular = Cytoplasmic (inside cells)
– Extracellular (outside cells) ECF ICF
Body’s fluid compartments. 1/3 • Total Body Water = WEIGHT x 0.5 (women) or 0.6 (men)
• Fat +ssue is ~ water free
The rule of 1/3 : • Cells (ICF) = Water x 2/3 • Fluids (ECF) = Water x 1/3
– Lymph = Fluids x 2/3 – Blood/plasma= Fluids x ¼
• Explana;ons – ICF = Inters++al = Intercellular = Lymph,
between the cells in the +ssues – Plasma = fluid por+on of the blood
Cells, ICF
Homeostasis
• Defini3on: Processes by which bodily equilibrium is maintained constant.
• Examples of Bodily homeostasis: • temperature • blood pressure • heart rate • blood glucose level • body fluid composi+on • Osmolarity • Extra cellular fluid (ECF) volume • Acid-‐Base balance
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Osmo+c pressure of drug solu+ons Freezing Point depression
• Reminder: the osmolarity of serum is ~290 mOsm/L (not lower than 210).
• Dominated by [Na+] and the associated anions. ~ 2*[Na]
• Isotonic osmolarity translates into ΔTf_depr=0.52o .
• If we know the ΔTf_depr for the desired drug concentra+on, one can add NaCl to match ΔTf_depr to make the solu+on isotonic with blood (or make net osmolarity equal to 290 mOsm/L
Distribu+on of Solutes in three fluids
K+ in cells
Cells
No albumin in lympth
Na+ in fluids
Electrochemical Equivalence (Eq).
• Mul3ply molar concentra3on by the ion charge
• Monovalent Ions (Na+, K+, Cl-‐): – 1 milliequivalent = 1 millimole
• Divalent Ions (Ca++, Mg++, and HPO4
2-‐) – 1 milli-‐equivalent = 0.5 millimole
Cells vs Fluids: Na+/K+-‐ATPase
• Na+/K+ pump or sodium-‐potassium pump is found in the plasma membrane of virtually every human cell and is common to all cellular life. It helps maintain cell poten+al and regulate cellular volume
• It creates both electric and chemical gradient
it pumps three sodium ions out of the cell for every two potassium ions pumped in.
(-‐) Nega+ve Charge and K+ Excess
3
2
(-‐) Posi+ve Charge and N+ Excess
Diure+cs • Reduc+on of [Na] leads to change in ECF
VOLUME • A “water pill”: elevates the rate of urine
excre+on (also, caffeine, alcohol, etc.). • Both loop and thiazide diure+cs block the
reabsorp+on of Na in kidneys and can therefore can lead to a decrease in the size of the ECFV.
• They differ in that loops produce a balanced loss of Na and Water à therefore Na concentra+on is usually undisturbed.
• Thiazide causes an unbalanced loss of Na and Water – such that more Na is lost rela+ve to water causing hyponatremia.
Thirst • High osmolarity of plasma leads to dry mouth and sensa+on of thirst.
• Ethanol changes osmolarity but does not change tonicity. Cells are permeable for ammonium and ethanol
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Water and Osmolarity • Body control systems regulate inges+on and excre+on: – constant total body water – constant total body osmolarity
• Osmolarity is iden+cal in all body fluid compartments (steady state condi+ons) – Body water will redistribute itself as necessary to accomplish this.
– Osmolarity balance: ICF vs ECF – Osmolarity balance between Plasma and interste+al fluid (lympth) is harder to maintain
Plasma vs Lymph: Edema • Edema is defined as so� +ssue swelling
due to expansion of the inters++al volume. Edema can be localized or generalized.
• Some extracellular fluid compartments, a.k.a. transcellular fluids (cerebrospinal fluid, intraocular fluid and joint fluid) do not communicate freely with the rest of the body.
Water flow
Albumin + blood proteins
Less Protein
Cells
Mechanisms maintaining inters++al fluid volume
• Plasma vs Lympth, the role of albumin: 70% of Ponc is due to albumin. Albumin size: ~ 10 nM (100A)
• Onco+c pressure = osmo;c pressure created by plasma protein molecules that are impermeable across the capillary membrane.
• Starling's Law: Hydrostatic Pressure - Oncotic pressure = net fluid movement out of capillary into inters++um.
• P = 120mmHg systolic pressure. The smallest pressure in capillaries ~ 20mmHg
60-‐80 nm • endocrine glands • intes+nes • pancreas • glomeruli of kidney
30-‐40 μm Allow cells to pass • Bone marrow • Lymph nodes • Adrenal glands
• < 10 nM • Regular capillaries • CNS (+ghter)
Human Serum Albumin & Drugs • HSA maintains osmo+c pressure • C=35 -‐ 50 g/L =3.5 -‐ 5.0 g/dL=0.5-‐0.75mM • Transports many drugs • Transports thyroid hormones, T3 and T4 • Transports other hormones, par+cularly fat soluble ones
• Transports fa|y acids ("free" fa|y acids) to the liver
• Transports unconjugated bilirubin (heme catabolism, yellow bruises and brown feces)
• Compe++vely binds calcium ions (Ca2+) • Buffers pH
Renal toxin CMPF in drug site 1 Stephen Curry
Albumin carries Bilirubin from destroyed hemes in the spleen to liver
15-‐20% of T3 and T4 -‐> HSA (majority by TBG) [ ]
Albumin and other drug binding proteins • 30 to 50 g/L HSA in blood (~0.5
to 0.75 mM) • HSA MW 67 kDa • Half life 20 days (drug half life
extension) • Likes to bind drugs with
carboxyls and/or hydrophobic areas
• Other proteins binding drugs – Lipoprotein – Glycoprotein – α, ß‚ and γ globulins.
• The bound por+on may act as a reservoir or depot from which the drug is slowly released in free form.
HSA with 6 palmi+c acids
Hypoalbuminemia • Liver disease (eg cirrhosis) • Excess excre+on by the kidneys • Excess loss in bowel (e.g., Ménétrier's
disease) • Wounds and Burns (plasma loss) • Increased vascular permeability • Acute disease states (‘nega+ve prot.’) • Muta+ons causing analbuminemia • Malnutri3on (starva+on)