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Chemical equilibria, principle of pH, buffers

Chemical equilibria, principle of pH, buffers. Basics of Medical Chemistry Course L ászló Csanády Department of Medical Biochemistry. v 1. C+D. A+B. v -1. Chemical equilibria. Reaction rate (v): Amount of product formed per unit time (mol/s, M/s). Rate law:

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Chemical equilibria, principle of pH, buffers

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  1. Chemical equilibria,principle of pH, buffers Basics of Medical Chemistry Course László Csanády Department of Medical Biochemistry

  2. v1 C+D A+B v-1 Chemical equilibria Reaction rate (v): Amount of product formed per unit time (mol/s, M/s). Rate law: For elementary (single-step) reactions the reaction rate is proportional to the concentrations of each reactant. v1=k1.|A|.|B| k1, k-1: reaction rate constants (M-1s-1) v-1=k-1.|C|.|D| |X|: instantaneous concentration (M)

  3. v1 C+D A+B v-1 Chemical equilibria At equilibrium the forward and the reverse rates are equal.

  4. v1 C+D A+B v-1 v1=v-1 k1.[A].[B]=k-1.[C].[D] [X]: equilibrium concentration (M) k1 k-1 [C].[D] [A].[B] K = = equilibrium constant Chemical equilibria At equilibrium the forward and the reverse rates are equal.

  5. C* A+B 2D [C*] [A].[B] [D].[D] [C*] K2 = K1 = [C*] [A].[B] [D]2 [C*] . "Law of Mass Action" K = K1. K2 = [D]2 [A].[B] K = overall equilibrium constant Chemical equilibria All chemical reactions can be broken down into a set of elementary steps. Equilibrium is achieved when all steps are at equilibrium:

  6. C+D A+B |C|.|D| |A|.|B| Q = reaction quotient Chemical equilibria Predicting the direction of a reaction: Q<K  reaction goes forward Q=K  reaction is at equilibrium Q>K  reaction goes backward

  7. C+D A+B I. Adding/removing reactants/products |C|.|D| |A|.|B| Q = = K 1. Initial state (equilibrium): |C|*.|D| |A|.|B| 3. Q = < K (|C|*+x).(|D|+x) (|A|-x).(|B|-x) Q = = K 4. Final state (new equilibrium): Le Chatelier principle When a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation. 2. Perturbation: remove product: |C||C|* (|C|*<|C|)  reaction goes forward

  8. C+D A+B I. Adding/removing reactants/products |C|.|D| |A|.|B| Q = = K 1. Initial state (equilibrium): |C|.|D| |A|*.|B| 3. Q = < K (|C|+x).(|D|+x) (|A|*-x).(|B|-x) Q = = K 4. Final state (new equilibrium): Le Chatelier principle When a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation. 2. Perturbation: add reactant: |A||A|* (|A|*>|A|)  reaction goes forward

  9. C+D A+B I. Adding/removing reactants/products |C|.|D| |A|.|B| Q = = K 1. Initial state (equilibrium): |C|*.|D| |A|.|B| 3. Q = > K (|C|*-x).(|D|-x) (|A|+x).(|B|+x) Q = = K 4. Final state (new equilibrium): Le Chatelier principle When a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation. 2. Perturbation: add product: |C||C|* (|C|*>|C|)  reaction goes backward

  10. C+D A |C|.|D| |A| Q = = K 1. Initial state (equilibrium): (|C|/2).(|D|/2) |A|/2 K 2 3. Q = = < K ((|C|/2)+x).((|D|/2)+x) (|A|/2)-x 4. Final state (new eq.): Q = = K Le Chatelier principle When a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation. II. Effect of dilution 2. Perturbation: increase volume by 2x: |X||X|/2  reaction goes forward

  11. C+D A |C|.|D| |A| Q = = K 1. Initial state (equilibrium): (2|C|).(2|D|) 2|A| 3. Q = = 2K > K (2|C|-x).(2|D|-x) 2|A|+x 4. Final state (new eq.): Q = = K Le Chatelier principle When a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation. II. Effect of pressure on gaseous reactions 2. Perturbation: increase pressure by 2x  volume decreases by 2x (p.V=const.):|X|2|X|  reaction goes backward

  12. C+ heat A |C| |A| Q = = K 1. Initial state (equilibrium):  reaction goes backward 3. |C|-x |A|+x 4. Final state (new eq.): Q = = K Le Chatelier principle When a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation. II. Effect of temperature 2. Perturbation: add heat (increase temperature)

  13. H+ H2O + H2OOH-+ H3O+ [H3O+][OH-] [H2O]2 H2O H+ + OH- K = ● [H2O]=(1000 g/l)/(18 g/mol)=55.5 mol/l=55.5 M ● in dilute solutions [H2O]  constant [H3O]+ sometimes referred to as [H+]: Kw=[H+].[OH-]=10-14 M2 Equilibria in aqueous solutions The water ion-product Kw=K.[H2O]2=[H3O+][OH-]

  14. H2O H+ + OH- }  [H+]=10-7M [OH-]=10-7M pH=7 pOH=7 Equilibria in aqueous solutions The principle of pH Definition: pH=-lg[H+] pOH=-lg[OH-] [H+].[OH-]=10-14 M2 pH+pOH=14 "Neutral" pH (pure water): [H+].[OH-]=10-14 M2 [H+]=[OH-]

  15. H2O H+ + OH- H2O H+ + OH- }  [H+]>10-7M [OH-]<10-7M pH<7 pOH>7 Equilibria in aqueous solutions The principle of pH Definition: pH=-lg[H+] pOH=-lg[OH-] [H+].[OH-]=10-14 M2 pH+pOH=14 Acidic pH (solution of an acid): H2O H+ + OH- [H+].[OH-]=10-14 M2 [H+]>[OH-]

  16. H2O H+ + OH- H2O H+ + OH- H2O H+ + OH- }  [H+]<10-7M [OH-]>10-7M pH>7 pOH<7 Equilibria in aqueous solutions The principle of pH Definition: pH=-lg[H+] pOH=-lg[OH-] [H+].[OH-]=10-14 M2 pH+pOH=14 Basic pH (solution of a base): [H+].[OH-]=10-14 M2 [H+]<[OH-]

  17. HAc H++Ac- [H+][Ac-] [HAc] Ka = conjugate acid conjugate base (pKa=-lgKa) Ac-+ H2O HAc + OH- [HAc][OH-] [Ac-] Kb = conjugate base conjugate acid (pKb=-lgKb) anion hydrolysis Equilibria in aqueous solutions Conjugate pairs of weak acids and bases Solution of a weak acid: Solution of a salt of a weak acid: NaAc Na+ + Ac- (strong electrolyte)

  18. [H+][Ac-] [HAc][OH-] [HAc] [Ac-] [H+][Ac-] [HAc] KaKb = . Ka = pKa+pKb = 14 [HAc][OH-] [Ac-] Kb = for a conjugate acid-base pair Equilibria in aqueous solutions Conjugate pairs of weak acids and bases (pKa=-lgKa) KaKb = [H+].[OH-]=Kw=10-14 M2 (pKb=-lgKb)

  19. NaAc Na+ + Ac- HAc H++Ac- conjugate acid conjugate base common ion effect [H+][Ac-] [HAc] [H+]cs ca Ka =  cs ca cs ca lgKa lg[H+]+lg Ac-+ H2O HAc + OH- conjugate base conjugate acid pH  pKa+lg Hendersson-Hasselbalch eq. anion hydrolysis Buffers Mixing a weak acid with its salt Result: [Ac-]  cs [HAc]  ca

  20. NH4Cl NH4+ + Cl- NH4+ NH3 + H+ conjugate acid conjugate base [H+][NH3] [NH4+] [H+]cb cs Ka =  cation hydrolysis common ion effect NH3 + H2O cb cs cb cs NH4++ OH- lgKa lg[H+]+lg conjugate base conjugate acid pH  pKa+lg Hendersson-Hasselbalch eq. Buffers Mixing a weak base with its salt Result: [NH3]  cb [NH4+]  cs

  21. Weak acid + its salt: Weak base + its salt: conj. base conj. acid cb cs cs ca cb ca pH  pKa+lg pH  pKa+lg pH  pKa+lg Buffers Summary: mixture of weak conjugate acid-base pair  acid: conj. acid  salt: conj. base  salt: conj. acid  base: conj. base The general formula:

  22. cb ca pH  pKa+lg Buffers Summary: mixture of weak conjugate acid-base pair Some simple consequences:  pH of a buffer does not depend on the absolute values of ca and cb – only their ratios matter (e.g., dilution does not affect pH)  for a "symmetrical buffer" (ca=cb) pH=pKa The general formula:

  23. Perturbation: add + x mol/l H+ H+ A- Compensation: A- binds almost x mol/l H+ cb ca HA } } [HA]=ca [A-] =cb cb-x ca+x [HA]=ca+x [A-] =cb-x pH  pKa+lg pH  pKa+lg OH- H+ H+ OH- OH- Buffers Buffers stabilize the pH of a solution HA H2O A-

  24. Compensation: HA releases almost x mol/l H+ HA H+ A- Perturbation: add + x mol/l OH- cb ca } } [HA]=ca [A-] =cb cb+x ca-x [HA]=ca-x [A-] =cb+x pH  pKa+lg OH- pH  pKa+lg H+ H+ OH- OH- Buffers Buffers stabilize the pH of a solution HA H2O A-

  25. Buffers Buffers stabilize the pH of a solution

  26. CO2 + H2O H2CO3 HCO3- + H+ K'=5.6 Ka=1.4.10-7 M (pKa=6.85) [H2CO3] [CO2] [HCO3-].[H+] [H2CO3] K' = Ka = [H2CO3] [CO2] [HCO3-].[H+] [H2CO3] [HCO3-].[H+] [CO2] K=K'Ka = = . [HCO3-] [CO2] [HCO3-] [CO2] lgK = lg[H+]+lg pH = pK+lg Buffers The carbon-dioxide/bicarbonate buffer

  27. CO2 + H2O H2CO3 HCO3- + H+ K'=5.6 Ka=1.4.10-7 M (pKa=6.85) } pHblood=7.4 [HCO3-]blood=24 mM [CO2]blood =1.2 mM [HCO3-] [CO2] pH = 6.1+lg [HCO3-] [CO2] pH = pK+lg Buffers The carbon-dioxide/bicarbonate buffer K=K'Ka =7.8.10-7 M  pK=6.1

  28. CO2 + H2O H2CO3 HCO3- + H+ blood capillary lung alveolus CO2(g) } pHblood=7.4 [HCO3-]blood=24 mM [CO2]blood =1.2 mM [HCO3-] [CO2] pH = 6.1+lg Buffers The carbon-dioxide/bicarbonate buffer pCO2= const. Henry's law: [CO]2(aq)=a.pCO2(g) [CO2(aq)]=const. A buffer in which one component is kept at constant cc.!

  29. acid challenge: + x M H+ [HCO3-]-x [CO2]+x [HCO3-]-x [CO2] pH = 6.1+lg pH = 6.1+lg [HCO3-] [CO2] exhale excess CO2 pH = 6.1+lg Buffers The carbon-dioxide/bicarbonate buffer A buffer in which one component is kept at constant cc.!

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