Chemical equilibria, principle of pH, buffers

Chemical equilibria,principle of pH, buffers

Basics of Medical Chemistry Course

László Csanády

Department of Medical Biochemistry

Chemical equilibria

A+B C+Dv1

v-1

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)

Chemical equilibria

A+B C+Dv1

v-1

At equilibriumthe forward and the reverse rates are equal.

Chemical equilibria

A+B C+Dv1

v-1

At equilibriumthe forward and the reverse rates are equal.

k1

k-1

[C].[D][A].[B]=K =

equilibrium constant

v1=v-1

k1.[A].[B]=k-1

.[C].[D]

[X]: equilibriumconcentration (M)

Chemical equilibria

All chemical reactions can be broken down into a set of elementary steps. Equilibrium is achieved when all steps are at equilibrium:

A+B C* 2D

[C*][A].[B]K1 =

[D].[D] [C*]K2 =

[C*][A].[B]K = K1

. K2 = [D]2

[C*].

[D]2

[A].[B]K =overall equilibrium constant

"Law ofMass Action"

Chemical equilibria

Predicting the direction of a reaction:

|C|.|D||A|.|B|Q =

A+B C+D

reaction quotient

Q<K reaction goes forwardQ=K reaction is at equilibriumQ>K reaction goes backward

Le Chatelier principleWhen a system at equilibrium is perturbed, it will reach a new equilibrium by counteracting the perturbation.

1. Initial state (equilibrium):|C|.|D||A|.|B|Q = = K

2. Perturbation: remove product: |C||C|* (|C|*<|C|)

|C|*.|D| |A|.|B|Q = < K3. reaction goes forward

4. Final state (new equilibrium):(|C|*+x).(|D|+x) (|A|-x).(|B|-x)Q = = K

I. Adding/removing reactants/products

A+B C+D



2. Perturbation: add reactant: |A||A|* (|A|*>|A|)

|C|.|D||A|*.|B|Q = < K3. reaction goes forward

4. Final state (new equilibrium):(|C|+x).(|D|+x)(|A|*-x).(|B|-x)Q = = K


A+B C+D



2. Perturbation: add product: |C||C|* (|C|*>|C|)

|C|*.|D| |A|.|B|Q = > K3. reaction goes backward

4. Final state (new equilibrium):(|C|*-x).(|D|-x)(|A|+x).(|B|+x)Q = = K


A+B C+D


1. Initial state (equilibrium):|C|.|D| |A|Q = = K

2. Perturbation: increase volume by 2x: |X||X|/2

reaction goes forward

4. Final state (new eq.):((|C|/2)+x).((|D|/2)+x) (|A|/2)-xQ = = K

II. Effect of dilution

A C+D

3.(|C|/2).(|D|/2) |A|/2Q = = < K

K2


1. Initial state (equilibrium):|C|.|D| |A|Q = = K

2. Perturbation: increase pressure by 2x volume decreases by 2x (p.V=const.): |X|2|X|

4. Final state (new eq.):(2|C|-x).(2|D|-x) 2|A|+xQ = = K

II. Effect of pressure on gaseous reactions

A C+D

reaction goes backward3.(2|C|).(2|D|) 2|A|Q = = 2K > K


1. Initial state (equilibrium):|C||A|Q = = K

2. Perturbation: add heat (increase temperature)

4. Final state (new eq.):|C|-x|A|+xQ = = K

II. Effect of temperature

A C+ heat

reaction goes backward3.

Equilibria in aqueous solutionsThe water ion-product

[H3O+][OH-] [H2O]2

K =

● [H2O]=(1000 g/l)/(18 g/mol)=55.5 mol/l=55.5 M● in dilute solutions [H2O] constant

Kw=K.[H2O]2=[H3O+][OH-]

H2O + H2O OH- + H3O+

H+

[H3O]+ sometimes referred to as [H+]:

Kw=[H+].[OH-]=10-14 M2 H2O H+ + OH-

Equilibria in aqueous solutionsThe principle of pH

Definition: pH=-lg[H+] pOH=-lg[OH-]

H2O H+ + OH-

"Neutral" pH (pure water):

[H+].[OH-]=10-14 M2 pH+pOH=14

[H+].[OH-]=10-14 M2

[H+]=[OH-] } [H+]=10-7M [OH-]=10-7M

pH=7 pOH=7

H2O H+ + OH-H2O H+ + OH-



Acidic pH (solution of an acid):

[H+].[OH-]=10-14 M2 pH+pOH=14

[H+].[OH-]=10-14 M2

[H+]>[OH-] } [H+]>10-7M [OH-]<10-7M

pH<7 pOH>7

H2O H+ + OH-

H2O H+ + OH-H2O H+ + OH-



Basic pH (solution of a base):

[H+].[OH-]=10-14 M2 pH+pOH=14

[H+].[OH-]=10-14 M2

[H+]<[OH-] } [H+]<10-7M [OH-]>10-7M

pH>7 pOH<7

H2O H+ + OH-

Equilibria in aqueous solutionsConjugate pairs of weak acids and bases

Solution of a weak acid:

Solution of a salt of a weak acid:

NaAc Na+ + Ac- (strong electrolyte)

HAcconjugate

acidconjugate

base

H+ + Ac- [H+][Ac-] [HAc]Ka =

(pKa=-lgKa)

[HAc][OH-] [Ac-]Kb =

(pKb=-lgKb)

HAc + OH-

conjugatebase

conjugateacid

Ac- + H2O

anion hydrolysis

[HAc][OH-] [Ac-]Kb =

Equilibria in aqueous solutionsConjugate pairs of weak acids and bases

[H+][Ac-] [HAc]Ka =

(pKa=-lgKa)

(pKb=-lgKb)

[H+][Ac-] [HAc][OH-] [HAc] [Ac-]KaKb = .

KaKb = [H+].[OH-]=Kw=10-14 M2

pKa+pKb = 14

for a conjugate acid-base pair

BuffersMixing a weak acid with its salt

HAcconjugate

acidconjugate

base

H+ + Ac-

NaAc Na+ + Ac-

HAc + OH-

conjugatebase

conjugateacid

Ac- + H2O

anion hydrolysis

Result:[Ac-] cs

[HAc] ca

[H+][Ac-] [HAc]Ka =

[H+]cs

ca

lgKa lg[H+]+lgcs

ca

pH pKa+lgcs

ca

Hendersson-Hasselbalch eq.

common ioneffect

NH4Cl NH4+ + Cl-

NH3 + H+

conjugateacid

conjugatebase

NH4+

cation hydrolysis

NH3 + H2Oconjugate

baseconjugate

acid

NH4+ + OH-

BuffersMixing a weak base with its salt

Result:[NH3] cb

[NH4+] cs

[H+][NH3] [NH4

+]Ka =

[H+]cb

cs

lgKa lg[H+]+lgcb

cs

pH pKa+lgcb

cs

Hendersson-Hasselbalch eq.

common ioneffect

pH pKa+lgcb

cs

Weak base + its salt:

pH pKa+lgcs

ca

Weak acid + its salt:

BuffersSummary: mixture of weak conjugate acid-base pair

conj. base

conj. acid

The general formula: pH pKa+lgcb

ca

acid: conj. acid salt: conj. base

salt: conj. acid base: conj. base

BuffersSummary: mixture of weak conjugate acid-base pair

The general formula: pH pKa+lgcb

ca

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

Buffers

H2OHA

A-

H+

OH-

H+

OH-

pH pKa+lgcb

ca

[HA]=ca

[A-] =cb} pH pKa+lg

cb-xca+x

[HA]=ca+x[A-] =cb-x

}

A-

HAH+

OH-

Compensation: A- bindsalmost x mol/l H+

Perturbation: add + x mol/l H+

Buffers stabilize the pH of a solution

Buffers

H2OHA

A-

H+

OH-

pH pKa+lgcb

ca

[HA]=ca

[A-] =cb} pH pKa+lg

cb+xca-x

[HA]=ca-x[A-] =cb+x }

H+

OH-

HA

A-

H+

OH-

Compensation: HA releasesalmost x mol/l H+

Perturbation: add + x mol/l OH-

Buffers stabilize the pH of a solution

BuffersBuffers stabilize the pH of a solution

BuffersThe carbon-dioxide/bicarbonate buffer

H2CO3 HCO3- + H+

CO2 + H2O

[H2CO3] [CO2]

K' =[HCO3

-].[H+] [H2CO3]

Ka =

Ka=1.4.10-7 M(pKa=6.85)

K'=5.6

[H2CO3] [CO2]

K=K'Ka =[HCO3

-].[H+] [H2CO3]

.[HCO3

-].[H+] [CO2]

=

[HCO3-]

[CO2]lgK = lg[H+]+lg

[HCO3-]

[CO2]pH = pK+lg


H2CO3 HCO3- + H+

CO2 + H2O

Ka=1.4.10-7 M(pKa=6.85)

K'=5.6

[HCO3-]

[CO2]pH = pK+lg

K=K'Ka =7.8.10-7 M pK=6.1

[HCO3-]

[CO2]pH = 6.1+lg

[HCO3-]blood=24 mM

[CO2]blood =1.2 mM } pHblood=7.4

blood capillarylung alveolus


H2CO3 HCO3- + H+

CO2 + H2O

[HCO3-]

[CO2]pH = 6.1+lg

[HCO3-]blood=24 mM

[CO2]blood =1.2 mM } pHblood=7.4

pCO2= const.CO2(g)

Henry's law: [CO]2(aq)=.pCO2(g) [CO2(aq)] =const.

A buffer in which one component is kept at constant cc.!


[HCO3-]

[CO2]pH = 6.1+lg

A buffer in which one component is kept at constant cc.!

acid challenge: + x M H+

[HCO3-]-x

[CO2]+xpH = 6.1+lg

exhale excess CO2

[HCO3-]-x

[CO2]pH = 6.1+lg

Documents

Chemical equilibria, principle of pH, buffers