Acids, Bases and Buffers

 

Many of the reactions that occur within living cells involve acids and bases, and reaction rates may be critically dependant on the acid - base ratio in the cell or cellular compartment.We therefore need to review our notions of acid - base chemistry, and enter into a fairly lengthy discussion of pH control and buffered systems.

 

Acids and Bases

 

(1)               Definitions:

Several definitions of acid and bases have arisen:

 

Arrhenius:

_††† Acids are substances capable of producing an excess of H+ ions in water.

 

Bronsted - Lowry:

_††† Acids are substances which can donate aproton in a chemical reaction.

_††† Bases are substances which can accept a proton in a chemical reaction.

 

All Arrhenius acids are this Bronsted - Lowry acids.

e.g. HCl H+ + Cl-

 

Water, however, is both a Bronsted base and a Bronsted acid:

††† H2O H++ OH-

 

†† H2O + H+ H3O+

 

Lewis:

_††† Acidsare electron - pair acceptors.

_††† Bases are electron - pair donors.

 

All Bronsted acids and bases are Lewis acids and bases.

 

Boron trifluoride, however, is a Lewis acid.

H3N: + BF3 H3N:BF3

 

All these versions of acids and bases can be seen in biological systems.For the purposes of our current discussion, however, we are concerned almost exclusively with Bronsted - Lowry acids and bases in aqueous solution.

 

(2)               Conjugate Pairs

 

All acids and bases form conjugate pairs.An acid gives up its proton; the resulting deprotonated molecule is now the conjugate base of the acid.

 

 

Conjugate Acid

 

Conjugate Base

 

H3C - COOH

 

H3C-COO-

 

NH4+

 

NH3

 

(2)               Strong Acids

 

Some mineral acids are strong acids, which dissociate completely in aqueous solution.There are only a handful of strong acids:

                      Hydrochloric

                      Hydrobromic

                      Hydroiodic

                      Nitric

                      Sulfuric

                      Perchloric

                      Chromic

                      Permanganic

 

Of these, the only one of biological importance is HCl, stomach acid.

 

(4)               Weak Acids

 

Most acids, and all the biologically significant ones (except HCl), dissociate only slightly in aqueous solution.For example, in a 100 mM solution of acetic acid:

 

H3C-COOH H+ + H3C-COO-††††††††

 

only about 1% of the molecules exist in the anion form.

 


In other words, the dissociation of a weak acid sets up an equilibrium.

 

(5)               Proton Transfer Rates

 

It is worthy of note that protons move around very rapidly compared to other ions.They do not simply move physically from place to place but participate in coupled association / dissociation reactions.In this way, proton movement through a solution resembles a current more than the simple diffusion of ions.

 

Acid / Base Equilibria:

 

Biological equilibria can normally be safely assumed to take place in dilute solution, near ideality.

 

They are governed by mass action laws you should remember from General Chemistry:

For the equilibrium reaction:

 

A + B C + D

 

 

 


Letís examine what happens in a glass of plain water?Water is both a Bronsted base and a Bronsted acid.Water molecules are constantly dissociating and recombining in the (overall) reaction:

 

H2O + H2O H3O+ + OH-

or

H2O H+ + OH-

 


The equilibrium constant for this reaction can be defined as follows:

Note that this is a very small number.At equilibrium, the concentration of H2O will be essentially unchanged at 55.5 M.Therefore, since [H2O] is constant, we can factor it out:

 


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

 

For acid solutions:†††††† [H+] > 10-7 M

For base solutions:††††† [H+] < 10-7 M

 

The pH scale provides a much more convenient measure of acidity than the absolute proton concentration.pH is defined as

 

pH = -log [H+]

For acid solutions:†††††† pH < 7

For base solutions:††††† pH > 7

 

and normal pH values range from 0 (extremely acidic) to 14 (extremely basic).

 

 

Substance

 

pH

 

Stomach acid

 

1.5 - 2.5

 

Coca-cola

 

2.5

 

Human saliva

 

6.5

 

Human blood

 

7.5

 

Human urine

 

5 - 8

 

Oven cleaner

 

14

 

Note that Kw is an ion product, not a true equilibrium constant.We can define the same terms for a weak acids in aqueous solution:

 

HA + H2O_†† H3O+ + A-

 


 

 

Kaís are characteristic of each acid and are a measure of it;s strength.The stronger the acid, the larger the value of Ka.Since Ka values are usually

                      rather small numbers, and

                      vary over several orders of magnitude,

it is convenient to us the log of the Ka

 

pKa = -log ( Ka )

 

The smaller the value of pKa, the stronger the acid.The Kaís and pKaís of some biochemically relevant acids are shown below:

 

 

Acid

 

Ka

 

pKa

 

Acetic

 

1.8 x 10-5

 

4.74

 

Formic

 

1.7 x 10-4

 

3.77

 

Benzoic

 

6.5 x 10-5

 

4.19

 

Carbonic

 

4.3 x 10-7

 

6.37

 

Imidazole

 

2.8 x 10-7

 

6.55

 

Phenol

 

1.3 x 10-10

 

9.89

 

 

The Ka can be used to determine pH of an aqueous solution of a weak acid.For example, whatís the pH of a 100mM solution of acetic acid?

 

We can solve this using the quadratic formula,

 

which gives us the result

 

[H+] = 0.00134 M

 

However!Remember that the characteristic of a weak acid is slight dissociation!Therefore, a reasonable assumption is that the concentration of acid, [HA], changes only slightly at equilibrium.It is often a very good approximation to treat [HA] as constant.If we repeat the above calculation and approximate [HA} = 0.1 M, then we get the result

 

[H+] = 0.00134 M

 

As long as [H+] < 5% [HA], this approximation is perfectly reasonable.There are very few biochemical situations where this approximation is seriously off.


 

Polyprotic Acids:

 

Some acids can donate more than one proton in chemical reactions.For example, phosphoric acid has 3 dissociable protons.Each dissociation represents an equilibrium between a conjugate acid and a conjugate base, and is characterized by its own pKa

 

H3PO4 ††H+ + H2PO4- ††2H+ + HPO4-2 3H+ + PO4-3

††††††††† pKa1†††††††††††††††††† pKa2††††††††††††††††††††† pKa3

pKa1 = 2.12

pKa2 = 7.20

pKa3 = 12.6

 

Titration Problems:

 

Letís start with 10 ml of a solution that contains some concentration of a strong acid, say HCl.We want to determine that acid concentration.We set up a titration, where we monitor the pH of the solution as we add base - say, 0.5M NaOH.

 

Adding NaOH converts the H+ present to water

 

OH- + H+ Ė> H2O

 

 

 

 

We notice that the solution reaches neutrality when we have added 8.5 ml of our 0.5 M NaOH solution.In order to achieve neutrality, moles OH- added = moles H+ originally there

 

 

Therefore, the 10 ml. of original acid solution must have contained 0.00425 mol acid, for an original concentration of 0.425 M.Alternatively, we can calculate via:

 

 


 

Titrating Weak Acids - itís different!

 

 

If we titrate a weak acid, say 0.1M acetic acid, with NaOH, we get quite a different picture.In the first place, the pH of 100mM HAc is 2.88, while the pH of 100mM HCl would be 1.in addition, however, the titration curve for HAc shows little change in pH until large amounts of NaOH have been added.This is a result of the equilibrium set up between a weak acid and itís conjugate base.The relationship between pH and this equilibrium is easily derived.

 

 

 

This expression is the Henderson - Hasselbachequation, and can be used to determinre the pH of solutions containing a conjugate acid in equilibrium with itís conjugate base.Such solutions, which stabilize pH against the addition of acid and base, are called buffers.Blood, lymph, and the cytoplasm of cells are all buffered solutions.

 

Predicting pH:

Letís make 1 liter of a solution that is 0.1 M in acetic acid ( pKa = 4.74 ) and 0.3 M in sodium acetate.Remember: acetate ion is the conjugate base of acetic acid.What is the pH of the resulting solution?

 

 

What is the buffering effect?


Letís look at an example:to 1 liter of H2O at pH 7, we add 100 mmol of HCl.Since HCl is a strong acid, this raises the [H+] concentration to 100 mM.The new pH will be -log(0.1), or 1.In other words, we have dropped the pH of the solution by 6 full pH units.

 

What happens if we add the same amount of HCl, only this time to 1 liter of our 0.4M HAc solution?Our starting pH, remember, is 5.24.What happens chemically when we add HCl to this solution?Remembering General Chemistry, a (relatively) strong acid and strong base will react to make a weaker acid and a weaker base.HCl is a much stronger acid than HAc; converseley, Cl- is a much weaker base than Ac-.Hence

 

HCl + Ac- ŗ Cl- + HAc

 

100 mmol of HCl converts 100 mmol of acetate ion to acetic acid.As a result, Henderson - Hasselbach tells us the new pH will be

 

 

In other words, instead of a ph change of 6 units, we have a pH change of less than 0.5 units.

 

Buffer Capacities and Dependencies

 

The pKa value of a buffer system varies with both temperature and ionic strength.

 

Ionic Strength:

The ionic strength of a system is the sum of contributions from all ions present:

 

††† where

Ci is the concentration of ion I,

Zi is the charge on ion i

Increasing ionic strength alters the effective pKa of a buffer.For example, the pKa2 listed above for phosphate, 7.2, is the pKa at ionic strength 0.At physiological conditions, the actual pKa2 for phosphate is about 6.86.

 

Temperature:

Different buffers show different thermal coefficients.The common biochemical buffer Tris (tris-hydroxymethylaminomethane) has a rather large thermal coefficient of Ė0.031 pH unite/oC.In going from 25oC to 37oC, the pKa drops from 8.30 to 7.77

 

Physiological Example: Blood pH Control

 

The normal pH of human blood is approximately 7.4, and is tightly regulated.If the pH falls below 7.4, the condition is known as acidosis; if the pH rises higher, alkalosis results.A pH below 6.8 or above 7.8 generally produces a visit to the coroner.

 

Blood pH is regulated by four buffer systems:

(8)               Carbonate††††††††††††††††††† H2CO3 H+ + HCO3-††††††††† pKa = 6.1

(9)               Phosphate††††††††††††††††††† H2PO4- H+ + HPO4-2†††††††† pKa = 7.2

(3)††††††† Plasma Proteins

(10)           Hemoglobin

 

The primary system, carbonate, has 3 interlocking equilibria:

 

CO2(g)CO2(aq) + H2OH2CO3 H+ + HCO3-

 

Excess H+ drives the reaction to the left.

Excess base pulls the system to the right.

 

Question:

Blood total dissolved carbonate is about 28 mM.What are the actual concentrations of carbonic acid and bicarbonate ion in normal human blood?

 

Answer:

We can determine the carbonic acid / bicarbonate ratio using the Henderson - Hasselbach equation:


 

 

Since total dissolved carbonate is about 28 mM:

 

[HCO3] = 1.3 mM

[H2CO3] = 26.7 mM

 

Diseases that effect the level of [HCO3-] are metabolic effects, due to changes in cellular metabolism.

Diseases that change [H2CO3] are respiratory effects; the lungs control the exchange of CO2, and therefore the concentration of H2CO3 .

 

Metabolic Acidosis:

Diseases such as diabetes or diarrhea result in an excess of H+ in the tissues.

[HCO3-] goes DOWN (equilibrium pushed to left)

Blood pH goes DOWN. (equilibrium to left; higher carbonic acid, lower bicarbonate)

 

Metabolic Alkalosis:

Vomiting causes loss of H+.

[HCO3-] goes UP (equilibrium pulled to right)

Blood pH goes UP. (equilibrium to right; lowerer carbonic acid, higher bicarbonate)

 

Respiratory Acidosis:

In conditions like emphysema, pneumonia, your lungs do not work effectively to clear CO2.

[H2CO3] goes UP (driven by carbon dioxide build-up.)

Blood pH goes DOWN (as carbonic acid accumulates.)

 

Respiratory Alkalosis:

When you hyperventilate or become hysterical, you blow off lots of CO2.

[H2CO3] goes DOWN (since its being withdrawn as CO2.)

Blood pH goes UP (less carbonic acid.)

 

Blood pH goes DOWN (as carbonic acid accumulates.)