Hello - I was planning to answer this question for you, but am called
away for other tasks. If I have a chance, I will finish the answer,
otherwise, another researcher may be able to furnish you with a
complete answer.
pKa is a property of a compound which can undergoe acid-base chemistry
and is a reflection of the compound's propensity to give up or accept
a hydrogen ion. It is related, quite intimately, to the more common
term of pH. Simply put, the pKa of compound X is related to the pH of
a solution of compound X when it is at equilibrium between it's acid
and base forms. In more depth, the pH is the negative logarithm of
the hydrogen ion concentration in a solution (a reflection of the
acidity of the solution - the more hydrogen ions, the more acidic the
solution, and the lower the pH).
The pKa is the negative logarithm of the equilibrium constant (Ka) of
the acid-base reaction of the compound of interest. The pKa of a
compound relates to how likely, at a give pH, the compound will be
ionized (that is either negatively charged because it gave up a
hydrogen ion, or positively charged because it has picked up an extra
hydrogen ion). This is important for the functional groups of many
organic and biologic molecules as the presence of a charge on a
functional group affects the solubility of the compound in water vs.
non-polar solvents (think fats in the body), and can also affect the
reactivity of the functional group with other molecules due to charge
interactions (postive ions react with negative ions).
Determining factors for the pKa of a compound relate to how well the
molecule can stabilize a charge - an ion is inherently more unstable
(due to reactivity) than a non-charged molecule. If a compound has a
way to stabilize a negative charge near the location of a hydrogen
atom, it will be more likely to give up that hydrogen ion, and thus
it's pKa will be low - it will be an acid - conversely, if a compound
can stabilize a positive charge, it will be more likely to accept a
hydrogen ion, and thus act as a base. Molecules can stabilize charges
either due to the inherent electronegativity (ability to pull
electrons close) of atoms in the molecule (known as inductive effects)
or due to the ability to spread the charge around the molecule in
delocalized electron bonds (resonance effects).
The importance of pKa to physiology can be found in at least three
broad areas. One, biologic systems need to preserve a relatively
constant environment, including control over the pH of the organism's
fluids. One way to acheive this is through the use of "buffers" - a
buffer is a compound which due to it's acid-base chemistry reacts to
changes in the environment to preserve a near constant pH that is near
the pKa of the buffering compound. The second broad area relates to
the presence of reactive functional groups on molecules (proteins,
lipids, and other small molecules) which need to be charged in order
to undergoe the desired reaction - these functional groups will only
be substantially charged when the pH differs from their pKa by a
sufficient amount to ensure a high probability of ionization. This is
seen in the reactive centers of enzymes, in the structural components
of molecules which change shape with pH (such as hemoglobin), and in
molecules that are attatched to other molecules in cells (such as
ATP). The third area relates to solubility and the ability of
compounds to distribute through an organism - charged compounds are
most soluble in polar solvents, like water, and are much less soluble
in non-polar substances, like lipids or fats. Thus, a charged
molecule will distribute only to watery fluids in an organism and will
be blocked by lipid layers (like cell walls), whereas uncharged
compounds will have the possibility of distributing across cell walls.
Considering all of the above, it would seem that the best place to
start would be a discussion of acid-base chemistry.
Acids & Bases
==============
For the sake of simplicity, we wlll only cover the topic of acids and
bases as they apply to aqueous solutions (water based solutions).
Water is composed of two atoms of hydrogen bound to one atom of oxygen
- schematically: H-O-H
Water undergoes spontaneous dissociation into two charged forms:
H - O - H <---> H(+) + OH(-)
water hydrogen hydroxide
ion
representing the chemical equilibrium of this equation
Kw = [H+][OH-] = 1.00 * 10^-14
which means that at equilibrium there are equal amounts of hydrogen
and hydroxide ions, both with a concentration of 1.00 * 10^-7.
The pH of a solution is defined as the negative log of the hydrogen
ion concentration, so, water at equilibrium contains 1.00 * 10^-7
hydrogen ions, and the negative log of this is equal to 7. This gives
us the basis of the pH chart with pH 7 representing neutrality. Lower
pH numbers represent more hydrogen ions in solution and are more
acidic, higher pH numbers represent more hydroxide ions in solution
and are more basic.
Acids are most conventionally defined as compounds which give up a
hydrogen ion (also sometimes referred to as a proton), while bases
accept a hydrogen ion. For instance, hydrochloric acid (a strong
acid) is one atom of hydrogen and one atom of chlorine: H-Cl. It
undergoes the following reaction:
H-Cl <----> H(+) + Cl(-)
note that all of these equations contain a double-headed arrow - these
reactions are equilibrium-type reactions which can progress in either
direction. This particular acid is a "strong" acid which means that
it almost entirely exists as the dissociated components, H+ and Cl-.
Calculating the pH of a strong acid solution is relatively straight
forward as you can assume that for each molecule of starting material,
one molecule of hydrogen will be produced. Thus, 0.5 M HCl will
produce 0.5 M of H+, which gives:
pH = -log(0.5) = 0.3
More commonly found in biological systems are 'weak' acids which are
not usually found completely dissociated into ions, but exist at
equilibrium with a fair amount of non-ionized starting material. An
example is acetic acid (vinegar): CH3CO2H
O O
|| ||
CH3-C-O-H <----> CH3-C-O- (-) + H(+)
Now, since weak acids do not completely dissociate, we must consider
the amount of starting material in our equation. The equilibrium
constant for the dissociation is defined as Ka (which in this case is
1.8*10^-5):
[CH3CO2-][H+]
Ka = ------------- = 1.8*10^-5
[CH3CO2H]
Example: Calculate the pH of a solution of 0.5M acetic acid
[CH3CO2-][H+] [x][x]
Ka = ------------- = 1.8*10^-5 = -------- so:
[CH3CO2H] [0.5M]
x^2 = 0.5 M *1.8*10^-5 and x = 0.003
so pH = -log(0.003) = 2.5
More complicated examples can be considered by considering how this
reaction actually proceeds in water:
CH3CO2H + H20 <----> H30(+) + CH3CO2(-)
the acetic acid acts as an acid and the water acts as a base on the
left side of the equation. For the reverse reaction (called the
conjugate reaction), the protonated water (H3O+) acts as an acid (the
conjugate acid) and the CH3CO2- acts as a base (the conjugate base).
This is the same if an acid and a base are mixed in solution.
Represented as:
A-H + B <----> A(-) + B-H(+)
where A-H = acid
B = base
A(-) = conjugate base
B-H(+) = conjugate acid
a very useful equation for calculating the pH of a solution using the
pKa is the Henderson-Hasselbach equation:
[acid]
pH = pKa - log ( -------- )
[base]
Strong bases obey the same principle as strong acids - they completely
dissociate in solution.
Weak bases obey the same rules as weak acids, they do not dissociate completely.
Note: when calculating the equilibrium for a base, consider the water
reaction to realize these two useful relations:
pH + pOH = 14
[H+][OH-] = 1.0 * 10^-14
Examples of calculating pKa for acids and bases:
1) A 4.85 x 10-3 mol sample of HY is dissolved in 0.095L of water. If
the pH of the solution is 2.68, what is the Ka for this acid?
M = 4.85 x 10-3 mol /0.095L = 0.051M
X = [H3O+] = 10-pH = 10-2.68 = 2.1 x 10-3
Ka = [H3O+] [Y-] / [HY] = x2/0.051
Assume x can be neglected and check later. (was o.k. to neglect x)
Ka = (2.1 x 10-3)2/0.051 = 8.6 x 10-5
from: http://216.239.51.104/search?q=cache:XzzrlsKz0lEJ:faculty.fortlewis.edu/CARROLL_M/C151ProbSet3Solns.doc+acid-base+%22calculate+pka%22&hl=en&ie=UTF-8
2) What is the pH of a buffer made from 0.12M H3BO3 and 0.82M NaH2BO3?
The Ka of boric acid is 5.75 x 10-10
Use Henderson-Hasselbach Here!
Calculate pKa = - log Ka = - log 5.75 x 10-10 = 9.24
pH = pKa + log [salt]/[acid] = 9.24 + log (0.82/0.12) = 10.07
from: http://216.239.51.104/search?q=cache:XzzrlsKz0lEJ:faculty.fortlewis.edu/CARROLL_M/C151ProbSet3Solns.doc+acid-base+%22calculate+pka%22&hl=en&ie=UTF-8
pKa and functional groups
==========================
References
============
A nice, simple page on acid-base chemistry:
http://www.shodor.org/unchem/basic/ab/
A nice slideshow series of a lecture on acid-base chemistry:
http://www.chem.neu.edu/Courses/1221PAM/acidbase/
An abitiously titled page:
http://www.chem.ubc.ca/courseware/330%20/pKa.html
A table of the pKa's of common functional groups:
http://www.sussex.ac.uk/Users/kafj6/information/pka/organic.html
A much more in-depth page concerning the calculation of the pKa for
side-groups in proteins. Discusses the effects of pKa on protein
stability and reaction:
http://mccammon.ucsd.edu/~jnielsen/manuals/pKa.html |
