Reminder: assigned homework problems for Chapter 2:
1, 2, 4, 5, 7, 13, 15
Questions
Any questions on the material from the previous lecture?
Section 2.8: The pH Scale
In the previous lecture, we discussed how a small amount of pure water exists in an ionized form, with both
[H+] and [OH-] in equal concentrations of 1x10-7M
The concentration of protons in water can vary over many orders of magnitude above and below its standard value
Changes in [H+] have significant effects on many biochemical processes. Consequently, a
logarithmic quantity, pH, was developed as a convenient scale for working with levels of [H+]
pH is defined as the negative of the base 10 log of the proton concentration:
Reciprocal Relation of [H+] and [OH-]
A change in 1 pH unit corresponds to a ten-fold change in concentration
Give a value of one, the other can be found by dividing the ion product Kw:
[OH-] = 1 x 10-14 / [H+]
[H+] = 1 x 10-14 / [OH-]
pH Values for Various Fluids
pH values less than 7 are acidic
pH values greater than 7 are basic
A pH value of 7 is neutral
pH of normal human blood is 7.4
Diabetics can have lower pH (acidosis)
Prolonged vomiting or hyperventilation can produce a higher pH (alkalosis)
pH of Strong Acid Solutions
If an acid such as hydrochloric acid (HCl) is added to water, the H+ and the Cl-
dissociate (almost) completely from each other
When this complete dissociation occurs, the acid is said to be a strong acid
One consequence of this is that the amount of a strong acid directly determines the resulting [H+]
and pH
For example, in a solution of 0.01 M HCl, there will be 0.01 M [H+]
This is 1 x 10-2 M [H+], so the pH of the solution is 2
pH of Strong Base Solutions
Similarly, for a strong base such as sodium hydroxide (NaOH), the Na+ and OH- ions
will dissociate completely from each other in water
A 0.01 M solution of NaOH will have an OH- concentration of 1 x 10-2
What is the pH?
[H+] = 1 x 10-14 / 1 x 10-2 = 1 x 10-12
The pH will be 12
Section 2.9: Weak Acids and pKa
Many acids, such as the amino acids in proteins and acetic acid (the main ingredient in vinegar), do
not dissociate completely in water
Such acids are called weak acids, and similarly, bases that do not completely dissociate
are called weak bases
Ka, the acid dissociation constant, is the equilibrium constant for the reaction of
a weak acid HA converting into a proton and the conjugate base, A-:
pKa
As with pH, the logarithmic scale is useful for working with Ka values that can
vary over many orders of magnitude
In analogy with the definition of pH, the parameter pKa is defined as:
Unlike pH (which represents a concentration), pKa represents an intrinsic property of acids
This property is the tendency to dissociate into [H+] and the conjugate base [A-]
pKa Values of Some Common Weak Acids
The Henderson-Hasselbalch Equation
If we create a solution of a weak acid, it is possible to find a simple relation between
the amount and pKa of the acid and the resulting pH of the solution
We start with the equation that defines the acid dissociation constant Ka:
Taking the log of both sides, we get:
Swapping sides for the Ka and H+ terms gives:
The Henderson-Hasselbalch Equation
This gives the pH in terms of the pKa of the acid and the log of the ratio of [A-] to [HA]:
This useful relation is called the Henderson-Hasselbalch equation
It is important to note that the concentrations in the equation are the final values of
[HA] and [A-], after they have come to equilibrium
Unlike the situation with strong acids, the final amount of the conjugate base of a dissociated
weak acid will generally be different from the initial amount that is added to the solution
Consequently, the calculations for determining weak acid concentrations are a little more complicated,
as we will see in an example
Titration of a Weak Acid
The pKa values of weak acids are determined by titration. This involves adding small increments
of a known amount of a strong base to the solution and measuring the resulting changes in pH
For example, titration of acetic acid gives the curve shown above.
Note that the pKa value is determined by an inflection point (minimum slope) at the midpoint of the
curve
At this point, there are equal concentrations of HA and A-.
Here, as given by the Henderson-Hasselbalch equation, the pH will be equal to the pKa
Use of the HH Equation
When the pH of a solution is previously established, such as the acidic environment of the stomach,
the Henderson-Hasselbalch (HH) equation is useful for determining how much of a weak acid will dissociate in
a given environment
For example, if the pH is > than the pKa of a weak acid, which species will predominate, [A-] or [HA]?
In this case, pH - pKa will be positive, so there must be more A- than HA (more deprotonated)
Which predominates if the pH is < than the pKa?
Here, pH - pKa will be negative, so there must be more HA than A- (more protonated)
Some Useful Math for pH Calculations
If y = log x, then x = 10y
log( x * y) = log( x ) + log( y )
log( x / y) = log( x ) - log( y )
-log( x ) = log( 1 / x )
log( 1 ) = 0
A Sample Calculation with HH
What is the pH of a solution of 0.1M acetic acid?
The Ka is 1.76 x 10-5M
We don't know the final concentration of [H+], so call it x
The equation for the dissociation constant Ka gives:
This is a quadratic equation with a = 1, b = 1.76 x 10-5, and c = -1.76 x 10-6,
giving x = 0.00132 (and a negative root, which we throw out)
The pH is then -log(0.00132) = 2.9
Note that if we assume that [HA] remains constant (usually valid for weak bases), we get a
simpler equation to solve: 1.76 x 10-5 = x2 / 0.1, x = 1.33 x 10-3, pH = 2.9
Polyprotic Acids
Titration of polyprotic acids (acids with multiple proton-donating groups) usually give a curve
with multiple inflection points, with one inflection point for each donating group:
Section 2.10: Buffers
Because a weak acid (or base) can exist in equilibrium with its conjugate, the equilibrium
can be maintained even when small amounts of [H+] or [OH-] are added to it
For example, consider a solution with equal amounts of a weak acid [HA] and conjugate base [A-]
If a small amount of [H+] is added, then as long as there is some [A-] available in the
solution, the [H+] can combine with it to produce [HA], maintaining the [H+] level
If a small amount of [OH-] is added, then as long as there is [HA] available in the solution, it can
dissociate to [H+] and [A-], providing some [H+] to combine with
the [OH-], again acting to maintain the existing [H+] level
A solution with this kind of ability to resist changes in pH is called a buffer
Physiological Buffering
An example of a buffering system in living organisms is found in the blood plasma of mammals
The buffering capacity of the blood is demonstrated by a comparison with saline and water
When 1 mL of 10 M HCL is added to saline or water, the pH is lowered from 7.0 to 2.0. By contrast,
the same amount of acid added to blood plasma produces a much smaller change in pH, from 7.4 to 7.2
The means for regulating the pH in the blood is through the carbon dioxide - carbonic acid - bicarbonate
buffer system
The Blood Buffering System
This system controls pH through the ratio of bicarbonate (HCO3-) to pCO2 in the lungs
When the pH in the blood decreases, pCO2 increases, lowering the [H+] in the blood and
restoring the pH level
If the pH of the blood rises, CO2 dissolves back into the blood, shifting the equlibrium
in the opposite direction
