36.4D: Balance and Determining Equilibrium - Biology

36.4D: Balance and Determining Equilibrium - Biology

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With hair cells in the inner ear that sense linear and rotational motion, the vestibular system determines equilibrium and balance states.

Learning Objectives

  • Describe the anatomy that enables equilibrium and balance

Key Points

  • The hair cells of the utricle and saccule of the inner ear extend into the otolith, a dense viscous substance with calcium carbonate crystals.
  • The otolith slides over the macula, tissue supporting the hair cells, in the direction of gravity when the head is moved due to its greater inertia, causing a pattern of hair cell depolarization interpreted by the brain as tilting.
  • The three semicircular canals of the inner ear are ring-like structures with one ring oriented in the horizontal plane and the other two rings oriented at approximately 45 degrees relative to the sagittal plane.
  • The ampulla, found at the base of each semicircular canal, contains hair cells that extend into the membrane that attaches to the top of the ampulla to an area called the cupula.
  • A head rotation causes the fluid in the semicircular canal to move, but with a lag which produces a deflection of the cupula in the direction opposite to the head rotation which in turn causes the hair cells to depolarize.
  • Using the hair cell depolarization information from all three ampullae, the direction and speed of head movements in all three dimensions can be detected by the vestibular system.

Key Terms

  • stereocilium: any of many nonmotile cellular structures resembling long microvilli; those of the inner ear are responsible for auditory transduction
  • equilibrium: the condition of a system in which competing influences are balanced, resulting in no net change
  • otolith: a small particle, comprised mainly of calcium carbonate, found in the inner ear of vertebrates, being part of the balance sense


Along with audition, the inner ear is responsible for encoding information about equilibrium, or the sense of balance. A similar mechanoreceptor—a hair cell with stereocilia —senses head position, head movement, and whether our bodies are in motion. These cells are located within the vestibule of the inner ear. Head position is sensed by the utricle and saccule, whereas head movement is sensed by the semicircular canals. The neural signals generated in the vestibular ganglion are transmitted through the vestibulocochlear nerve to the brain stem and cerebellum. Together, these components make up the vestibular system.

Linear acceleration

The utricle and saccule are both largely composed of macula tissue (plural = maculae). The macula is composed of hair cells surrounded by support cells. The stereocilia of the hair cells extend into a viscous gel called the otolith. The otolith contains calcium carbonate crystals, making it denser and giving it greater inertia than the macula. Therefore, gravity will cause the otolith to move separately from the macula in response to head movements. Tilting the head causes the otolith to slide over the macula in the direction of gravity. The moving otolith layer, in turn, bends the sterocilia to cause some hair cells to depolarize as others hyperpolarize. The exact tilt of the head is interpreted by the brain on the basis of the pattern of hair-cell depolarization.

Rotational movement

The semicircular canals are three ring-like extensions of the vestibule. One is oriented in the horizontal plane, whereas the other two are oriented in the vertical plane. The anterior and posterior vertical canals are oriented at approximately 45 degrees relative to the sagittal plane. The base of each semicircular canal, where it meets with the vestibule, connects to an enlarged region known as the ampulla. The ampulla contains the hair cells that respond to rotational movement, such as turning your head from side to side when saying “no.” The stereocilia of these hair cells extend into the cupula, a membrane that attaches to the top of the ampulla. As the head rotates in a plane parallel to the semicircular canal, the fluid lags, deflecting the cupula in the direction opposite to the head movement. The semicircular canals contain several ampullae, with some oriented horizontally and others oriented vertically. By comparing the relative movements of both the horizontal and vertical ampullae, the vestibular system can detect the direction of most head movements within three-dimensional (3-D) space.

36.4D: Balance and Determining Equilibrium - Biology

Calculating Equilibrium Constants

  • the balanced equation for the reaction system, including the physical states of each species. From this the equilibrium expression for calculating Kc or Kp is derived.
  • the equilibrium concentrations or pressures of each species that occurs in the equilibrium expression, or enough information to determine them. These values are substitued into the equilibrium expression and the value of the equilibrium constant is then calculated.
  • Calculating K from Known Equilibrium Amounts
  • Calculating K from Initial amounts and One Known Equilibrium Amount
  • Calculating K from Known Initial Amounts and the Known Change in Amount of One of the Species
  • Write the equilibrium expression for the reaction.
  • Determine the molar concentrations or partial pressures of each species involved.
  • Subsititute into the equilibrium expression and solve for K.

[CO2] = 0.1908 mol CO2/2.00 L = 0.0954 M
[H2] = 0.0454 M
[CO] = 0.0046 M
[H2O] = 0.0046 M

Balance is tricky and depends on a lot of things, including, to some degree, your sight. Balance is achieved and maintained by a complex set of sensorimotor control systems that include sensory input from vision (sight), proprioception (touch), and the vestibular system (motion, equilibrium, spatial orientation) integration of that sensory input and motor output to the eye and body muscles. Your vision helps you see where your head and body are in relationship to the world around you and to sense motion between you and your environment.

Very simply put, to blindfold someone is to take out the contribution of vision to balance. So, if the other systems involved in balance are off even a bit, blindfolding someone will interfere with their ability to keep their balance, even on two legs, let alone one.

Here are those systems in more detail.

Proprioception. In your joints, muscles, tendons, skin, and other areas, you have proprioceptors, that tell your brain where yoor aody parts (arms, legs, etc) are in relation to self in space. Because we live on a planet with gravity, even if we are blindfolded, if we are standing correctly, our feet will sent our brain signals that will in turn allow the brain to judge our position in space with regard to gravity and we will keep our feet firmly planted on the ground in a way which will maintain us upright in a constantly regulated position (if we sense less pressure from the bottom of our right great toe, we will adjust by leaning forward and to the right a bit until out=r brain says, "ok, right there!" This happens from all the skin and joint proprioceptors responding at the same time. Notice that once vision is blocked, our bodies become relatively very still we focus on our balance. We move tentatively.

As people age, they lose some of their propioceptive abilities. That's one of the reasons for falls in the elderly.

Inner ear. In our inner ear are the semi-circular canals, three on each side, which are oriented at

90° to each other so we cover 3 dimensions. In these canals is fluid which sloshes about when we move our heads, change directions, bend over, etc. The fluid moving about is detected by fine hair-like projections on the sensory cells lining the canal called stereocilia - like a wave would be detected by your leg in shallow ocean water. These semicircular canals help us to remain oriented in space. Now, the semicircular canals are also attached to otolith organs - two chambers which are concerned with gravity. They have fine crystals in them - called otoconia - which move according to our head's position with relationship to "down", or gravity.

If we stand perfectly still (probably not possible without support), everything is read by the vestibular system (the semicircular canals and the otolithic organs) as normal, and we stay upright (there is a constant communication between our vestibular system and our brain). So, when blindfolded, we can stay upright even if we shake our heads, bend them forward or back, etc (within reason). As we age, things can degenerate in this vestibular system, which affects our balance, and results in more falls in the elderly. (Diseases in the young can also affect this.)

Vestibulo-ocular Reflex. A complicated system which reflexly coordinated input from your vestibular system and your vision in head movement. If someone suddenly turns your head, your eyes will move in the equal and opposite manner, that is, your eyes will stay focused on the object on which they were focused just before your head was moved. This system is what allows you to easily keep reading something while you shake your head from side to side (not the case if you move the print side to side).

Transduction of Sound

When sound waves reach the ear, the ear transduces this mechanical stimulus (pressure) into a nerve impulse (electrical signal) that the brain perceives as sound.

Learning Objectives

Describe the transduction of sound and the relevant ear anatomy

Key Takeaways

Key Points

  • The human ear has three distinct functional regions: the outer ear, which collects sound waves the middle ear, which represents the sound waves as pressure, and the inner ear, which converts those pressure signals into electrical signals that the brain perceives as sound.
  • The outer ear involves the pinna (the external shell-shaped structure on the outside of the head), which assists in collecting sound waves the meatus (the external canal) and the tympanic membrane, also known as the eardrum.
  • The middle ear exists between the eardrum and the oval window (the external border with the inner ear) and consists of three separate bones: the malleus, the incus, and the stapes.
  • While the middle ear cavity is filled with air, the inner ear is filled with fluid.
  • The inner ear exists on the other side of the oval window from the middle ear, by the temple of the human head, and consists of three parts: the semicircular canals, the vestibule, and the cochlea.
  • Within the cochlea, the inner hair cells are most important for conveying auditory information to the brain.

Key Terms

  • ossicle: a small bone (or bony structure), especially one of the three of the middle ear
  • cochlea: the complex, spirally coiled, tapered cavity of the inner ear in which sound vibrations are converted into nerve impulses
  • transduce: to convert energy from one form to another

Vibrating objects, such as vocal cords, create sound waves or pressure waves in the air. When these pressure waves reach the ear, the ear transduces this mechanical stimulus (pressure wave) into a nerve impulse (electrical signal) that the brain perceives as sound. The pressure waves strike the tympanum, causing it to vibrate. The mechanical energy from the moving tympanum transmits the vibrations to the three bones of the middle ear. The stapes transmits the vibrations to a thin diaphragm called the oval window, which is the outermost structure of the inner ear.

Diagram of the middle ear: The middle ear exists between the tympanic membrane (the boundary with the outer ear) and the oval window (the boundary with the inner ear) and consists of three bones: the malleus (meaning hammer), the incus (meaning anvil), and the stapes (meaning stirrup).

The structures of the inner ear are found in the labyrinth, a bony, hollow structure that is the most interior portion of the ear. Here, the energy from the sound wave is transferred from the stapes through the flexible oval window and to the fluid of the cochlea. The vibrations of the oval window create pressure waves in the fluid (perilymph) inside the cochlea. The cochlea is a whorled structure, like the shell of a snail, and it contains receptors for transduction of the mechanical wave into an electrical signal. Inside the cochlea, the basilar membrane is a mechanical analyzer that runs the length of the cochlea, curling toward the cochlea’s center.

Inner ear: The inner ear can be divided into three parts: the semicircular canals, the vestibule, and the cochlea, all of which are located in the temporal bone.

The mechanical properties of the basilar membrane change along its length, such that it is thicker, tauter, and narrower at the outside of the whorl (where the cochlea is largest), and thinner, floppier, and broader toward the apex, or center, of the whorl (where the cochlea is smallest). Different regions of the basilar membrane vibrate according to the frequency of the sound wave conducted through the fluid in the cochlea. For these reasons, the fluid-filled cochlea detects different wave frequencies (pitches) at different regions of the membrane. When the sound waves in the cochlear fluid contact the basilar membrane, it flexes back and forth in a wave-like fashion. Above the basilar membrane is the tectorial membrane.

Transduction: In the human ear, sound waves cause the stapes to press against the oval window. Vibrations travel up the fluid-filled interior of the cochlea. The basilar membrane that lines the cochlea gets continuously thinner toward the apex of the cochlea. Different thicknesses of membrane vibrate in response to different frequencies of sound. Sound waves then exit through the round window. In the cross section of the cochlea (top right figure), note that in addition to the upper canal and lower canal, the cochlea also has a middle canal. The organ of Corti (bottom image) is the site of sound transduction. Movement of stereocilia on hair cells results in an action potential that travels along the auditory nerve.

The site of transduction is in the organ of Corti (spiral organ). It is composed of hair cells held in place above the basilar membrane like flowers projecting up from soil, with their exposed short, hair-like stereocilia contacting or embedded in the tectorial membrane above them. The inner hair cells are the primary auditory receptors and exist in a single row, numbering approximately 3,500. The stereocilia from inner hair cells extend into small dimples on the tectorial membrane’s lower surface. The outer hair cells are arranged in three or four rows. They number approximately 12,000, and they function to fine tune incoming sound waves. The longer stereocilia that project from the outer hair cells actually attach to the tectorial membrane. All of the stereocilia are mechanoreceptors, and when bent by vibrations they respond by opening a gated ion channel (refer to [link]). As a result, the hair cell membrane is depolarized, and a signal is transmitted to the chochlear nerve. Intensity (volume) of sound is determined by how many hair cells at a particular location are stimulated.

The hair cells are arranged on the basilar membrane in an orderly way. The basilar membrane vibrates in different regions, according to the frequency of the sound waves impinging on it. Likewise, the hair cells that lay above it are most sensitive to a specific frequency of sound waves. Hair cells can respond to a small range of similar frequencies, but they require stimulation of greater intensity to fire at frequencies outside of their optimal range. The difference in response frequency between adjacent inner hair cells is about 0.2 percent. Compare that to adjacent piano strings, which are about six percent different. Place theory, which is the model for how biologists think pitch detection works in the human ear, states that high frequency sounds selectively vibrate the basilar membrane of the inner ear near the entrance port (the oval window). Lower frequencies travel farther along the membrane before causing appreciable excitation of the membrane. The basic pitch-determining mechanism is based on the location along the membrane where the hair cells are stimulated. The place theory is the first step toward an understanding of pitch perception. Considering the extreme pitch sensitivity of the human ear, it is thought that there must be some auditory “sharpening” mechanism to enhance the pitch resolution.

When sound waves produce fluid waves inside the cochlea, the basilar membrane flexes, bending the stereocilia that attach to the tectorial membrane. Their bending results in action potentials in the hair cells, and auditory information travels along the neural endings of the bipolar neurons of the hair cells (collectively, the auditory nerve) to the brain. When the hairs bend, they release an excitatory neurotransmitter at a synapse with a sensory neuron, which then conducts action potentials to the central nervous system. The cochlear branch of the vestibulocochlear cranial nerve sends information on hearing. The auditory system is very refined, and there is some modulation or “sharpening” built in. The brain can send signals back to the cochlea, resulting in a change of length in the outer hair cells, sharpening or dampening the hair cells’ response to certain frequencies.

Higher Processing

The inner hair cells are most important for conveying auditory information to the brain. About 90 percent of the afferent neurons carry information from inner hair cells, with each hair cell synapsing with 10 or so neurons. Outer hair cells connect to only 10 percent of the afferent neurons, and each afferent neuron innervates many hair cells. The afferent, bipolar neurons that convey auditory information travel from the cochlea to the medulla, through the pons and midbrain in the brainstem, finally reaching the primary auditory cortex in the temporal lobe.

Immigration, Extinction, and Island Equilibrium

Equilibrium is an important concept that permeates many disciplines. In chemistry we think about the point where the rate of forward reaction is equal to the rate of backward reaction. In economics we think of the point where supply equals demand. In physics we can see how gravity is balanced by forward velocity to create things like planetary orbits.

No matter which discipline we are examining, the core idea remains the same: Equilibrium is a state where opposing forces are balanced.

In biology, equilibrium is so important that it can mean the difference between life or death for a species, it can decide whether they will thrive or become extinct.

In The Song of the Dodo, David Quammen dives into how equilibrium affects a species’ ability to survive, and how it impacts our ability to save animals on the brink of extinction.

Historically, the concept of island equilibrium was studied with a focus on the interplay between evolution (as the additive) and extinction (as the subtractive). It was believed that speciation, the process where one species becomes two or more species, caused any increase in the number of inhabitants on an island. In this view, the insularity of islands created a remoteness that could only be overcome by the long processes of evolution.

However, Robert MacArthur and E.O. Wilson, the co-authors of the influential Theory of Island Biogeography, realized that habitats would show a tendency towards equilibrium much sooner than could be accounted for by speciation. They argued the ongoing processes that most influenced this balance were immigration and extinction.

The type of extinctions we’re referring to in this case are local extinctions, specific to the island in question. A species can go extinct on a particular island and yet be thriving elsewhere it depends on local conditions.

As for immigration, it’s just what you’d expect: The movement of species from one place to another. Island immigration describes the many ingenious ways in which plants, animals, and insects travel to islands. For instance, not only will insects hitch rides on birds and debris (man made or natural, think garbage and sticks/uprooted seaweed), animals will do the same if the debris is massive enough.

Seeds, meanwhile, make the trip in the feces of birds, which helps to introduce new plant species to the island, while highly motivated swimmers (escapees of natural disasters/predators/famine) and hitchhikers on human ships (think rats) make it over in their own unusual ways.

We can plot this process of immigration and extinction graphically, in a way you’re probably familiar with. Quammen explains:

The decrease in immigration rate and the increase in extinction rate are graphed not against elapsed time but against the number of species present on a given island. As an island fills up with species, immigration declines and extinction increases, until they offset each other at an equilibrium level. At that level, the rate of continuing immigration is just canceled by the rate of continuing extinction, and there is no net gain or loss of species. The phenomenon of offsetting increase and decrease – the change of identities on the roster of species – is known as turnover. One species of butterfly arrives, another species of butterfly dies out, and in the aftermath the island has the same number of butterfly species as before. Equilibrium with turnover.

So while the specific species inhabiting the island will change over time, the numbers will tend to roll towards a balanced point where the two curves intersect.

Of course, not all equilibrium graphs will look the like one above. Indeed, MacArthur and Wilson hoped this theory would be used not just to explain equilibriums, but to also help predict potential issues.

When either curve is especially steep – reflecting the fact that immigration decreases especially sharply or extinction increases especially sharply – their crossing point shifts leftward, toward zero. The shift means that, at equilibrium, in this particular set of circumstances, there will be relatively few resident species.

In other words, high extinction and low immigration yield an impoverished ecosystem. To you and me it’s a dot in Cartesian space, but to an island it represents destiny.

There are two key ideas that can help us understand the equilibrium point on a given island.

First, the concept of species-area relationship: We see a larger number of a given species on larger islands and a smaller number of a given species on smaller islands.

Second, the concept of species quantity on remote islands: Immigration is much more difficult the further away an island is from either a mainland or a cluster of other islands, meaning that fewer species will make it there.

In other words, size and remoteness are directly correlated to the fragility of any given species inhabiting an island.

Equilibrium, immigration, evolution, extinction – these are all ideas that bleed into so many more areas than biogeography. What happens to groups when they are isolated? Jared Diamond had some interesting thoughts on that. What happens to products or businesses which don’t keep up with co-evolution? They go extinct due to the Red Queen Effect. What happens to our mind and body when we feel off balance? Our life is impoverished.

Reading a book like The Song of the Dodo helps us to better understand these key concepts which, in turn, helps us more fundamentally understand the world.

Linear acceleration

The utricle and saccule are both largely composed of macula tissue (plural = maculae). The macula is composed of hair cells surrounded by support cells. The stereocilia of the hair cells extend into a viscous gel called the otolith. The otolith contains calcium carbonate crystals, making it denser and giving it greater inertia than the macula. Therefore, gravity will cause the otolith to move separately from the macula in response to head movements. Tilting the head causes the otolith to slide over the macula in the direction of gravity. The moving otolith layer, in turn, bends the sterocilia to cause some hair cells to depolarize as others hyperpolarize. The exact tilt of the head is interpreted by the brain on the basis of the pattern of hair-cell depolarization .

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How Buffers Work: A Quantitative View

The kidneys and the lungs work together to help maintain a blood pH of 7.4 by affecting the components of the buffers in the blood. Therefore, to understand how these organs help control the pH of the blood, we must first discuss how buffers work in solution.

Acid-base buffers confer resistance to a change in the pH of a solution when hydrogen ions (protons) or hydroxide ions are added or removed. An acid-base buffer typically consists of a weak acid, and its conjugate base (salt) (see Equations 2-4 in the blue box, below). Buffers work because the concentrations of the weak acid and its salt are large compared to the amount of protons or hydroxide ions added or removed. When protons are added to the solution from an external source, some of the base component of the buffer is converted to the weak-acid component (thus using up most of the protons added) when hydroxide ions are added to the solution (or, equivalently, protons are removed from the solution see Equations 8-9 in the blue box, below), protons are dissociated from some of the weak-acid molecules of the buffer, converting them to the base of the buffer (and thus replenishing most of the protons removed). However, the change in acid and base concentrations is small relative to the amounts of these species present in solution. Hence, the ratio of acid to base changes only slightly. Thus, the effect on the pH of the solution is small, within certain limitations on the amount of H + or OH - added or removed.

The Carbonic-Acid-Bicarbonate Buffer in the Blood

By far the most important buffer for maintaining acid-base balance in the blood is the carbonic-acid-bicarbonate buffer. The simultaneous equilibrium reactions of interest are

We are interested in the change in the pH of the blood therefore, we want an expression for the concentration of H + in terms of an equilibrium constant (see blue box, below) and the concentrations of the other species in the reaction (HCO3 - , H2CO3, and CO2).

Recap of Fundamental Acid-Base Concepts

An acid is a chemical species that can donate a proton (H + ), and a base is a species that can accept (gain) a proton, according to the common Br ø nstead-Lowry definition. (A subset of the Br ø nstead-Lowry definition for aqueous solutions is the Arrhenius definition, which defines an acid as a proton producer and a base as a hydroxide (OH - ) producer.) Hence, the conjugate base of an acid is the species formed after the acid loses a proton the base can then gain another proton to return to the acid. In solution, these two species (the acid and its conjugate base) exist in equilibrium.

Recall from this and earlier experiments in Chem 151 and 152 the definition of pH:

where [H + ] is the molar concentration of protons in aqueous solution. When an acid is placed in water, free protons are generated according to the general reaction shown in Equation 3. Note: HA and A - are generic symbols for an acid and its deprotonated form, the conjugate base.

Equation 3 is useful because it clearly shows that HA is a Br ø nstead-Lowry acid (giving up a proton to become A - ) and water acts as a base (accepting the proton released by HA). However, the nomenclature H3O + is somewhat misleading, because the proton is actually solvated by many water molecules. Hence, the equilibrium is often written as Equation 4, where H2O is the base:

The Law of Mass Action and Equilibrium Constants

Using the Law of Mass Action, which says that for a balanced chemical equation of the type

in which A, B, C, and D are chemical species and a, b, c, and d are their stoichiometric coefficients, a constant quantity, known as the equilibrium constant (K), can be found from the expression:

where the brackets indicate the concentrations of species A, B, C, and D at equilibrium.

Equilibrium Constant for an Acid-Base Reaction

Using the Law of Mass Action, we can also define an equilibrium constant for the acid dissociation equilibrium reaction in Equation 4. This equilibrium constant, known as Ka, is defined by Equation 7:

Equilibrium Constant for the Dissociation of Water

One of the simplest applications of the Law of Mass Action is the dissociation of water into H + and OH - (Equation 8).

The equilibrium constant for this dissociation reaction, known as Kw, is given by

(H2O is not included in the equilibrium-constant expression because it is a pure liquid.) Hence, we can see that increasing the OH - concentration of an aqueous solution has the effect of decreasing the H + concentration, because the product of these two concentrations must remain constant at a given temperature. Thus, in water, the equilibrium in Equation 8 underlies the equivalency of the Lowry definition of a base (an H + acceptor) and the Arrhenius definition of a base (an OH - producer).

To more clearly show the two equilibrium reactions in the carbonic-acid-bicarbonate buffer, Equation 1 is rewritten to show the direct involvement of water:

The equilibrium on the left is an acid-base reaction that is written in the reverse format from Equation 3. Carbonic acid (H2CO3) is the acid and water is the base. The conjugate base for H2CO3 is HCO3 - (bicarbonate ion). (Note: To view the three-dimensional structure of HCO3 - , consult the Table of Common Ions in the Periodic Properties tutorial from Chem 151.) Carbonic acid also dissociates rapidly to produce water and carbon dioxide, as shown in the equilibrium on the right of Equation 10. This second process is not an acid-base reaction, but it is important to the blood's buffering capacity, as we can see from Equation 11, below.

The derivation for this equation is shown in the yellow box, below. Notice that Equation 11 is in a similar form to the Henderson-Hasselbach equation presented in the introduction to the Experiment (Equation 16 in the lab manual). Equation 11 does not meet the strict definition of a Henderson-Hasselbach equation, because this equation takes into account a non-acid-base reaction (i.e., the dissociation of carbonic acid to carbon dioxide and water), and the ratio in parentheses is not the concentration ratio of the acid to the conjugate base. However, the relationship shown in Equation 11 is frequently referred to as the Henderson-Hasselbach equation for the buffer in physiological applications.

In Equation 11, pK is equal to the negative log of the equilibrium constant, K, for the buffer (Equation 12).

This quantity provides an indication of the degree to which HCO3 - reacts with H + (or with H3O + as written in Equation 10) to form H2CO3, and subsequently to form CO2 and H2O. In the case of the carbonic-acid-bicarbonate buffer, pK=6.1 at normal body temperature.

Derivation of the pH Equation for the Carbonic-Acid-Bicarbonate Buffer

We may begin by defining the equilibrium constant, K1, for the left-hand reaction in Equation 10, using the Law of Mass Action:

Ka (see Equation 9, above) is the equilibrium constant for the acid-base reaction that is the reverse of the left-hand reaction in Equation 10. It follows that the formula for Ka is

The equilibrium constant, K2, for the right-hand reaction in Equation 10 is also defined by the Law of Mass Action:

Because the two equilibrium reactions in Equation 10 occur simultaneously, Equations 14 and 15 can be treated as two simultaneous equations. Solving for the equilibrium concentration of carbonic acid gives

Rearranging Equation 16 allows us to solve for the equilibrium proton concentration in terms of the two equilibrium constants and the concentrations of the other species:

Because we are interested in the pH of the blood, we take the negative log of both sides of Equation 17:

Recalling the definitions of pH and pK (Equations 2 and 12, above), Equation 18 can be rewritten using more conventional notation, to give the relation shown in Equation 11, which is reproduced below:

As shown in Equation 11, the pH of the buffered solution (i.e., the blood) is dependent only on the ratio of the amount of CO2 present in the blood to the amount of HCO3 - (bicarbonate ion) present in the blood (at a given temperature, so that pK remains constant). This ratio remains relatively constant, because the concentrations of both buffer components (HCO3 - and CO2) are very large, compared to the amount of H + added to the blood during normal activities and moderate exercise. When H + is added to the blood as a result of metabolic processes, the amount of HCO3 - (relative to the amount of CO2) decreases however, the amount of the change is tiny compared to the amount of HCO3 - present in the blood. This optimal buffering occurs when the pH is within approximately 1 pH unit from the pK value for the buffering system, i.e., when the pH is between 5.1 and 7.1.

However, the normal blood pH of 7.4 is outside the optimal buffering range therefore, the addition of protons to the blood due to strenuous exercise may be too great for the buffer alone to effectively control the pH of the blood. When this happens, other organs must help control the amounts of CO2 and HCO3 - in the blood. The lungs remove excess CO2 from the blood (helping to raise the pH via shifts in the equilibria in Equation 10), and the kidneys remove excess HCO3 - from the body (helping to lower the pH). The lungs' removal of CO2 from the blood is somewhat impeded during exercise when the heart rate is very rapid the blood is pumped through the capillaries very quickly, and so there is little time in the lungs for carbon dioxide to be exchanged for oxygen. The ways in which these three organs help to control the blood pH through the bicarbonate buffer system are highlighted in Figure 3, below.

Figure 3

This figure shows the major organs that help control the blood concentrations of CO2 and HCO3 - , and thus help control the pH of the blood.

Removing CO2 from the blood helps increase the pH.
Removing HCO3 - from the blood helps lower the pH.

Why the Optimal Buffering Capacity Is at pH=pK

Why is the buffering capacity of the carbonic-acid-bicarbonate buffer highest when the pH is close to the pK value, but lower at normal blood pH? The answer to this question lies in the shape of the titration curve for the buffer, which is shown in Figure 4, below.

Titration Curve for the Bicarbonate-Buffer System

It is possible to plot a titration curve for this buffer system, just as you did for your solution in the acid-base-equilibria experiment. In this plot, the vertical axis shows the pH of the buffered solution (in this case, the blood). The horizontal axis shows the composition of the buffer: on the left-hand side of the plot, most of the buffer is in the form of carbonic acid or carbon dioxide, and on the right-hand side of the plot, most of the buffer is in the form of bicarbonate ion. Note that as acid is added, the pH decreases and the buffer shifts toward greater H2CO3 and CO2 concentration. Conversely, as base is added, the pH increases and the buffer shifts toward greater HCO3 - concentration (Equation 10).

Figure 4

This is the titration curve for the carbonic-acid-bicarbonate buffer. Note that the pH of the blood (7.4) lies outside the region of greatest buffering capacity (green).

Note: The percent buffer in the form of HCO3 - is given by the formula:

The slope of the curve is flattest where the pH is equal to the pK value (6.1) for the buffer. Here, the buffering capacity is greatest because a shift in the relative concentrations of bicarbonate and carbon dioxide produces only a small change in the pH of the solution. However, at pH values higher than 7.1, the slope of the curve is much higher. Here, a shift in the relative concentrations of bicarbonate and carbon dioxide produces a large change in the pH of the solution. Hence, at the physiological blood pH of 7.4, other organs must help to control the amounts of HCO3 - and CO2 in the blood to keep the pH relatively constant, as described above.

Other pH-Buffer Systems in the Blood

Other buffers perform a more minor role than the carbonic-acid-bicarbonate buffer in regulating the pH of the blood. The phosphate buffer consists of phosphoric acid (H3PO4) in equilibrium with dihydrogen phosphate ion (H2PO4 - ) and H + . The pK for the phosphate buffer is 6.8, which allows this buffer to function within its optimal buffering range at physiological pH. The phosphate buffer only plays a minor role in the blood, however, because H3PO4 and H2PO4 - are found in very low concentration in the blood. Hemoglobin also acts as a pH buffer in the blood. Recall from the "Hemoglobin" tutorial from Chem 151 that hemoglobin protein can reversibly bind either H + (to the protein) or O2 (to the Fe of the heme group), but that when one of these substances is bound, the other is released (as explained by the Bohr effect). During exercise, hemoglobin helps to control the pH of the blood by binding some of the excess protons that are generated in the muscles. At the same time, molecular oxygen is released for use by the muscles.

Questions on How Buffers Work: A Quantitative View

  • If blood had a normal pH of 6.1 instead of 7.2, would you expect exercise to result in heavy breathing? Justify your answer.
  • How would a graph like that found in Figure 4 differ for the phosphate buffer system?

Defining Factors

Homeostasis is the term used to describe the internal stability needed for survival of an organism, including humans and animals. This is a narrow scope of conditions within the living creature, such as temperature and pH balance, and it is separate from the external environment. If the homeostasis conditions needed for a certain organism are not met, disease or death may occur. If homeostasis refers to the entire internal environment, equilibrium is narrowed to specific mechanisms. Equilibrium references a state of balance within a system, such as sweating to cool off and return to 98.6 Fahrenheit after your body’s temperature increases from exercising. Equilibrium can also be used to discuss other topics, such as finding balance of an object’s weight or supply and demand.

Examples of Equilibrium

A system in equilibrium requires no energy to maintain its condition. A simple example is a tank of water with a membrane across the middle. If you add dye to one side that is able to diffuse across the membrane, over time the concentration of dye molecules will become the same on both sides of the membrane. At this point, it won’t change and the system will be in equilibrium. The pH of natural systems is an example of equilibrium in a biological system. Without inputs like acid rain carrying in additional H+ ions, a pond or lake will remain at a constant pH because it will be in the state of lowest entropy.