Chemical Equilibrium in Hemoglobin and Oxygen
- Page ID
- 418906
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)This Exemplar will teach the following concept(s) from the ACS Examinations Institute General Chemistry ACCM:
VIII. A. Both physical and chemical changes may occur in either direction (e.g., from reactants to products, or products to reactants).
VIII. C. 1. A. The equilibrium state is characterized by a constant, designated K, which provides quantitative information of the extent of a reaction and is related to the ratio of the concentrations of reactants and products.
VIII. E. 1. The direction of change in a system that is perturbed from equilibrium is predictable—it will change so as to minimize the perturbation.
VIII. G. Equilibrium concepts have important applications in several sub-disciplines of chemistry
Introduction
Hemoglobin is a molecule located in red blood cells. It is responsible for transporting oxygen from the lungs to other tissues within the body through the blood.1 It contains iron –the “heme” group– in the center of the molecule which allows it to bind to four oxygen molecules in its subunits.2 Hemoglobin binds to oxygen to create oxyhemoglobin, which is the characteristic bright-red color of blood. We can apply concepts from chemistry, such as equilibrium, the equilibrium constant, and Le Chatelier's Principle, to explain the interactions between hemoglobin and oxygen.
Figure \(\PageIndex{1}\): Hemoglobin in the Red Blood Cells3
Chemical Equilibrium
Chemical equilibrium is a dynamic process where the forward reaction equals the rate of the reverse reaction.4 At equilibrium, there is no observable change in the concentration of reactants and products.
\[A(g)+B(g)⇄C(g) \label{Example} \]
Assume that the same number of moles of gaseous A and B are present in a closed vessel with no concentration of gaseous C. Collisions between the reactant molecules (A and B) will cause the chemical reaction to occur and products to form (C). As the reaction proceeds, the concentration of A and B depletes and the forward reaction rate slows. Simultaneously, the concentration of C increases, and the reverse reaction rate increases. At some point, the two reactions will reach equilibrium—the moment when the rates of the reactants being consumed to create products and the rate of products broken to be reactants are equal.
In product-favored reactions, the equilibrium position lies far to the right. In reactant-favored reactions, the equilibrium position lies far to the left. The equilibrium position is constant unless stress is added, which is explained by Le Chatelier’s Principle.
Hemoglobin-Oxygen Equilibrium
The equilibrium equation of hemoglobin and oxygen is:
\[Hb(aq)+4O_2(g)⇄Hb(O_2)_4(aq) \label{Hemoglobin} \]
The forward reaction represents oxyhemoglobin synthesis, which occurs in the lungs.1 The reverse reaction represents the decomposition of hemoglobin in the tissues as oxygen is used and converted into carbon dioxide. At normal body and environmental conditions, there is a dynamic equilibrium. The forward and reverse reactions proceed at equal rates and oxygen is healthily produced and used. Disequilibrium can cause negative health effects, which will be explored further.
The Equilibrium Constant
The ratio of the product and reactant concentrations equals K, the equilibrium constant.3 Solids and liquids are excluded from the calculation. There is only one equilibrium constant for a reaction at a set temperature. K is only affected by a change in temperature.
Look at the modified equation of equation \ref{Example} from above:
\[aA(g)+bB(g)⇄cC(g)\]
Where a, b, and c are the coefficients of a balanced equation. In this case, the equilibrium constant expression can be made:
\[K_{eq}=\frac{[C]^c} {[A]^a[B]^b}\]
The equilibrium constant can be written in terms of partial pressure as well.
\[K_{p}=\frac{[P_C]^c} {[P_A]^a[P_B]^b}\]
Refer to the dissociation expression of oxyhemoglobin.
\[Hb(O_2)_4(aq)⇄Hb(aq)+4O_2(g) \nonumber\]
At equilibrium in the following reaction at room temperature, \(P_{O_2}\) = 27 torr and \(K_{p}\) = 180. What is the ratio of \(P_{Hb}\) to \(P_{Hb(O_2)_4}\) at equilibrium?9
- Solution
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First, we write the partial pressure equilibrium constant expression from the balanced chemical equation.
\[K_{p}=\frac{[P_{Hb}][P_{O_2}]^4} {[P_{Hb(O_2)_4}]} \nonumber\]
Then, we substitute the known equilibrium concentration and K value:
\[180=\frac{[P_{Hb}][27]^4} {[P_{Hb(O_2)_4}]} \nonumber\]
Rearranging the equation using algebra, we get:
\[\frac{[P_{Hb}]} {[P_{Hb(O_2)_4}]}=\frac{180} {27^4} \nonumber\]
\[\frac{[P_{Hb}]} {[P_{Hb(O_2)_4}]} = 0.245 \nonumber\]
Le Chatelier’s Principle
Le Chatelier’s principle states that if a system at equilibrium is stressed by a change in pressure, temperature, or concentration, the equilibrium position will shift in the direction that reduces the added stress.4
If products or reactants are added to a reaction, there is a loss of balance of concentrations, and the equilibrium position is disrupted.5 Increasing the reactant concentration leads to an equilibrium shift to the right, in favor of the direction consuming the reactants. An increase in product concentration will shift the equilibrium position left, towards the reactants. Further, if a reactant or product is removed, the equilibrium will shift in the direction of the loss.
Pressure is caused by gas molecules colliding with the sides of their container. Fewer gas molecules mean fewer collisions and lower pressure. Therefore, when pressure is increased, the equilibrium position will shift to the side with fewer gas molecules. The opposite is true when pressure is decreased. Another way to think about it is with the ideal gas law. Volume is directly proportional to the moles of gas and inversely proportional to pressure. When pressure is increased, volume decreases and the system will shift to decrease the moles of gas. Note that additions of inert (chemically unreactive) do not affect the equilibrium position.
Le Chatelier’s Principle can also be used to qualitatively measure the effect of a change in temperature. Change in temperature also alters the equilibrium constant, K. If the temperature is increased to an exothermic reaction (where energy is a product), the equilibrium position will shift left towards the reactants to counteract the stress. This decreases the equilibrium constant, K. If the temperature is increased in an endothermic reaction, the equilibrium position will shift right towards the products and increase K. The opposite is true when the temperature is decreased. There are many applications of chemical equilibrium and Le Chatelier’s principle in biological processes that can explain illnesses, such as with hemoglobin and oxygen.
Given the hemoglobin oxygen equilibrium equation below, predict the shift in equilibrium position in response to each of the following conditions using Le Chatelier’s principle.
\[Hb(aq)+4O_2(g)⇄Hb(O_2)_4(aq) \nonumber\]
a) Hiking to higher elevations with significantly lower air pressure.
b) Bringing a pressurized oxygen tank with you on the hike.
c) Mary was born and raised in high altitudes, and her body adapted to produce more hemoglobin than the average person.
- Solution
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a) Shift left. A decrease in pressure will shift the equilibrium position to the side with fewer gas molecules. The reactant side has 4 moles of gas molecules, while the products have none.
b) Shift right. An increase in oxygen concentration (reactant) will push the equilibrium position to the products.
c) Shift right. An increase in hemoglobin concentration (reactant) will push the equilibrium position to the products.
Hypoxia
Hypoxia is a state where there are low levels of oxygen in the blood. This is when hemoglobin does not transport sufficient oxygen to the tissues for the body’s needs. Symptoms of hypoxia include confusion, rapid heart rate, difficulty breathing, bluish skin, and restlessness. Severe cases are life-threatening. In part A of the example problem, the shift left in the equilibrium position indicates that less oxyhemoglobin will be produced. This is why people experience acute mountain sickness at high elevations.6 Interventions such as bringing a pressurized oxygen tank along on a steep hike would restore equilibrium and ensure a healthier trip.
Hypoxia can also be caused by anemia, which is a common condition that affects about 3 million people in the United States. Anemia occurs when the body produces fewer healthy red blood cells and hemoglobin than normal, which decreases the concentration of oxyhemoglobin in the body.7 Anemia can be treated by taking iron supplements, vitamins, or medicine that increase the number of red blood cells and restore the equilibrium position.
Another cause of hypoxia can be carbon monoxide poisoning, which is explored in the following exercise.8
Carbon monoxide is a dangerous and prevalent gas. Burning fuels, wood, and carbon-containing molecules produce carbon monoxide. Common exposures to this gas include cigarette smoke, car gas exhaust, and fires. When carbon monoxide is breathed into the lungs, it binds to hemoglobin and is transported through the red blood cells. The equilibrium expression of this reaction is:
\[Hb(aq)+4CO(g) →Hb(CO)_4(aq) \nonumber\]
Carbon monoxide binds stronger to hemoglobin in comparison to oxygen to produce carboxyhemoglobin. Use the provided background above. A firefighter puts out house fires and California bush fires and is constantly exposed to carbon monoxide. How will this affect the equilibrium position between hemoglobin and oxygen?
- Answer
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Shift left. There is less hemoglobin available to react with oxygen in the presence of carbon monoxide, so the equilibrium position shifts towards the reactants. Less oxyhemoglobin is produced and hypoxia occurs.
References
- Libretexts. “Hemoglobin: Oxygen Transport in Mammals.” Chemistry LibreTexts, Libretexts, 1 May 2022, https://chem.libretexts.org/Courses/Saint_Marys_College_Notre_Dame_IN/CHEM_342%3A_Bio-inorganic_Chemistry/Readings/Metals_in_Biological_Systems_(Saint_Mary's_College)/Oxygen_transport_and_Storage/Red_Blood_(Mammals)/Hemoglobin%3A_Oxygen_transport_in_mammals
- Pittman RN. Regulation of Tissue Oxygenation. San Rafael (CA): Morgan & Claypool Life Sciences; 2011. Chapter 4, Oxygen Transport. Available from: https://www.ncbi.nlm.nih.gov/books/NBK54103/
- Libretexts. “19.3: Equilibrium Constant.” Chemistry LibreTexts, Libretexts, 9 Aug. 2022, https://chem.libretexts.org/Bookshel...brium_Constant.
- Zumdahl, Steven S., and Donald J. DeCoste. “Chemical Equilibrium .” Chemical Principles, 8th ed., Cengage, Boston, Massachusetts , 2017, https://ng.cengage.com/static/nb/ui/...tId=908960&. Accessed 2022.
- BC Open Textbooks- Shifting Equilibria: Le Chatelier’s Principle. Ball, D. and J. Key. (2014). Introductory Chemistry – 1st Canadian Edition. Victoria, B.C.: BCcampus. Retrieved from https://opentextbc.ca/introductorychemistry/.
- Peacock AJ. ABC of oxygen: oxygen at high altitude. BMJ. 1998 Oct 17;317(7165):1063-6. doi: 10.1136/bmj.317.7165.1063. PMID: 9774298; PMCID: PMC1114067.
- “What Is Anemia?” National Heart Lung and Blood Institute, U.S. Department of Health and Human Services, https://www.nhlbi.nih.gov/health/anemia.
- Blumenthal, I. “Carbon monoxide poisoning.” Journal of the Royal Society of Medicine vol. 94,6 (2001): 270-2. doi:10.1177/014107680109400604
- Lecture 12: O2 Binding by Myoglobin & Hemoglobin. https://www.andrew.cmu.edu/course/03...ec12/Lec12.pdf.