The Inner Workings of pH Homeostasis in our Blood

Learning Objectives

This Exemplar will teach the following concept(s) from the ACS Examinations Institute General Chemistry ACCM:

• VII. D. 2. b. For some reactions, particular acid–base chemistry, the concept of pKa, pKb, or pKw can both illustrate the relationship between the equilibrium constant of forward and reverse reactions, and provide qualitative reasoning for reaction extents. 

• VIII. G. 1. a. Acid-base chemistry, particularly in water, forms an important example of equilibrium systems. Conceptual and quantitative understanding of this form of equilibrium system is important.

• VIII. G. 1. c. pH is used in quantitative descriptions of acid–base chemistry.

• VIII. G. 2. a. Weak acid–base systems are capable of forming buffer systems that tend to resist changes in the pH of the system.

• VIII. G. 2. b. Conceptual and quantitative understanding of buffers is important.

Introduction:

Have you ever wondered what would happen if you chugged a strong acid like 12 M HCl? Although you probably wouldn't live to tell the tale, you can bet your body tried everything within its power to protect itself and engaged a multitude of failsafe mechanisms in place to lessen the blow of this rapid pH change. This amazing ability that we have is due to our buffer systems. What are buffer systems you might ask? Simply put, a buffer is any solution that is able to resist changes in pH.¹

pH is a measurement of how acidic or how basic a solution is. The pH scale ranges from 0 to 14, with the middle point of 7 indicating a neutral solution. pHs greater than 7 indicate basic or alkaline substances and less H⁺ ions whereas pHs lower than 7 indicate acidic substances and the presence of more H⁺ ions. More abstractly put, pH is a measure of the relative concentrations of hydrogen and hydroxyl ions within a solution. Specifically, pH is a log-based scale and it is calculated using the concentration of H⁺ ions in a solution:

\[ pH = -\log_{10} [H^+] \nonumber\]

Thus, an inverse relationship is established between the pH and H⁺ ion concentration ([H⁺]) in a solution. As [H⁺] decreases, pH increases, resulting in a more basic solution. On the contrary, as [H⁺] increases, pH decreases, resulting in a more acidic solution.

 

Importance of Buffers:

Essentially, most biochemical processes are a result of effective buffer systems. Buffer systems often have a specific pH range they are most effective in. For example, enzymes require specific pH levels to function effectively to catalyze reactions. Anything beyond or under that range will render the buffer system ineffective to changes in hydroxide or hydronium disturbances. In other words, the buffer system will be ineffective in preventing changes in pH. To calculate what the buffer range of a buffer system is, there is a simple rule as depicted: 

\[ pH = pK_a \pm 1 \nonumber\]

 

Types of Buffers

In a more complex context, buffers must require that either a weak acid and its conjugate base are present or a weak base and its conjugate acid are present. These tenants are what allow for buffer systems to regulate our pH. Another important calculation to know is how to calculate the pH of a buffer system (without any disturbances). To do this, use the Henderson-Hasselbach equation²: 

\[ pH = pK_a + \log_{10} (\frac{[Base]}{[Acid]}) \nonumber\]

This equation contextualizes pH and pK_a as fundamentally connected and growing closer to each other as the logarithmic ratio of base and acid concentration approaches 1. Therefore, pH and pK_a must be equal when the concentrations of acids and bases are equal. 

To better understand how strong acid and strong base disturbances affect both weak acid and weak base buffer systems, see Figure 1 below for the four unique combinations that can occur.

First, the key step to identify what reaction is taking place when a strong acid/base is added to a buffer system is to determine the major species of the reaction. Then, choose the strongest acid and strongest base species that does not produce a strong acid/base when reacted together. The result is the reaction is what occurs when a disturbance occurs to the system

. Figure 1: Identifying strongest species and building reactions from buffer solution & titrant.

 

Based on the reactions that take place, it is clear that when a strong acid is added, the buffer system minimizes its effects by quickly changing it to a weaker acid. Similarly, when a strong base is added, the buffer system quickly changes it to a weaker base, reducing pH change. 

 

Blood pH

Perhaps the most important buffer system in our body is the carbonic acid/bicarbonate ion system. The rest of this discussion will focus on how this buffer system is regulated and how all the previous concepts mentioned apply in the context of our very own bloodstream.

For our body and all associated systems to properly function and operate, it is paramount to maintain a constant blood pH. As previously mentioned, the buffer responsible for maintaining human blood pH involves a system consisting of carbonic acid (H₂CO₃) and bicarbonate ions (HCO₃^-).³ The relationship is represented below:

\[ H_2CO_3 + H_2O \leftrightharpoons HCO_3^- + H_3O^+ \nonumber\]

Here, H₂CO₃ acts as a weak acid and HCO₃^- acts as its conjugate base. 

Consider the two following situations and their resulting effects: 

Scenario 1

1) An acidic substance enters the bloodstream:

• Bicarbonate ions neutralize hydronium ions

  • Forms water and carbonic acid (already existing in buffer system)

• Hydronium ions are removed from blood

  • pH is prevented from becoming more acidic 

Scenario 2

2) A basic substance enters the bloodstream:

• Carbonic acid neutralizes hydroxide ions

  • Forms water and bicarbonate ions (already existing in buffer system)

• Hydroxide ions are removed from blood

  • pH is prevented from becoming more basic

When you consider this back-and-forth process, it is observed that as either hydroxide or hydronium ions are neutralized, the concentrations of bicarbonate ions and carbonic acid experience changes. These changes are relatively small and will not cause detrimental issues. Thus, the buffer system, simply put, makes sure the blood does not become either overly acidic or basic, which would then indeed cause adverse effects.

One thing to note is where this buffer system—specifically the carbonic acid and bicarbonate ions—initially come from? The answer is an enzyme known as carbonic anhydrase.⁴ Within the body, carbonic anhydrase aids in the conversion of CO₂ (metabolic byproduct) and H₂O into carbonic acid (H₂CO₃) and bicarbonate ions (HCO₃^-). Carbonic anhydrase also helps with the dissociation of carbonic acid into bicarbonate ions and back.

Example \(\PageIndex{1}\)

Let's look at what happens to the pH when a strong acid is added to the carbonic acid/bicarbonate acid buffer system. 

There is a 100 mL buffer solution with 0.5 M H₂CO₃ and 3 M HCO₃^-. A 10 mL of 1 M HCl is added to the solution. Calculate the pH of the buffer before the disturbance and after.

*Note that the Molar concentrations above are not consistent with the molar concentrations in the blood. This is just a model.

Solution

(Pre-Disturbance):

Henderson-Hasselbach:

\( pH = pK_a + \log_{10} (\frac{[Base]}{[Acid]}) \nonumber\)

\( pH = 6.7 + \log_{10} (\frac{[3]}{[0.5]}) \nonumber\)

\( pH = 7.5 \)

 

(Post Disturbance):

Reaction	H^+      +      HCO3^-     →    H2CO3
I	10 mmol	300  mmol	50 mmol
C	-10 mmol	-10 mmol	+10 mmol
E	0 mmol	290 mmol	60 mmol

 

Henderson-Hasselbach:

\( pH = pK_a + \log_{10} (\frac{[Base]}{[Acid]}) \nonumber\)

[base] = \( \frac{290 mmol}{110 mL} \) = 2.64 M

[acid] = \( \frac{60 mmol}{110 mL} \) = 0.55 M

\( pH = pK_a + \log_{10} (\frac{[2.64]}{[0.55]}) \nonumber\)

\( pH = 7.4 \)

 

Despite an addition of a strong acid that is fairly concentrated, the buffer only allows the system to reach a pH of 7.4 compared to 7.5

 

Example \(\PageIndex{2}\)   

Let's look at what happens to the pH when a strong base is added to the carbonic acid/bicarbonate acid buffer system

There is a 100mL buffer solution with 0.5 M H₂CO₃ and 3 M HCO₃^-. A 10 mL of 1 M NaOH is added to the solution. Calculate the pH of the buffer before the disturbance and after

*Note that the Molar concentrations above are not consistent with the molar concentrations in the blood. Just a model.

Solution

(Pre-Disturbance):

Henderson-Hasselbach:

\( pH = pK_a + \log_{10} (\frac{[Base]}{[Acid]}) \nonumber\)

\( pH = 6.7 + \log_{10} (\frac{[3]}{[0.5]}) \nonumber\)

\( pH = 7.5 \)

 

(Post Disturbance):

Reaction	OH-        +         H2CO3          →          HCO3-            +   H2O
I	10 mmol	50  mmol	300 mmol
C	-10 mmol	-10 mmol	+10 mmol
E	0 mmol	40 mmol	310 mmol

 

Henderson-Hasselbach:

\( pH = pK_a + \log_{10} (\frac{[Base]}{[Acid]}) \nonumber\)

[base] = \( \frac{310 mmol}{110 mL} \) = 2.82 M

[acid] = \( \frac{40 mmol}{110 mL} \) = 0.36 M

\( pH = pK_a + \log_{10} (\frac{[2.82]}{[0.36]}) \nonumber\)

\( pH = 7.6 \)

 

Despite addition of a strong base that is fairly concentrated, the buffer only allows the system to reach a pH of 7.6 compared to 7.5.

Buffer Capacity

Buffers are extremely varied in acid and base components along with molar ratios required to produce a set change in pH. The vast range of buffer compositions can be quantified by their primary character of effectiveness in resisting alkaline and acidic influence. Buffer capacity is a parameter used to represent this character, measured as the number of moles of OH^- / H₃O⁺ required to produce a unit change in pH per liter of buffer.⁵

\[ Buffering\;Capacity = (\frac{[Mole\;of\;OH^-\;or\;H_3O^+]}{[∆pH\;\cdot\;Volume\;of\;Buffer]}) \nonumber\]

Despite the variability in weak acid/base composition of buffer solutions, buffer capacity in an experimental context often depends primarily on the concentration of the buffered solution. The inverse proportionality between pH change and buffer concentration means that buffer capacity increases directly as buffer concentration increases.⁶ Therefore, a doubled buffer concentration results in a doubled buffer capacity.

Figure 2: Buffer pH Curves & NaOH Fluctuations^7 Analysis of buffer capacities at various concentrations. NaOH is the strong base used to agitate the stable buffer pH range (approximately 5.00 for all buffers).

 

As shown in this NaOH buffer capacity assay, buffer solutions can exhibit lower capacity in concentrations below 0.0250 M, but molarities above 0.0500 M can resist extremely high volumes of acids/bases and limit pH to steady fluctuations.

Now that we understand what buffering capacity is, let's calculate the value using the information from Example 2.

Example \(\PageIndex{3}\) Determine the buffering capacity when 10 mL of 1M HCl is added to a 100 mL H2CO3 / HCO3^- buffer solution with concentrations of  0.5 M H2CO3 and  3 M HCO3^- with a pH change of 0.1 Solution \( Buffering\;Capacity = (\frac{[Mole\;of\;OH^-\;or\;H_3O^+]}{[∆pH\;\cdot\;Volume\;of\;Buffer]}) \nonumber\) \( Buffering\;Capacity = (\frac{[0.01\;mol\;H^+]}{[0.1\;\cdot\;0.1\;L]}) \nonumber\) \( Buffer\;Capacity = 1\;M \nonumber\)

 

References:

1. Acid/Base Reactions. https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_ Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Acids_and_Bases/Acid_Base_Reactions. (accessed 2022-12-07).

2. Henderson-Hasselbach Equation. https://chemistrytalk.org/henderson-hasselbalch-equation. (accessed 2022-12-07).

3. Properties of Blood as a Buffer and Blood Glucose. https://iastate.pressbooks.pub/curehumanphysiology/chapter /properties-of-blood-as-a-buffer-and-blood-glucose/. (accessed 2022-12-07).

4. Carbonic Anhydrase. http://hyperphysics.phy-astr.gsu.edu/hbase/Organic/carbanh.html. (accessed 2022-12-07).

5. Mennah-Govela, Y. A.; Singh, R. P.; Bornhorst, G. M. Royal Society of Chemistry 2019, 10 (9), 6074–6087. (accessed 2022-12-07).

6. Buffer Capacity and Buffer Range. https://chem.libretexts.org/Courses/Grand_Rapids_Community_College/CHM_12 0_-_Survey_of_General_Chemistry/8%3A_Acids_and_Bases/8.09_Buffer_Capacity_and_Buffer_Range. (accessed 2022-12-07).

7. Buffered Solutions. https://chem.libretexts.org/Courses/...ered_Solutions . (Accessed 2022-12-07).