Buffer Solutions in the Body Revision Notes for OCR A-Level Chemistry A

Buffer solutions in the body

Introduction to pH control in the body

Living organisms contain buffer solutions throughout their biological systems to maintain essential pH levels. Human health depends critically on precise pH control, as different parts of the body require specific pH values to function effectively.

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Enzymes are particularly sensitive to pH changes, with each enzyme having an optimal pH at which it works best. Even small deviations from this optimal pH can significantly reduce enzyme activity, affecting vital biological processes.

This pH control is achieved through various buffer systems, particularly in the blood plasma.

Blood plasma pH range

Blood plasma must be maintained within a narrow pH range of 7.35 to 7.45 for proper bodily function. The normal, healthy blood pH is 7.40. This tight control is achieved primarily through a mixture of buffers, with the carbonic acid-hydrogencarbonate buffer system being the most significant.

Understanding pH sensitivity

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The pH Scale is Highly Sensitive

A difference of just 0.30 pH units represents a two-fold change in $\text{H}^+(\text{aq})$ concentration. This means that although the range 7.10 to 7.70 (which is $7.40 \pm 0.30$ ) might not seem very different from the healthy blood pH of 7.40, the difference in acidity or alkalinity is actually very large in chemical terms.

Consequences of pH imbalance

When blood pH deviates from the normal range, serious medical conditions can develop:

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Acidosis occurs when pH falls below 7.35. This condition can cause:

Extreme fatigue
Shortness of breath
In severe cases, shock or death

Alkalosis occurs when pH rises above 7.45. This condition can cause:

Muscle spasms
Light-headedness
Nausea

The carbonic acid-hydrogencarbonate buffer system

The primary buffer system controlling blood pH involves carbonic acid ( $\text{H}_2\text{CO}_3$ ) and its conjugate base, the hydrogencarbonate ion ( $\text{HCO}_3^-$ ). This system operates according to the following equilibrium:

$\text{H}_2\text{CO}_3(\text{aq}) \rightleftharpoons \text{H}^+(\text{aq}) + \text{HCO}_3^-(\text{aq})$

This buffer system functions similarly to other weak acid-conjugate base buffers, but plays a critical role in maintaining life.

Response to added acid

When acid is added to blood, increasing the concentration of $\text{H}^+(\text{aq})$ ions, the buffer system responds in three steps:

The concentration of $[\text{H}^+(\text{aq})]$ increases
The $\text{H}^+(\text{aq})$ ions react with the conjugate base, $\text{HCO}_3^-(\text{aq})$
The equilibrium position shifts to the left, removing most of the added $\text{H}^+(\text{aq})$ ions

Response to added alkali

When alkali is added to blood in the form of $\text{OH}^-(\text{aq})$ ions, the buffer system responds differently:

The concentration of $[\text{OH}^-(\text{aq})]$ increases
The small existing concentration of $\text{H}^+(\text{aq})$ ions reacts with the $\text{OH}^-(\text{aq})$ ions to form water:

$\text{H}^+(\text{aq}) + \text{OH}^-(\text{aq}) \rightarrow \text{H}_2\text{O}(\text{l})$

The carbonic acid dissociates to restore $\text{H}^+(\text{aq})$ ions, shifting the equilibrium position to the right

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Understanding Le Chatelier's Principle in Action

This buffer system is a perfect example of Le Chatelier's principle at work:

Adding acid → equilibrium shifts LEFT to remove excess H⁺
Adding alkali → equilibrium shifts RIGHT to restore H⁺

Calculating the buffer concentration ratio in healthy blood

We can calculate the exact ratio of hydrogencarbonate ions to carbonic acid molecules in healthy blood using equilibrium principles and the Henderson-Hasselbalch equation.

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Worked Example: Concentration Ratio at pH 7.40

The $\text{p}K_\text{a}$ for the carbonic acid-hydrogencarbonate equilibrium is 6.1 at body temperature. Let's determine the ratio of $\text{HCO}_3^-$ to $\text{H}_2\text{CO}_3$ in healthy blood at pH 7.40.

Step 1: Express the ratio in terms of $K_\text{a}$ and $[\text{H}^+(\text{aq})]$

Starting with the equilibrium equation:

$\text{H}_2\text{CO}_3(\text{aq}) \rightleftharpoons \text{H}^+(\text{aq}) + \text{HCO}_3^-(\text{aq})$

The acid dissociation constant is:

$K_\text{a} = \frac{[\text{H}^+(\text{aq})][\text{HCO}_3^-(\text{aq})]}{[\text{H}_2\text{CO}_3(\text{aq})]}$

Rearranging to find the ratio:

$\frac{[\text{HCO}_3^-(\text{aq})]}{[\text{H}_2\text{CO}_3(\text{aq})]} = \frac{K_\text{a}}{[\text{H}^+(\text{aq})]}$

Step 2: Convert pH into $[\text{H}^+(\text{aq})]$ and $\text{p}K_\text{a}$ into $K_\text{a}$

$[\text{H}^+(\text{aq})] = 10^{-\text{pH}} = 10^{-7.40} = 3.98 \times 10^{-8} \text{ mol dm}^{-3}$

$K_\text{a} = 10^{-\text{p}K_\text{a}} = 10^{-6.1} = 7.9 \times 10^{-7} \text{ mol dm}^{-3}$

Step 3: Calculate the $\text{HCO}_3^-/\text{H}_2\text{CO}_3$ ratio

$\frac{[\text{HCO}_3^-(\text{aq})]}{[\text{H}_2\text{CO}_3(\text{aq})]} = \frac{K_\text{a}}{[\text{H}^+(\text{aq})]} = \frac{7.9 \times 10^{-7}}{3.98 \times 10^{-8}} = \frac{20}{1}$

Result: In healthy blood, there are 20 hydrogencarbonate ions for every 1 carbonic acid molecule. This ratio is crucial for maintaining the correct blood pH.

How the body manages carbonic acid levels

The human body continuously produces more acidic materials than alkaline materials through normal metabolic processes. The hydrogencarbonate ions in the buffer system convert these acidic materials to carbonic acid. However, if carbonic acid were allowed to accumulate, it would eventually overwhelm the buffer system.

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The Body's Clever Solution

To prevent carbonic acid buildup, the body has a clever mechanism: carbonic acid is converted to carbon dioxide gas, which is then expelled from the body through the lungs during breathing. This process ensures that the buffer system can continue to function effectively.

The Henderson-Hasselbalch equation

An alternative method for calculating the pH of buffer solutions uses the Henderson-Hasselbalch equation. This equation provides a direct relationship between pH, $\text{p}K_\text{a}$ , and the concentration ratio of conjugate base to weak acid:

$\text{pH} = \text{p}K_\text{a} + \log\frac{[\text{A}^-(\text{aq})]}{[\text{HA}(\text{aq})]}$

Where:

$[\text{A}^-(\text{aq})]$ is the concentration of the conjugate base
$[\text{HA}(\text{aq})]$ is the concentration of the weak acid

This equation makes it easy to see how the base/acid concentration ratio controls the pH.

When acid and base concentrations are equal

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When the concentrations of acid and conjugate base are the same:

$\frac{[\text{A}^-(\text{aq})]}{[\text{HA}(\text{aq})]} = 1$

$\log 1 = 0$

Therefore: pH = pKₐ

This shows that when a buffer contains equal amounts of weak acid and conjugate base, its pH equals the $\text{p}K_\text{a}$ of the weak acid.

Example calculation using Henderson-Hasselbalch equation

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Worked Example: Calculating Buffer pH

For a buffer solution containing 0.100 mol dm $^{-3}$ CH $_3$ COOH ( $\text{p}K_\text{a}$ = 4.76) and 0.300 mol dm $^{-3}$ CH $_3$ COONa:

$\text{pH} = \text{p}K_\text{a} + \log\frac{[\text{CH}_3\text{COO}^-(\text{aq})]}{[\text{CH}_3\text{COOH}(\text{aq})]}$

$\text{pH} = 4.76 + \log\frac{0.300}{0.100}$

$= 4.76 + \log 3 = 4.76 + 0.48 = 5.24$

Although this equation may appear more complex initially, the calculation is often simpler than using the standard equilibrium expression method, especially when you need to find pH directly from concentrations.

Remember!

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Key Points to Remember:

Blood plasma pH must be maintained between 7.35 and 7.45, with normal healthy blood at pH 7.40
The carbonic acid-hydrogencarbonate buffer system is the primary pH control mechanism in blood, involving the equilibrium: $\text{H}_2\text{CO}_3(\text{aq}) \rightleftharpoons \text{H}^+(\text{aq}) + \text{HCO}_3^-(\text{aq})$
Acidosis (pH < 7.35) and alkalosis (pH > 7.45) cause serious medical conditions with potentially fatal consequences
In healthy blood, the ratio of $[\text{HCO}_3^-]$ to $[\text{H}_2\text{CO}_3]$ is 20:1, calculated using $\text{p}K_\text{a} = 6.1$ at body temperature
The body prevents carbonic acid buildup by converting it to carbon dioxide gas, which is exhaled through the lungs
The Henderson-Hasselbalch equation provides an alternative calculation method: $\text{pH} = \text{p}K_\text{a} + \log\frac{[\text{A}^-]}{[\text{HA}]}$

Exam Focus Checklist:

Be able to write the equilibrium equation for the carbonic acid-hydrogencarbonate buffer system
Explain how this buffer responds to added acids and bases using Le Chatelier's principle
Calculate the concentration ratio of buffer components using either the standard $K_\text{a}$ expression or the Henderson-Hasselbalch equation
Know the normal blood pH range and the medical terms for pH imbalances
Understand why a small pH change represents a large change in hydrogen ion concentration
Explain how the body removes excess carbonic acid through conversion to carbon dioxide

Buffer Solutions in the Body (OCR A-Level Chemistry A): Revision Notes