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Ch.17 - Additional Aspects of Aqueous Equilibria
Chapter 17, Problem 29b

(b) What is the ratio of HCO3- to H2CO3 in an exhausted marathon runner whose blood pH is 7.1?

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1
Identify the relevant chemical species involved, which are bicarbonate ion (HCO3-) and carbonic acid (H2CO3).
Use the Henderson-Hasselbalch equation for the bicarbonate buffer system in blood: pH = pKa + log([HCO3-]/[H2CO3]).
Find the pKa value of carbonic acid, which is typically around 6.1 at body temperature.
Substitute the given pH value (7.1) and the pKa value into the Henderson-Hasselbalch equation.
Solve the equation for the ratio [HCO3-]/[H2CO3] by isolating this term and using basic algebraic operations.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Buffer Systems

Buffer systems in the body, particularly the bicarbonate buffer system, help maintain pH levels in the blood. This system involves a dynamic equilibrium between carbonic acid (H2CO3) and bicarbonate ions (HCO3-), which can absorb excess hydrogen ions (H+) or release them to stabilize pH. Understanding this balance is crucial for analyzing changes in blood pH, especially in physiological conditions like exhaustion.
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Acid-Base Balance

Acid-base balance refers to the mechanisms the body uses to maintain a stable pH in the blood and other fluids. The normal blood pH range is approximately 7.35 to 7.45, and deviations can indicate metabolic or respiratory issues. In the case of an exhausted marathon runner with a pH of 7.1, this indicates acidosis, which can result from increased lactic acid production and depletion of bicarbonate.
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Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a solution to the concentration ratio of an acid and its conjugate base. For the bicarbonate buffer system, it can be expressed as pH = pKa + log([HCO3-]/[H2CO3]). This equation is essential for calculating the ratio of bicarbonate to carbonic acid in the blood, allowing for a quantitative understanding of how the body compensates for changes in pH.
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