Problem 66 - General Chemistry: Principles and Modern Applications

Question

In the human body, the enzyme carbonic anahydrase catalyzes the interconversion of \(\mathrm{CO}_{2}\) and \(\mathrm{HCO}_{3}^{-}\) by either adding or removing the hydroxide anion. The overall reaction is endothermic. Explain how the following affect the amount of carbon dioxide: (a) increasing the amount of bicarbonate anion; (b) increasing the pressure of carbon dioxide; (c) increasing the amount of carbonic anhydrase; (d) decreasing the temperature.

Step-by-Step Solution

Answer

a) The amount of carbon dioxide increases, b) The amount of carbon dioxide is unaffected, c) The amount of carbon dioxide is unaffected, d) The amount of carbon dioxide decreases.

Step 1: Response to Anion Increase

(a) If the amount of bicarbonate anion (\(\mathrm{HCO}_{3}^{-}\)) is increased, according to Le Chatelier's principle, the reaction would be expected to shift in the direction that would reestablish equilibrium, thus in the direction where \(\mathrm{HCO}_{3}^{-}\) is used up, i.e. towards the formation of \(\mathrm{CO}_{2}\). Thus the amount of carbon dioxide would increase.

Step 2: Response to Pressure Increase

(b) An increase in the pressure of \(\mathrm{CO}_{2}\) would push the reaction towards the direction that decreases the pressure. Since this reaction has equal number of moles of gas on either side of the equation, increasing the pressure would have no effect on the direction of the equilibrium. So, the amount of carbon dioxide would not change.

Step 3: Response to Increased Enzyme

(c) For an enzyme catalyzed reaction, increasing the amount of the enzyme i.e., carbonic anhydrase, doesn't change the position of the equilibrium but increases the rate at which it is established. Thus, the increase in enzymatic content doesn't alter the amount of carbon dioxide.

Step 4: Response to Temperature Decrease

(d) Since it's stated the reaction is endothermic, it absorbs heat. Thus, decreasing the temperature would drive the reaction to the direction that absorbs heat to increase the temperature, i.e., towards the formation of bicarbonate ions \(\mathrm{HCO}_{3}^{-}\) and thus reducing the amount of \(\mathrm{CO}_{2}\) .

Key Concepts

Le Chatelier's Principle

Le Chatelier's Principle is like a rule of thumb for predicting how a chemical system at equilibrium responds to external changes. It states that when a system at equilibrium experiences a change in concentration, temperature, volume, or pressure, the equilibrium will shift to counteract the inflicted change and re-establish a new equilibrium state.

This principle is crucial to understanding many chemical processes, including those relevant to biology, such as the carbonic anhydrase reaction in the human body. For instance, when the concentration of bicarbonate anion is increased, as per Le Chatelier's principle, the system will adjust to reduce the concentration of this anion by converting it to carbon dioxide and water. This reaction highlights how cells can regulate the concentrations of various species dynamically to maintain homeostasis.

Endothermic Reactions

Endothermic reactions are processes that absorb energy from their surroundings, typically in the form of heat. This means that such reactions require an input of energy to proceed. The carbonic anhydrase reaction involved in the interconversion of carbon dioxide is endothermic, so it absorbs heat.

This impacts the equilibrium position whenever there's a temperature change. If the temperature is decreased, the system responds by shifting the equilibrium towards the endothermic process — in this case, the formation of bicarbonate ions — to try to absorb more heat and restore balance. Understanding these reactions is important not just in biochemistry, but also in industrial processes where temperature control is critical.

Chemical Equilibrium

Chemical equilibrium occurs when a reaction and its reverse reaction occur at the same rate, leading to the concentrations of the reactants and products remaining constant over time. It doesn't mean the reactants and products are in equal concentration, but rather that their ratio doesn't change.

In the carbonic anhydrase reaction, equilibrium can be affected by changes in bicarbonate anion levels, pressure, and carbonic anhydrase amounts. Le Chatelier’s principle helps predict the shifts in equilibrium with these changes; however, altering the amount of enzyme—while it speeds up the rate at which equilibrium is reached—doesn't shift the equilibrium itself.

Enzyme Catalysis

Enzymes are biological catalysts that accelerate chemical reactions in living organisms without being consumed in the process. Enzyme catalysis is vital for sustaining life because it increases the rate of reaction to a biologically useful speed. Carbonic anhydrase, for example, is an enzyme that catalyzes the rapid interconversion of carbon dioxide and bicarbonate anion.

Increasing the amount of carbonic anhydrase in a system will speed up the attainment of equilibrium but doesn't actually change the position of equilibrium. This concept is fundamental in the development of pharmaceuticals and understanding metabolic pathways, where the efficiency of enzyme-catalyzed reactions is paramount.