Problem 97 - Chemistry Matter and Change

Question

Electrochemical Biological Reactions Standard reduction potentials for some important biological reactions are given in Table \(20.2 .\) The strongest oxidizing agent generally available in biological systems is molecular oxygen. Consider the oxidation of reduced nicotinamide-adenine-dinucleotide \((N A D H)\) by molecular oxygen. The reaction is the following. $$2 \mathrm{NADH}+2 \mathrm{H}^{+}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NAD}^{+}+2 \mathrm{H}_{2} \mathrm{O}$$ Calculate the cell potential of this reaction using table 20.1 on page 712 and Table 20.2 .

Step-by-Step Solution

Answer

The cell potential for the reaction is 0.91 V.

Step 1: Identify Given Half-Reactions

From the reaction and the tables, identify the half-reactions. 1) The oxidation half-reaction involving NADH is \( \mathrm{NADH} + \mathrm{H}^+ \rightarrow \mathrm{NAD}^+ + \mathrm{H}_2O\). 2) The reduction half-reaction involves oxygen: \( \mathrm{O}_2 + 4\mathrm{H}^+ + 4e^- \rightarrow 2\mathrm{H}_2O\).

Step 2: Find Standard Reduction Potentials

Consult Table 20.2 for standard reduction potentials from the tables. Assume standard conditions: \( E^\circ (\mathrm{NAD}^+ / \mathrm{NADH}) = -0.32 \text{ V} \). The reduction potential for oxygen is \( E^\circ (\mathrm{O}_2 + 4\mathrm{H}^+ / 2\mathrm{H}_2O) = +1.23 \text{ V} \).

Step 3: Reverse the Oxidation Potential

For the oxidation half-reaction \( \mathrm{NADH} \rightarrow \mathrm{NAD}^+ \), reverse the sign of its potential since it is provided as a reduction potential: \( E^\circ (\mathrm{NADH} / \mathrm{NAD}^+) = +0.32 \text{ V} \).

Step 4: Calculate Cell Potential

Use the formula for cell potential: \[E_{\text{cell}}^\circ = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}} \] Substitute the values: \[E_{\text{cell}}^\circ = 1.23 \text{ V} - 0.32 \text{ V} = 0.91 \text{ V}\] The calculated cell potential for the reaction is \(0.91 \text{ V}\).

Key Concepts

Redox Reactions

Redox reactions, short for reduction-oxidation reactions, are chemical processes in which the oxidation states of atoms are changed. These reactions are characterized by the transfer of electrons between chemical species. In a redox reaction, one species undergoes oxidation by losing electrons, while the other species undergoes reduction by gaining electrons. Consider the biological reaction involving NADH and oxygen: \(2 \mathrm{NADH}+2 \mathrm{H}^{+}+\mathrm{O}_{2} \rightarrow 2 \mathrm{NAD}^{+}+2 \mathrm{H}_{2} \mathrm{O}\). Here, NADH is oxidized as it loses electrons and protons to become NAD\(^+\). Meanwhile, oxygen is reduced to form water. Understanding redox reactions is crucial, as they are foundational to many biochemical processes, including cellular respiration and photosynthesis. Biological systems rely heavily on these reactions to harness energy from nutrients.

Standard Reduction Potential

Standard reduction potential \((E^0)\) indicates the tendency of a chemical species to be reduced, and it is measured under standard conditions (25°C, 1 atm pressure, and 1 M concentration). It is expressed in volts and can be positive or negative. A more positive \(E^0\) means a greater tendency to gain electrons (reduce), while a negative \(E^0\) suggests a tendency to lose electrons (oxidize).In our reaction example, the table gives standard reduction potentials as follows:

• \(E^0 (\mathrm{O}_2/\mathrm{H}_2\mathrm{O}) = +1.23 \text{ V}\)
• \(E^0 (\mathrm{NAD}^+ / \mathrm{NADH}) = -0.32 \text{ V}\)

To calculate the cell potential, the reduction potential of the half-reaction at the anode (oxidation) has to be reversed. Thus, understanding standard reduction potentials is key to determining the overall feasibility and direction of electrochemical reactions.

Biological Systems

In biological systems, redox reactions are essential for processes such as metabolic pathways and energy production. These reactions help in transforming nutrients into usable energy. The reaction between NADH and oxygen is a prime example of how redox reactions drive biological processes. Molecular oxygen, often referred to as the ultimate electron acceptor in biological systems, facilitates the production of ATP (adenosine triphosphate), the energy currency of cells. Oxygen's high standard reduction potential makes it an effective oxidizing agent, crucial for processes like oxidative phosphorylation. Biochemical pathways meticulously control these reactions to fuel life processes efficiently. Understanding the applications of redox reactions in biology helps explain everything from respiration to photosynthesis, underlying the energy flow in living organisms.

Half-Reaction

A half-reaction is part of a redox reaction that involves either oxidation or reduction alone. It simplifies the analysis of redox reactions by showing the electron transfer clearly;For the given example:

• Oxidation Half-Reaction: \(\mathrm{NADH} + \mathrm{H}^+ \rightarrow \mathrm{NAD}^+ + \mathrm{H}_2O\). Here, NADH loses electrons and is oxidized to NAD\(^+\).
• Reduction Half-Reaction: \(\mathrm{O}_2 + 4\mathrm{H}^+ + 4e^- \rightarrow 2\mathrm{H}_2O\). In this process, oxygen gains electrons and is reduced to form water.

The use of half-reactions is vital for understanding the movement of electrons between reactants and for calculating cell potentials. Breaking down complex reactions into half-reactions allows us to balance redox equations more effectively and deduce the roles of different chemical species.