(b) Using the standard reduction potentials in Appendix E, calculate the standard voltage generated by the hydrogen fuel cell in an acidic solution.

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Identify the half-reactions involved in the hydrogen fuel cell. In an acidic solution, the reactions are: the oxidation of hydrogen (H₂) and the reduction of oxygen (O₂).

Write the oxidation half-reaction: H₂(g) → 2H⁺(aq) + 2e⁻. The standard reduction potential for this reaction is 0 V, as it is the reference electrode.

Write the reduction half-reaction: O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l). Look up the standard reduction potential for this reaction in Appendix E, which is typically +1.23 V.

Calculate the standard cell potential (E°cell) by using the formula: E°cell = E°cathode - E°anode. Substitute the values: E°cathode = +1.23 V (for the reduction of O₂) and E°anode = 0 V (for the oxidation of H₂).

Combine the half-reactions to write the overall balanced equation for the hydrogen fuel cell and verify that the number of electrons lost in the oxidation half-reaction equals the number gained in the reduction half-reaction.

Key Concepts

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

Standard Reduction Potentials

Standard reduction potentials are measured voltages that indicate the tendency of a chemical species to gain electrons and be reduced. These values are typically listed in tables and are measured under standard conditions (1 M concentration, 1 atm pressure, and 25°C). The more positive the standard reduction potential, the greater the species' ability to be reduced. In electrochemical cells, these potentials are crucial for determining the overall cell voltage.

Electrochemical Cells

Electrochemical cells convert chemical energy into electrical energy through redox reactions. A hydrogen fuel cell is a type of electrochemical cell that uses hydrogen and oxygen as reactants to produce electricity, water, and heat. In acidic solutions, the reactions occur at the anode and cathode, where hydrogen is oxidized and oxygen is reduced, respectively. The cell voltage is calculated by the difference in standard reduction potentials of these half-reactions.

Nernst Equation

The Nernst equation relates the cell potential to the concentrations of the reactants and products in an electrochemical reaction. It allows for the calculation of the actual cell voltage under non-standard conditions. While the question specifies standard conditions, understanding the Nernst equation is essential for comprehending how changes in concentration or temperature can affect the voltage generated by the cell. It emphasizes the dynamic nature of electrochemical systems.

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The Nernst Equation

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Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the LiCoO2 cathode found in most Li-ion batteries. (a) Calculate the mass percent lithium in each electrode material.

Textbook Question

Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the LiCoO2 cathode found in most Li-ion batteries. (b) Which material has a higher percentage of lithium? Does this help to explain why batteries made with LiMn2O4 cathodes deliver less power on discharging?

Textbook Question

Li-ion batteries used in automobiles typically use a LiMn2O4 cathode in place of the LiCoO2 cathode found in most Li-ion batteries. (c) In a battery that uses a LiCoO2 cathode, approximately 50% of the lithium migrates from the cathode to the anode on charging. In a battery that uses a LiMn2O4 cathode, what fraction of the lithium in LiMn2O4 would need to migrate out of the cathode to deliver the same amount of lithium to the graphite anode?

Textbook Question

(a) Which reaction is spontaneous in the hydrogen fuel cell: hydrogen gas plus oxygen gas makes water, or water makes hydrogen gas plus oxygen gas?