PEMFC Properties Analysis

Listing options for PEMFC

If option c is "All of the above," logically speaking, at least one other option must be true. Evaluating each option will clarify whether they are indeed accurate or not.

Analyzing PEM attributes

I'm noting the proton exchange membrane (PEM) properties for fuel cells: permeable to protons, impermeable to electrons, stable, and hydrophilic. This ensures efficient proton transport and prevents internal short-circuiting.

Evaluating ionic mobility

I’m working through the idea that the proton exchange membrane uses hydrated ionic domains to transport protons, not traditional porosity. This makes me consider its selective ion permeability, particularly for H+ ions.

Understanding proton conduction

OK, let me see. PEM reliability straight through other ions is signified as true. Hydrophilic traits help water transport, aligning with conduction principles.

To determine which option is true for a proton exchange membrane fuel cell (PEMFC), let's analyze each one:

Option a: Block electronic charge mobility

• True. The membrane in a PEMFC must be impermeable to electrons to prevent internal short-circuiting. Electrons should flow through the external circuit to generate electrical power, so the membrane blocks electronic charge mobility.

Option b: Adequate porosity permitting ionic mobility

• False. Proton exchange membranes are dense polymers like Nafion, which conduct protons through hydrated ionic domains within the polymer structure, not through pores. Porosity is not the mechanism for proton transport in PEMFCs.

Option c: All of the above

• Since option b is false, "All of the above" cannot be true.

Option d: Selective ion permeation properties permitting only H⁺ ion mobility

• True. The membrane selectively allows only protons (H⁺ ions) to pass through while blocking other ions, which is essential for the fuel cell's operation.

Option e: Hydrophilic properties

• True. The membrane must be hydrated to conduct protons effectively. Hydrophilic properties help retain water, facilitating proton conduction.

Option f: Presence of H⁺ ion with adequate available sites in its backbone structure for mobility

• True. Membranes like Nafion have sulfonic acid groups in their backbone that provide sites for proton conduction. H⁺ ions dissociate from these groups and move through the membrane.

Since options a, d, e, and f are true but b is false, and "All of the above" is not correct, the most accurate single choice is option d.

Answer: d. Selective ion permeation properties permitting only H⁺ ion mobility

Understanding fuel cell dynamics

Fuel cells convert chemical energy into electrical energy. The above options assess statements about fuel cell efficiency, voltage, and balance. Analyzing each statement's accuracy reveals the non-truthful ones.

Breaking down options

I’m analyzing each statement's truth. Option a defines the EMF variation with reactants and products using the Nernst equation. It’s TRUE. Next up, option b.

Analyzing fuel cell efficiency, which shifts with temperature changes, is essential. The delicate balance of Gibbs free energy and enthalpy is crucial for understanding this trend.

Assessing fuel cell dynamics

Option d is correct, but options c and f are false statements about fuel cell efficiency and voltage dependence on pressure.

To determine which statements are NOT true regarding fuel cells, let's analyze each option:

Option a: EMF in a fuel cell varies with activity of the reactants and products

• True. According to the Nernst equation, the electromotive force (EMF) of a fuel cell depends on the activities (or concentrations/pressures) of the reactants and products.

Option b: Fuel cell efficiency decreases with rise in temperature

• True. Fuel cell efficiency is given by the ratio of Gibbs free energy change (ΔG) to enthalpy change (ΔH), i.e., Efficiency = ΔG/ΔH. As temperature increases, ΔG becomes less negative (since ΔG = ΔH − TΔS), leading to decreased efficiency.

Option c: Fuel cell efficiency remains constant irrespective of temperature

• False. As explained above, fuel cell efficiency decreases with increasing temperature because ΔG changes with temperature.

Option d: Fuel cell efficiency is always less than ideal thermodynamic efficiency

• True. The actual efficiency is always less than the ideal (thermodynamic) efficiency due to real-world losses like overpotentials, ohmic losses, and mass transport limitations.

Option e: For stable fuel cell, both charge and mass balance is essential

• True. Stable operation requires that both electrons and ions (charge) and reactants and products (mass) are properly balanced.

Option f: Fuel cell voltage is independent of pressure

• False. The Nernst equation shows that cell voltage depends on the partial pressures of gaseous reactants and products. Therefore, voltage is pressure-dependent.

Option g: (c) and (f)

• This option identifies options c and f as the statements that are NOT true.

Conclusion:

The statements that are NOT true are Option c and Option f.

Answer: g. (c) and (f)

Breaking down fuel consumption

OK, let's map out the total moles of H_2 by calculating the electric charge per hour for each load using Faraday's laws and determining the total moles consumed.

Calculating total charge

I’m mapping out the oxidation reaction at the anode, where hydrogen is consumed and electrons are transferred. Using Faraday's constant, I’m working out the total charge for each operational period to sum them up.

Calculating charge and moles

I determined the charges for two periods, combined them, and found the total moles of electrons transferred. Then, I calculated the moles of H_2 consumed by using the reaction's stoichiometric ratio.

To determine the total number of moles of hydrogen gas (H_2) consumed by the fuel cell, we'll use Faraday's laws of electrolysis, which relate the amount of substance consumed to the total electric charge passed through the cell.

Step 1: Calculate the Total Charge Passed

First, calculate the total electric charge (Q) passed during each operation period:

1. First Period

   • Current (I_1): 2 A
   • Time (t_1): 1 hour = 1 × 3600 s = 3600 s
   • Charge (Q_1): $Q_1 = I_1 \times t_1 = 2 \, \text{A} \times 3600 \, \text{s} = 7200 \, \text{C}$

2. Second Period

   • Current (I_2): 5 A
   • Time (t_2): 2 hours = 2 × 3600 s = 7200 s
   • Charge (Q_2): $Q_2 = I_2 \times t_2 = 5 \, \text{A} \times 7200 \, \text{s} = 36,000 \, \text{C}$

Total Charge (Q_total): $Q_{\text{total}} = Q_1 + Q_2 = 7200 \, \text{C} + 36,000 \, \text{C} = 43,200 \, \text{C}$

Step 2: Calculate the Total Moles of Electrons Transferred

Using Faraday's constant ($F = 96,485 \, \text{C/mol e}^-$):

$n_e = \frac{Q_{\text{total}}}{F} = \frac{43,200 \, \text{C}}{96,485 \, \text{C/mol e}^-} \approx 0.4478 \, \text{mol e}^-$

Step 3: Calculate the Moles of H_2 Consumed

The oxidation reaction at the anode is:

$\text{Anode: } \text{H}_2 \rightarrow 2\text{H}^+ + 2e^-$

This means that 2 moles of electrons are transferred for every 1 mole of H_2 consumed.

$n_{\text{H}_2} = \frac{n_e}{2} = \frac{0.4478 \, \text{mol e}^-}{2} \approx 0.2239 \, \text{mol H}_2$

Step 4: Select the Correct Option

Comparing the calculated value (~0.224 mol H_2) with the provided options:

• Option b: 0.224 moles

This matches our calculation.

Answer: b. 0.224 moles

Analyzing the options

I’m digging into the question about a fuel cell reaction and examining each option to determine the total exchange of electrons in the REDOX process.

Calculating electron exchange

I'm piecing together the total electron exchange in a fuel cell reaction, considering electrons transferred per fuel molecule and their role in the balanced redox reaction.

Tracing hydrogen-oxygen reactions

OK, let me see. I’m mapping out the hydrogen-oxygen fuel cell reaction: hydrogen at the anode releases 2 electrons, and oxygen at the cathode uses these electrons to form water.

Identifying electron flow

I'm mapping out the total electron exchange in the redox process, comparing options. Option d suggests 2, but I'm also exploring others like 4 and 3.

Breaking down the reaction

OK, let me see. The overall reaction for 2 moles of H_2 and 1 mole of O_2 transfers 4 moles of electrons. This calculation helps determine the theoretical voltage and efficiency of the hydrogen fuel cell.

Evaluating electron exchange

I’m mapping out the methanol fuel cell reaction and counting 6 electrons per mole of methanol. Considering this and the hydrogen fuel cell, I lean towards 4 electrons.

Considering electron pathways

I'm examining the electron movement in a hydrogen fuel cell. It’s interesting to see that 2 electrons move at the anode and 4 at the cathode, possibly due to the oxygen reduction reaction.

Jenlining hydrogen reactions

Balancing hydrogen reactions at the anode and cathode involves ensuring equal electron exchange for proper fuel cell function. Progressing methodically towards achieving equilibrium.

To determine the total exchange of electrons in the redox process of a fuel cell reaction with molar concentrations of fuel and oxidants and with charge and mass balance, let's consider a typical fuel cell reaction—specifically, the hydrogen-oxygen fuel cell, which is the most common example.

Half-Reactions in a Hydrogen Fuel Cell:

1. Anode Reaction (Oxidation):

   $$\text{H}_2 \rightarrow 2\text{H}^+ + 2e^-$$
   • Each mole of hydrogen gas ($\text{H}_2$) loses 2 electrons.

2. Cathode Reaction (Reduction):

   $$\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$$
   • Each mole of oxygen gas ($\text{O}_2$) gains 4 electrons.

Balancing the Half-Reactions:

To ensure both charge and mass balance, we need to balance the number of electrons transferred in both half-reactions. Multiply the anode reaction by 2 so that the number of electrons matches the cathode reaction:

• Adjusted Anode Reaction:

  $$2\text{H}_2 \rightarrow 4\text{H}^+ + 4e^-$$

• Cathode Reaction (as is):

  $$\text{O}_2 + 4\text{H}^+ + 4e^- \rightarrow 2\text{H}_2\text{O}$$

Overall Cell Reaction:

Total Exchange of Electrons:

• At the Anode: 4 electrons are released.
• At the Cathode: 4 electrons are consumed.
• Total Electrons Exchanged in the Redox Process: 4 electrons.

Conclusion:

• The total exchange of electrons in the redox process is 4.
• This matches Option c in the provided choices.

Answer: c. 4