Fuel Cell Process Sequence

Analyzing fuel cell processes

I’m mapping out the steps involved in a fuel cell’s operation, from fuel transport to energy release, to identify the correct sequence from the given options.

Fuel cell operation

Hydrogen gas reaches the anode, splitting into protons and electrons, creating an electric current. Oxygen gas at the cathode forms water with electrons and protons, releasing energy.

Mapping out transport processes

I reviewed the steps of hydrogen fuel cells, detailing fuel and oxidant transport, catalytic action, electrochemical reactions, and charge transport. They participate while deriving electricity and heat.

Mapping the sequence

I’m piecing together the steps of a process that involves fuel and oxidant supply, catalytic action, electrochemical reactions, charge transport, product removal, and energy release. This chain of events ensures the process functions effectively and efficiently.

To determine the correct sequence of processes in the working of a fuel cell, let's analyze each step in the context of a typical fuel cell operation:

1. Fuel Transport: The fuel (e.g., hydrogen gas) is supplied to the anode side of the fuel cell.
2. Oxidant Transport: The oxidant (e.g., oxygen from air) is supplied to the cathode side.
3. Catalytic Action: At the anode, catalysts facilitate the oxidation of the fuel, splitting hydrogen molecules into protons and electrons.
4. Electrochemical Reaction: These reactions occur at both electrodes—oxidation at the anode and reduction at the cathode.
5. Charge (Ion and Electron) Transport: Electrons flow through the external circuit (providing electric power), and protons move through the electrolyte to the cathode.
6. Product Removal: Water (the product of the reaction) is formed at the cathode and needs to be removed from the cell.
7. Energy Release: The cell releases energy in the form of electricity and heat.

Putting these steps in order, we get the sequence: 1, 2, 3, 4, 5, 6, 7.

Among the given options, option (f) matches this sequence.

Answer: Option (f): 1, 2, 3, 4, 5, 6 & 7

Calculating water production

I’m figuring out the water production rate from a 20-cell fuel stack, each with a 100 cm² electrode and 0.8 A cm⁻² current density, under steady fuel and oxidant conditions.

Calculating water production

I’m figuring out the water production rate in a hydrogen fuel cell by linking it to electron flow and current density. This involves calculating the total current and using the number of electrons transferred per mole.

Calculating current and water production

OK, let's figure out the total current for the series stack by multiplying the current density by the active area. Then, using Faraday's laws, I’ll find the moles of electrons per hour to determine the water production rate.

Calculating moles

I’m mapping out the moles of electrons per second using Faraday's law, with a current of 80 A and Faraday's constant. Next, I’ll determine the moles of H_2O produced per second.

Calculating moles

I’m working out moles of H_2O per second from moles of electrons, converting to hourly moles, and then figuring out the mass of H_2O per hour.

Crunching the numbers

I’m working through the math to find the moles of H_2O per hour. After calculating the numerator and denominator, I approximate the moles to 1.492 mol/h and then refine it for greater precision.

Breaking down the calculations

First, I approximate 192,970 × 1.49 to 287,525. Then, dividing 288,000 by 192,970 yields approximately 1.492. Multiplying this by the molar mass of H_2O (18 g/mol) gives a mass of approximately 26.8578 g/h.

Reassessing water production

The water produced in a series stack is cumulative across all cells. If each cell produces 215 g/h at 80 A, then 20 cells will cumulatively produce 8600 g/h.

Recalculating mass

I'm thinking through the total water production per hour by multiplying the mass per cell by the number of cells, arriving at 537.156 g/h. Comparing this with the options shows a close match to 588 g/h.

Breaking down calculations

I calculated the moles of electrons per hour by dividing the current (80 A) by the number of coulombs per mole (96485 C/mol), which gave approximately 2.984 mol e⁻/h. Then, I calculated the moles of H_2O per hour per cell by dividing the moles of electrons per hour by 2, resulting in 1.492 mol/h.

Adjusting my assumptions

I’m working through the current assumption for the stack, considering specific values for electrodes and the total current per cell to align with the provided options.

Confirming calculations

I’m thinking about the alignment of current density calculations with the actual current flow area. The total current per cell, derived from the overlapping electrode area, stands verified at 80 A.

Revisiting the calculation

I'm rethinking the total current calculation and considering the active area for 20 cells in series, aiming to match the closest option of 588 g/h per stack.

Assessing cell arrangement

I'm working through whether the cells are arranged in series or parallel, considering the consistency of current. I'm also examining the total current calculation, which might involve both electrode sides.

Calculating total current

I’m working through the formula for total current, multiplying current density by the total electrode area per cell. The inconsistency here needs further attention.

Calculating total current

I’m thinking through the current density and total area to find the fuel cell's total current. The result is 1600 A, assuming proportionality between total current and cell area.

Clarifying current contributions

I’m piecing together current in a stack, differentiating the 80 A per stack with cells in series from the total water production, which is the product of the current per cell and the number of cells.

OK, let's see. Calculating the hourly flow of electrons involves multiplying current by 3600 and dividing by Faraday's constant. ajusted for different currents, the resulting moles and mass of water each hour are consistent.

Mapping out total current

Calculating the total current by multiplying current density with total area, which yields 1600 A. This leads to the moles of electrons and subsequently the water produced per hour, checking for consistency.

To determine the rate of water production by the fuel cell stack, we'll follow these steps:

1. Calculate the Total Current Generated by the Stack:

   • Current Density ($J$): $0.8 \, \text{A/cm}^2$
   • Active Area per Cell ($A_{\text{cell}}$): $100 \, \text{cm}^2$
   • Number of Cells ($N$): $20$

   The total active area ($A_{\text{total}}$) is:

   $$A_{\text{total}} = N \times A_{\text{cell}} = 20 \times 100 \, \text{cm}^2 = 2000 \, \text{cm}^2$$

   The total current ($I_{\text{total}}$) is:

   $$I_{\text{total}} = J \times A_{\text{total}} = 0.8 \, \text{A/cm}^2 \times 2000 \, \text{cm}^2 = 1600 \, \text{A}$$

2. Calculate the Total Charge Passed per Hour:

   • Time ($t$): $1 \, \text{hour} = 3600 \, \text{seconds}$

   Total charge ($Q$) is:

   $$Q = I_{\text{total}} \times t = 1600 \, \text{A} \times 3600 \, \text{s} = 5,760,000 \, \text{C}$$

3. Calculate the Moles of Electrons Transferred:

   • Faraday's Constant ($F$): $96,485 \, \text{C/mol}$

   Moles of electrons ($n_e$) are:

   $$n_e = \frac{Q}{F} = \frac{5,760,000 \, \text{C}}{96,485 \, \text{C/mol}} \approx 59.72 \, \text{mol}$$

4. Determine Moles of Water Produced: The electrochemical reaction in a hydrogen fuel cell is:

   $$2H_2 + O_2 \rightarrow 2H_2O$$

   This means 2 moles of electrons produce 1 mole of water.

   Moles of water ($n_{H_2O}$) are:

   $$n_{H_2O} = \frac{n_e}{2} = \frac{59.72 \, \text{mol}}{2} \approx 29.86 \, \text{mol}$$

5. Calculate Mass of Water Produced per Hour:

   • Molar Mass of Water ($M_{H_2O}$): $18 \, \text{g/mol}$

   Mass of water ($m_{H_2O}$) is:

   $$m_{H_2O} = n_{H_2O} \times M_{H_2O} = 29.86 \, \text{mol} \times 18 \, \text{g/mol} \approx 537.5 \, \text{g/h}$$

6. Compare with the Given Options: The calculated mass of water produced is approximately 537.5 g/h.

   Among the options provided, Option (b) is the closest at 588 g/h per stack.

Answer: Option (b): 588 g of H_2O per hour per stack

Calculating total charge

I’m working through the total charge passed during the fuel cell's operation, considering the duration and current load. This involves multiplying the current by time to find the cumulative charge.

Breaking down the charge

First, I calculate the charge for each period by multiplying current and time. Then, I add these charges and divide by Faraday's constant to find the moles of electrons transferred.

Crunching the numbers

I’ve verified units and calculations, leading to 0.447 moles of electrons. Using the stoichiometric relationship, this translates to approximately 0.224 moles of hydrogen.

To calculate the total number of moles of hydrogen (H_2) consumed by the fuel cell during the operation, we'll follow these steps:

1. Calculate the Total Charge Passed During the Operation

First Period:

• Current ($I_1$): 2 A
• Time ($t_1$): 1 hour $= 3600 \, \text{s}$

Total charge for the first period ($Q_1$):

Second Period:

• Current ($I_2$): 5 A
• Time ($t_2$): 2 hours $= 7200 \, \text{s}$

Total charge for the second period ($Q_2$):

Total Charge ($Q_{\text{total}}$):

2. Calculate the Total Moles of Electrons Transferred

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

3. Determine the Moles of Hydrogen Consumed

The anodic reaction in the fuel cell is:

This shows that 1 mole of H_2 produces 2 moles of electrons. Therefore, the moles of hydrogen consumed ($n_{\text{H}_2}$) are:

4. Select the Closest Option

The calculated moles of hydrogen consumed are approximately 0.224 moles.

Answer: Option (b): 0.224 moles