Question

A direct methanol fuel cell generates 1000 A at 0.3 V at STP. Methanol and air are supplied to the fuel cell at 0.003 and 0.03 mol/s, respectively. Calculate (a) the output mass flux (mol/s) of methanol (v MeOH , out ), air (v air, out ), water (v H 2 O, out ), and carbon dioxide(v CO 2 , out ); (b) the stoichiometric factors for methanol (λ MeOH ) and air (λ air ); and (c) the heat generation rate (J/s) for this fuel cell assuming Δ h^rxn =−719.19 kJ/mol for methanol combustion at STP.

Answer 1

To calculate the mass fluxes of the substances in a direct methanol fuel cell, the stoichiometric ratios from the chemical reaction are used. The stoichiometric factors indicate the ratio of actual to needed flow rates, and the heat generation rate is determined using the enthalpy change of the reaction and the rate of methanol consumption.

Step-by-step explanation:

Direct Methanol Fuel Cell Analysis

The problem involves a direct methanol fuel cell (DMFC) which generates electrical power through the chemical reaction of methanol with oxygen. To address the questions posed, we must first understand the balance of reactants and products in the cell's operation.

For the DMFC operating at the given rates of methanol (0.003 mol/s) and air supply (0.03 mol/s), the output mass fluxes of reactants and products are not directly given, but can be determined based on stoichiometric ratios from the balanced chemical equation:

CH3OH(l) + 3/2 O2(g) → CO2(g) + 2 H2O(l)

• v MeOH, out: The output mass flux of methanol is equal to the input rate minus the rate at which it reacts and is consumed in the fuel cell.
• v air, out: The output flux of air would be the total input rate of air minus the rate at which oxygen is consumed in the reaction.
• v H2O, out: The water produced is a product of the reaction, based on the stoichiometry of the reaction.
• v CO2, out: Similarly, CO2 output flux is determined by the stoichiometry, and it is produced at a rate proportional to the methanol consumption.

The stoichiometric factors for methanol (λ MeOH) and air (λ air) indicate the ratio of the actual flow rate to the rate that would be needed for complete reaction based simply on stoichiometry.

The heat generation rate (J/s) for this fuel cell can be calculated using the enthalpy change of the reaction, ΔHrxn, and the rate at which methanol is consumed:

Heat generation rate (J/s) = ΔHrxn × rate of reaction (mol/s)

Since ΔHrxn is given as −719.19 kJ/mol, we can calculate the total heat generation rate by multiplying this value by the rate of methanol consumption in mol/s.