One approach to using hydrocarbon fuels in a fuel cell is to...

One approach to using hydrocarbon fuels in a fuel cell is to "reform" the hydrocarbon to obtain hydrogen, which is then fed to the fuel cell. As a part of the analysis of such a procedure, consider the reaction $\mathrm{CH}_{4}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons 3 \mathrm{H}_{2}+\mathrm{CO}$. Determine the equilibrium constant for this reaction at a temperature of $800 \mathrm{K}$

Key Concepts

Chemical Equilibrium

Chemical equilibrium is the state in a reversible chemical reaction where the rates of the forward and reverse reactions are equal, resulting in no net change in the concentrations of reactants and products. This concept is fundamental in chemical thermodynamics and indicates that the reaction has reached a stable balance under given conditions.

Equilibrium Constant

The equilibrium constant (K) is a dimensionless number that quantifies the ratio of the concentrations (or partial pressures) of the products to the reactants at equilibrium. It is derived from the law of mass action and provides insight into the extent of a reaction under specified conditions, allowing predictions about the composition of the system at equilibrium.

Temperature Dependence and the van't Hoff Equation

The equilibrium constant is dependent on temperature, meaning that any change in temperature can shift the equilibrium position of a reaction. The van't Hoff equation describes this dependency by relating the change in the equilibrium constant to the enthalpy change of the reaction, offering a thermodynamic framework to understand how increasing or decreasing temperature will affect the balance between reactants and products.

Reforming Reactions in Fuel Cells

Reforming reactions, such as steam reforming, convert hydrocarbons into hydrogen by reacting them with water at high temperatures. This process is crucial in applications like fuel cells, where hydrogen generated from hydrocarbon fuels is used for electrochemical energy conversion. Understanding the equilibrium of such reactions is important for optimizing hydrogen production and ensuring efficient fuel cell performance.

Transcript

00:01 We're told that one approach to using hydrocarbon fuels in a fuel cell is to reform the hydrocarbon to get the strip the oxygen or hydrogen off of it, or some of the hydrogen off of it, which is then fed to the fuel cell.

00:15 As part of the analysis of such a procedure, we want to consider the reforming section and determine the equilibrium constant for this reaction at a temperature of 800 kelvin.

00:29 Okay, so we can, we're going to need the heat capacity of methane.

00:41 Again, i'm going to use methane here.

00:43 I didn't specify it, but that's probably the most likely culprit here of doing the reforming process.

00:52 So we can look up the, we can calculate the specific, the heat capacity at an at a roughly, at a roughly, a temperature of 550 kelvin, which is kind of a mean between 300 and 800.

01:08 And we get 49 .3 kilojoules per kilomol.

01:12 So we can figure out the entope of the c of the methane at 800 kelvin, and that is just the entropy of formation, and this is in a megajoules basis here, so plus the, the heat capacity and then minus and then times the change in temperature here.

01:38 And so we wind up with minus 50 .1 kilojoules per kilomol.

01:43 Now the thing is here we need to we need to figure out what the we want to figure out what the k is.

01:52 So we need to get the gims function which means we need the entropy and the entropy.

02:00 So there's the absolute entropy for methane at this, at 800 calvin, and we can look it up at reference, and then the adjustment, not at reference, but at 800 kelvin, and then the adjustment, no, the reference and then the adjustment because of the pressure, or pressure of the temperature, and we get 0 .235 megajoules per kilowat, and so the dissociation reaction, we have here is we're basically putting in water so that we can strip off some h2 and we place it with some oxygen so we get carbon monoxide and hydrogen out.

02:51 So we can see here that we have six hydrogen over here and oxygen and carbon.

03:01 So we're basically kind of taking this and sticking it over here and then making more hydrogen.

03:08 But we don't know where we are, you know, how much we have here and how much we have here.

03:14 And that's what we want to figure out.

03:18 And so let's see here...

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