# Coal Gasifier - Thermodynamics Question

Tags:
1. Nov 19, 2015

### Rett

1. The problem statement, all variables and given/known data
The problem is in the attached picture. I simply do not know what an "equilibrium equation" is and what it means by the composition. My professor is unbelievably difficult to get a straight, understandable answer from. I've already taken thermodynamics, but we did not learn about coal gasifiers.

2. Relevant equations
k = (ycc * ydd) / (yaa * ybb) when P = Patm

3. The attempt at a solution
I believe that the boxed in equations are the answers to part (a), the "independent reaction equations" and there would be 2 of them.
My teacher made it sound like these were also the "equilibrium equations" as the answer for part (b), but then where would the "composition" come from?

I believe that the equilibrium equation would be something like this:
(y/2) O2 + (y) C + x H2O --> aCH4 + bH2 + cH2O + dCO + eCO2
And then the composition would be the coefficients, but my teacher made me believe that this was incorrect.

Can someone give an example of what an "equilibrium equation" is? I know there is something called the "equilibrium constant", which he gave us a handout to find values for, but I have no clue how to use it.
Then I will attempt to solve for the equilibrium equation and the composition of this one and then check back in.

Thanks!

2. Nov 19, 2015

### Staff: Mentor

Come on, you took thermodynamics and you don't know what the reaction and equilibrium is?

You have a mixture components of which undergo several reactions, when the mixture leaves the gasifier all reactions are at equilibrium. This is not different from any other chemical system.

You have two reaction equations written in pencil - what are they?

3. Nov 24, 2015

### Rett

The equations are:
CO + H2O = CO2 + H2
CO + 3H2 = H2O + CH4

I took thermo, I didn't say I was very good at it though. I'm confused about how to solve for the composition from the equilibrium equations and from the input of O2, H2O and C to the output of CH4, H2, H2O, CO, and CO2.

4. Nov 24, 2015

### Staff: Mentor

No problem with reading them, I asked what they are - why are they included? (hint: they are quite useful here).

Have you heard about mass balance? Or at least about mass conservation?

5. Nov 24, 2015

### Staff: Mentor

Take as a basis 1 kmol of C fed to the reactor. Based on the problem statement, how many kmol of C atom, O atom, and H atom are fed to the reactor?Let a, b,c,d, and e represent, respectively, the corresponding number of kmols of CH4, H2, H2O, CO, and CO2 in the product. In terms of a, b,c,d, e, and x, write a steady state mass balance on the reactor for C atom, O atom, and H atom. What do you get so far?

Chet