How Do You Modify the Stoichiometry for Sulfur-Included Food Waste Degradation?

[gfd43tg]

Homework Statement

There's no problem statement, I'm doing this as part of my project

For degradation of food wastes to methane, the general formula is given for food waste (without sulfur)

$C_{n}H_{a}O_{b}N_{c} + (n - \frac {a}{4} - \frac {b}{2} + \frac {3c}{4})H_{2}O \rightarrow (\frac {n}{2} + \frac {a}{8} - \frac {b}{4} - \frac {3c}{8})CH_{4} + (\frac {n}{2} - \frac {a}{8} + \frac {b}{4} + \frac {3c}{8})CO_{2} + cNH_{3}$

However, for my purpose I need to include sulfur, so my formula should be
$C_{n}H_{a}O_{b}N_{c}S_{d}$

Homework Equations

The Attempt at a Solution

This part with the N and S are easy, but figuring out the other stuff is of course my issue.
$C_{n}H_{a}O_{b}N_{c}S_{d} + (...)H_{2}O \rightarrow (...) CH_{4} + (...)CO_{2} + cNH_{3} + dH_{2}S$

 

[Borek]

CH₄ and CO₂ don't change.

Can't say whole equation makes much sense to me, it looks rather arbitrary.

 

[gfd43tg]

I imagine they would change, since you are using hydrogen to make H2S instead of going into CH4, right? This is a pseudo reaction of course, I'm trying to model solid wastes to methane from anaerobic digestion without having to model all the many reactions involved in a real digestion

 

[Borek]

OK, you are right, they are not independent.

 

[Chestermiller]

What you do is call x the coefficient of H2O, y the coefficient of CH4, and z the coefficient of CO2. Then you do an atom balance on H, C, and O. This gives you three linear algebraic equations in the three unknowns x, y, and z. Just solve for these unknowns.

Chet

 

[gfd43tg]

What you do is call x the coefficient of H2O, y the coefficient of CH4, and z the coefficient of CO2. Then you do an atom balance on H, C, and O. This gives you three linear algebraic equations in the three unknowns x, y, and z. Just solve for these unknowns.

Chet

Thanks, now time to crank out the algebra