- #1

igowithit

- 6

- 1

## Homework Statement

Methane is mixed with air at a 16:1 per mass ratio at 1atm and 298K. Calculate the mass fraction of argon, nitrogen, oxygen, and methane in the final mixture

## Homework Equations

## The Attempt at a Solution

First, change mass ratio of reactants to mole ratio

$$

\frac{16 g CH_4}{16 g/mol CH_4} = 1 mol CH_4

$$

$$

\frac{1 g Air}{28.97 g/mol Air} = 0.0345 mol Air

$$

or in nice round terms,

$$

29 mol CH_4

$$

$$

1 mol Air

$$

leading to

$$

29 CH_4 + 1*(0.00933Ar + 0.7809N_2 + 0.2095O_2) = aCH_4 + bCO_2 + cAr + dN_2 + eO_2 + fH_2O + gH_2 + hOH

$$

I feel like this is way too many products to reasonably allow for a timely solution. Anyways, setting up a mass balance for each of the 5 elements in the equation leads to

$$

C: 29 = a + b

$$

$$

H: 4*29 = 4a + 2f + 2g + h

$$

$$

Ar: 0.00933 = c

$$

$$

N: 2*0.7809 = 2d

$$

$$

O: 2*0.2095 = 2b + 2e + f + h

$$

we now know c and d just from these equations leaving us with 3 equations but 7 unknowns (a,b,e,f,g,h,and T). Set up ##K_p## equations based of stoichiometric equations. I'll make a guess at temperature, therefore I only have to set up 3 ##K_p## equations to go with the 3 mass balance equations I already have. However, this is where I'm stuck. When I do this, I end up with crazy complex equations that even Matlab can't solve for the coefficients.

I feel like I have entirely too many products, but I don't know how to pick and choose which ones to keep and which ones to remove. Is there any easier path to take for this problem?