Use the matrix methods to balance the following chemical reaction CH4+ H2O = CO2
ID: 865945 • Letter: U
Question
Use the matrix methods to balance the following chemical reaction CH4+ H2O = CO2+H2O a) what's the matrix for this system? b) what's the rank of this matrix? c) how many(if any) free variables are present in this system? d)What's the basis for the solution?Use the matrix methods to balance the following chemical reaction CH4+ H2O = CO2+H2O a) what's the matrix for this system? b) what's the rank of this matrix? c) how many(if any) free variables are present in this system? d)What's the basis for the solution?
CH4+ H2O = CO2+H2O a) what's the matrix for this system? b) what's the rank of this matrix? c) how many(if any) free variables are present in this system? d)What's the basis for the solution?
Explanation / Answer
The reaction is incorrect. It is oxidation of methane or called Combustion of methane
It should have been
CH4 + O2 ---> CO2 + H2O
a CH4 + b O2 ---> c CO2 + d H2O
We have 3 different elements, C, H and O, so we will need three different equations and 4 variables. We are trying to calculate the values of a, b, c and d, the coefficients of the reaction. The two equations look like this:
C: 1a + 0b +1c = 0d
H: 4a + 0b - 0c = 2d
O: 0a + 2b - 2c = 1d
A = [1 0 1
4 0 0
0 2 -2]
det A = 1 [(0) -0)] - 0 + 1 (8-0) ]
= -0 - 0 +8
= 8
B = [ 0
2
1 ]
A-1 * B * det A = [1
2
1]
a = 1 b = 2 c = 1 d = 2