Use the matrix methods to balance the following chemical reaction CH4+ H2O = CO2

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

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.