cnh2n 2 + o2

To balance the equation CNH2N + O2 = CO2 + H2O + N2 using the algebraic method step-by-step, you must have experience solving systems of linear equations. The most common methods are substitution/elimination and linear algebra, but any similar method will work.

Step 1: Label Each Compound With a Variable

Label each compound (reactant or product) in the equation with a variable vĩ đại represent the unknown coefficients.

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a CNH2N + b O2 = c CO2 + d H2O + f N2

Step 2: Create a System of Equations

Create an equation for each element (C, N, H, O) where each term represents the number of atoms of the element in each reactant or product.

C:	1a	+	0b	=	1c	+	0d	+	0f
N:	2a	+	0b	=	0c	+	0d	+	2f
H:	2a	+	0b	=	0c	+	2d	+	0f
O:	0a	+	2b	=	2c	+	1d	+	0f

Step 3: Solve For All Variables

Use substitution, Gaussian elimination, or a calculator vĩ đại solve for each variable.

  • 1a - 1c = 0
  • 2a - 2f = 0
  • 2a - 2d = 0
  • 2b - 2c - 1d = 0

Use your graphing calculator's rref() function (or an online rref calculator) vĩ đại convert the following matrix into reduced row-echelon-form:

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[ 1	 0	-1	 0	 0	0]
[ 2	 0	 0	 0	-2	0]
[ 2	 0	 0	-2	 0	0]
[ 0	 2	-2	-1	 0	0]

The resulting matrix can be used vĩ đại determine the coefficients. In the case of a single solution, the last column of the matrix will contain the coefficients.

Simplify the result vĩ đại get the lowest, whole integer values.

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  • a = 2 (CNH2N)
  • b = 3 (O2)
  • c = 2 (CO2)
  • d = 2 (H2O)
  • f = 2 (N2)

Step 4: Substitute Coefficients and Verify Result

Count the number of atoms of each element on each side of the equation and verify that all elements and electrons (if there are charges/ions) are balanced.

2 CNH2N + 3 O2 = 2 CO2 + 2 H2O + 2 N2

Reactants Products
C22✔️
N44✔️
H44✔️
O66✔️

Since there is an equal number of each element in the reactants and products of 2CNH2N + 3O2 = 2CO2 + 2H2O + 2N2, the equation is balanced.